{"id":20369,"date":"2018-11-23T08:54:53","date_gmt":"2018-11-23T08:54:53","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=20369"},"modified":"2023-02-14T14:31:30","modified_gmt":"2023-02-14T14:31:30","slug":"convection-convective-heat-transfer","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/","title":{"rendered":"Convection &#8211; Convective Heat Transfer"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"sue-shadow-wrap sue-content-wrap sue-shadow-inline-no\"><div   id="8n9s8rpp6h"    class=\"sue-shadow sue-shadow-style-vertical\">\n<div   id="8n9s8rpp6h"    class=\"sue-panel\" data-url=\"\" data-target=\"self\" style=\"background-color:#ffffff;color:#333333;border-radius:0px;-moz-border-radius:0px;-webkit-border-radius:0px;box-shadow:none;-moz-box-shadow:none;-webkit-box-shadow:none;border:1px solid #cccccc\"><div   id="8n9s8rpp6h"    class=\"sue-panel-content sue-content-wrap\" style=\"padding:15px;text-align:left\">\n<div class=\"su-heading su-heading-style-modern-1-dark su-heading-align-left\" id=\"\" style=\"font-size:13px;margin-bottom:20px\"><div   id="8n9s8rpp6h"    class=\"su-heading-inner\">\n<h2>Article Summary &amp; FAQs<\/h2>\n<\/div><\/div>\n<h3>What is convection?<\/h3>\n<p>In general,\u00a0<strong>convection<\/strong>\u00a0is either the\u00a0<strong>mass transfer<\/strong>\u00a0or the\u00a0<strong>heat transfer<\/strong> due to the\u00a0<strong>bulk movement<\/strong>\u00a0of molecules within fluids such as gases and liquids.<\/p>\n<h3>Key Facts<\/h3>\n<p>Heat transfer is usually classified into various mechanisms, such as:<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><strong><a title=\"Thermal Conduction \u2013 Heat Conduction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\">Heat Conduction<\/a>. <\/strong>Heat conduction, also called diffusion, occurs within a body or between two bodies in contact. It is the direct microscopic exchange of kinetic energy of particles through the boundary between two systems.<\/li>\n<li><strong><a title=\"Convection \u2013 Convective Heat Transfer\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/\">Heat Convection<\/a>. <\/strong>Heat convection depends on a mass movement from one region of space to another. Heat convection occurs when the bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid.<\/li>\n<li><strong><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/radiation-heat-transfer\/thermal-radiation-radiant-heat\/\">Thermal Radiation<\/a>. <\/strong>Radiation is heat transfer by electromagnetic radiation, such as sunshine, with no need for the matter to be present in the space between bodies.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>Conduction<\/strong>\u00a0and\u00a0<strong>convection<\/strong>\u00a0are similar in that both mechanisms require the presence of a material medium (in comparison to thermal radiation).<\/p>\n<p><strong>At the surface<\/strong>, it must be emphasized that<strong>\u00a0<\/strong>energy flow occurs\u00a0<strong>purely by conduction,\u00a0<\/strong>even in conduction. It is because there is always a<strong> thin stagnant fluid film layer\u00a0on the heat transfer surface.\u00a0<\/strong>But in the next layers, both conduction and diffusion-mass movement occur at the molecular or macroscopic levels.<\/p>\n<p>Despite the complexity of\u00a0<strong>convection<\/strong>, the rate of convection heat transfer is observed to be\u00a0<strong>proportional<\/strong>\u00a0to the\u00a0<strong>temperature difference<\/strong>\u00a0and is conveniently expressed by\u00a0<strong>Newton\u2019s law of cooling.<\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/newtons-law-of-cooling\/\"><strong>Newton\u2019s law of cooling<\/strong><\/a> states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings, provided the temperature difference is small and the nature of radiating surface remains the same.<\/p>\n<p>The\u00a0<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-nusselt-number\/\"><strong>Nusselt number<\/strong><\/a> is used to describe the ratio of the\u00a0<strong>thermal energy convected<\/strong>\u00a0to the fluid to the\u00a0<strong>thermal energy conducted<\/strong>\u00a0within the fluid.<\/p>\n<p>For fully developed (hydrodynamically and thermally)\u00a0<a title=\"Turbulent Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/turbulent-flow\/\">turbulent flow<\/a>\u00a0in a smooth circular tube, the local\u00a0<a title=\"What is Nusselt Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-nusselt-number\/\">Nusselt number<\/a>\u00a0may be obtained from the well-known\u00a0<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/dittus-boelter-equation\/\"><strong>Dittus-Boelter equation<\/strong><\/a>.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/boiling-and-condensation\/\"><strong>Boiling and condensation<\/strong><\/a>\u00a0differ from other forms of convection in that they depend on the\u00a0<strong>latent heat of vaporization<\/strong>, which is\u00a0<strong>very high<\/strong>\u00a0for common\u00a0<a title=\"What is Pressure \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-pressure-physics\/\">pressures<\/a>. Therefore large amounts of heat can be transferred during boiling and condensation essentially at a constant temperature.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:10px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\">\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What is the convective heat transfer coefficient?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>What is the convective heat transfer coefficient?<\/strong><\/p>\n<p>The\u00a0<strong>convective heat transfer coefficient,<\/strong>\u00a0h, can be defined as:<\/p>\n<p><em>The rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature difference.<\/em><\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-modern-light su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>What is natural convection?<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<strong>What is natural convection?<\/strong><\/p>\n<p>In\u00a0<strong>natural convection<\/strong>, fluid surrounding a heat source receives heat, becomes\u00a0less dense, and rises <strong>by thermal expansion<\/strong>. Thermal expansion of the fluid plays a crucial role. In other words, heavier (more dense) components will fall, while lighter (less dense) components rise, leading to bulk fluid movement.<\/p>\n<\/div><\/div>\n<\/div>\n<\/div><\/div>\n<\/div><\/div>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Convection-Convective-Heat-Transfer-comparison-min.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20378\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Convection-Convective-Heat-Transfer-comparison-min-281x300.png\" alt=\"Convection - Convective Heat Transfer\" width=\"281\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Convection-Convective-Heat-Transfer-comparison-min-281x300.png 281w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Convection-Convective-Heat-Transfer-comparison-min.png 739w\" sizes=\"(max-width: 281px) 100vw, 281px\" \/><\/a>In general, <strong>convection<\/strong> is either the <strong>mass transfer<\/strong> or the <strong>heat transfer<\/strong> due to the <strong>bulk movement<\/strong> of molecules within fluids such as gases and liquids. Although liquids and gases are generally not very good conductors of heat, they can transfer heat quite rapidly <strong>by convection<\/strong>.<\/p>\n<p><strong>Convection<\/strong> takes place through <strong>advection<\/strong>, <strong>diffusion,<\/strong> or both. Convection cannot occur in most solids because neither significant diffusion of matter nor bulk current flows can occur. Diffusion of heat occurs in rigid solids, but that is called <a title=\"Thermal Conduction \u2013 Heat Conduction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\">thermal conduction<\/a>.<\/p>\n<p>The process of heat transfer between a surface and a fluid flowing in contact with it is called <strong>convective heat transfer<\/strong>. In engineering, convective heat transfer is one of the major mechanisms of <a title=\"Heat Transfer\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/\"><strong>heat transfer<\/strong><\/a>. When heat is transferred from one fluid to another through a barrier, convection is involved on both sides of the barrier. In most cases, the main <a title=\"Thermal Resistance \u2013 Analogy to Electric Resistance\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-resistance-thermal-resistivity\/thermal-resistance-analogy-to-electric-resistance\/\">resistance<\/a> to heat flow is by convection. <strong>Convective heat transfer<\/strong> takes place both by thermal diffusion (the random motion of fluid molecules) and by advection, in which matter or heat is transported by the larger-scale motion of currents in the fluid.<\/p>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Mechanisms of Convection<\/h2>\n<p>In <a title=\"Thermal Conduction \u2013 Heat Conduction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\"><strong>thermal conduction<\/strong><\/a>, <a title=\"What is Energy \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/\">energy<\/a> is transferred as <a title=\"Heat in Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-in-thermodynamics\/\">heat<\/a> either due to <strong>the migration of free electrons <\/strong>or <strong>lattice vibrational waves (<a title=\"What is Phonon \u2013 Definition\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/what-is-phonon-definition\/\">phonons<\/a>). <\/strong>There is no movement of mass in the direction of energy flow, and <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/\">heat transfer<\/a> by <strong>conduction<\/strong> depends on the driving \u201cforce\u201d of <strong>temperature difference. Conduction<\/strong> and <strong>convection<\/strong> are similar in that both mechanisms require the presence of a material medium (in comparison to thermal radiation). On the other hand, they are different in that convection requires the presence of fluid motion.<\/p>\n<p><strong>At the surface<\/strong>, it must be emphasized that<strong>\u00a0<\/strong>energy flow occurs\u00a0<strong>purely by conduction, <\/strong>even in conduction. It is because there is always a<strong><span style=\"font-weight: 400;\"><strong> thin stagnant fluid film layer<\/strong> on the heat transfer surface. <\/span><\/strong>But in the next layers, both conduction and diffusion-mass movement occur at the molecular or macroscopic levels. Due to the mass movement, the rate of energy transfer is higher. The higher the mass movement rate, the thinner the stagnant fluid film layer will be, and the higher the heat flow rate.<\/p>\n<p>It must be noted <strong>nucleate boiling<\/strong> at the surface effectively disrupts this stagnant layer. Therefore, nucleate boiling significantly increases the ability of a surface to transfer thermal energy to the bulk fluid.<\/p>\n<p>As was written, heat transfer through a fluid is by convection in the presence of mass movement and conduction in its absence. Therefore, thermal conduction in a fluid can be viewed as the limiting case of convection, corresponding to the case of quiescent fluid.<\/p>\n<h3>Convection as a Conduction with Fluid Motion<\/h3>\n<p>Some experts do not consider convection to be a fundamental mechanism of heat transfer since it is essentially heat conduction in the presence of fluid motion. They consider it to be a <strong>special case of thermal conduction<\/strong>, known as \u201c<strong>conduction with fluid motion<\/strong>\u201d. On the other hand, it is <strong>practical<\/strong> to recognize convection as a separate heat transfer mechanism despite the valid arguments to the contrary.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Velocity Boundary Layer<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In general, when a fluid flows over a <strong>stationary surface<\/strong>, e.g., the flat plate, the bed of a river, or the wall of a pipe, the fluid touching the surface is brought to <strong>rest<\/strong> by the <strong>shear stress<\/strong> to at the wall. The <a title=\"Boundary Layer\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/boundary-layer\/\"><strong>boundary layer<\/strong><\/a> is the region in which flow adjusts from zero velocity at the wall to a maximum in the mainstream of the flow. The concept of boundary layers is important in all viscous fluid dynamics and the theory of heat transfer.<\/p>\n<p>Basic characteristics of all <strong>laminar and turbulent boundary layers<\/strong> are shown in the developing flow over a flat plate. The stages of the formation of the boundary layer are shown in the figure below:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Boundary-layer-on-flat-plate.png\"><img loading=\"lazy\" class=\"aligncenter size-large wp-image-14390\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Boundary-layer-on-flat-plate-1024x357.png\" alt=\"Boundary layer on flat plate\" width=\"669\" height=\"233\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Boundary-layer-on-flat-plate-1024x357.png 1024w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Boundary-layer-on-flat-plate-300x104.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/05\/Boundary-layer-on-flat-plate.png 1025w\" sizes=\"(max-width: 669px) 100vw, 669px\" \/><\/a><\/p>\n<p><strong>Boundary layers<\/strong> may be either<strong> laminar<\/strong>\u00a0or <strong>turbulent,<\/strong> depending on the value of <strong>the <a title=\"Reynolds Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\">Reynolds number<\/a><\/strong>.<\/p>\n<p>See also: <a title=\"Boundary Layer\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/boundary-layer\/\">Boundary Layer<\/a><\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span> Thermal Boundary Layer<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/thermal-boundary-layer-convection-min.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20375\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/thermal-boundary-layer-convection-min-159x300.png\" alt=\"thermal boundary layer - convection\" width=\"159\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/thermal-boundary-layer-convection-min-159x300.png 159w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/thermal-boundary-layer-convection-min.png 337w\" sizes=\"(max-width: 159px) 100vw, 159px\" \/><\/a>Similarly, as a <strong>velocity boundary layer<\/strong> develops when there is fluid flow over a surface, a <strong>thermal boundary layer<\/strong> must develop if the bulk temperature and surface temperature differ. Consider flow over an isothermal flat plate at a constant temperature of <strong>T<sub>wall<\/sub><\/strong>. At the leading edge, the temperature profile is uniform with <strong>T<sub>bulk<\/sub><\/strong>. Fluid particles that come into contact with the plate achieve thermal equilibrium at the plate\u2019s surface temperature. At this point, energy flow occurs at the surface <strong>purely by conduction<\/strong>. These particles exchange energy with those in the adjoining fluid layer (by conduction and diffusion), and temperature gradients develop in the fluid. The region of the fluid in which these temperature gradients exist is the <strong>thermal boundary layer<\/strong>. Its <strong>thickness<\/strong>, <strong>\u03b4<sub>t<\/sub><\/strong>, is typically defined as the distance from the body at which the temperature is 99% of the temperature found from an inviscid solution. With increasing distance from the leading edge, the effects of heat transfer penetrate farther into the stream, and the thermal boundary layer grows.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Prandtl-Number-materials-table.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-20299\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Prandtl-Number-materials-table.png\" alt=\"Prandtl Number - materials\" width=\"388\" height=\"173\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Prandtl-Number-materials-table.png 388w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Prandtl-Number-materials-table-300x134.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/a>The ratio of these two thicknesses (velocity and thermal boundary layers) is governed by the <a title=\"What is Prandtl Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\">Prandtl number<\/a>, defined as the<strong> ratio<\/strong> of <strong>momentum diffusivity<\/strong> to <a title=\"Thermal Diffusivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/heat-conduction-equation\/thermal-diffusivity\/\"><strong>thermal diffusivity<\/strong><\/a>. A Prandtl number of unity indicates that momentum and thermal diffusivity are comparable, and velocity and thermal boundary layers almost coincide with each other. If the Prandtl number is less than 1, which is the case for air at standard conditions, the thermal boundary layer is thicker than the velocity boundary layer. If the Prandtl number is greater than 1, the thermal boundary layer is thinner than the velocity boundary layer. Air at room temperature has a <strong>Prandtl number<\/strong> of <strong>0.71,<\/strong> and for <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/\">water<\/a>, at 18\u00b0C, it is around <strong>7.56<\/strong>, which means that the thermal diffusivity is more dominant for air than for water.<\/p>\n<p>Similarly, as for <a title=\"What is Prandtl Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\"><strong>Prandtl Number<\/strong><\/a>, the <a title=\"What is Lewis Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-lewis-number\/\"><strong>Lewis number<\/strong><\/a> physically relates the relative thickness of the thermal layer and mass-transfer (concentration) boundary layer. The <a title=\"What is Schmidt Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-schmidt-number\/\"><strong>Schmidt number<\/strong><\/a> physically relates the relative thickness of the velocity boundary layer and mass-transfer (concentration) boundary layer.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Lewis-Number-Prandtl-Number-Schmidt-Number.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20325\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Lewis-Number-Prandtl-Number-Schmidt-Number.png\" alt=\"Lewis Number - Prandtl Number - Schmidt Number\" width=\"177\" height=\"195\" \/><\/a><\/p>\n<p>where n = 1\/3 \u00a0for most applications in all three relations. These relations, in general, are applicable only for <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/laminar-flow-viscous\/\">laminar flow<\/a> and are not applicable to <a title=\"Turbulent Boundary Layer\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/turbulent-flow\/turbulent-boundary-layer\/\">turbulent boundary layers<\/a> since turbulent mixing, in this case, may dominate the diffusion processes.<\/div><\/div><\/div>\n<p>Heat transfer by <strong>convection<\/strong> is more difficult to analyze than heat transfer by <a title=\"Thermal Conduction \u2013 Heat Conduction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\">conduction<\/a> because no single property of the heat transfer medium, such as <a title=\"Thermal Conductivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/\">thermal conductivity<\/a>, can be defined to describe the mechanism. <strong>Convective heat transfer<\/strong> is complicated by the fact that it involves <strong>fluid motion as well as heat conduction<\/strong>. Heat transfer by convection varies from situation to situation (upon the fluid flow conditions), and it is frequently coupled with the <a title=\"Flow Regime\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/flow-regime\/\">mode of fluid flow<\/a>. In forced convection, the rate of heat transfer through a fluid is much higher by convection than by conduction.<\/p>\n<p>In practice, analysis of heat transfer by convection is treated <strong>empirically<\/strong> (by direct experimental observation). Most problems can be solved using so-called <a title=\"Characteristic Numbers\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/\">characteristic numbers <\/a>(e.g., <strong>Nusselt number<\/strong>). <strong>Characteristic numbers<\/strong> are dimensionless numbers used to describe a character of heat transfer. They can be used to compare a <strong>real situation<\/strong> (e.g., heat transfer in a pipe) with a <strong>small-scale model<\/strong>. Experience shows that convection heat transfer strongly depends on the fluid properties, <strong>dynamic viscosity<\/strong>, <a title=\"Thermal Conductivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/\"><strong>thermal conductivity<\/strong><\/a>, <a title=\"What is Density \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-density-physics\/\"><strong>density<\/strong><\/a>, and <strong><a title=\"Heat Capacity \u2013 Specific Heat Capacity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-capacity\/\">specific heat<\/a><\/strong>, as well as the <strong>fluid velocity<\/strong>. It also depends on the geometry and the <a title=\"Relative Roughness of Pipe\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/relative-roughness-of-pipe\/\">roughness <\/a>of the solid surface, and the type of fluid flow. All these conditions affect especially the <strong>stagnant film thickness<\/strong>.<\/p>\n<p>Convection involves the transfer of heat between a surface at a given temperature (T<sub>wall<\/sub>) and fluid at a bulk temperature (T<sub>b<\/sub>). The exact definition of the bulk temperature (T<sub>b<\/sub>) varies depending on the details of the situation.<\/p>\n<ul>\n<li>For flow adjacent to a hot or cold surface, T<sub>b<\/sub> is the temperature of the fluid \u201cfar\u201d from the surface.<\/li>\n<li>For boiling or condensation, T<sub>b<\/sub> is the <a title=\"Saturation \u2013 Boiling Point\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturation-boiling-point\/\">saturation temperature <\/a>of the fluid.<\/li>\n<li>For flow in a pipe, T<sub>b<\/sub> is the average temperature measured at a particular cross-section of the pipe.<\/li>\n<\/ul>\n<h2>Newton\u2019s Law of Cooling for Convection<\/h2>\n<p>Despite the complexity of <strong>convection<\/strong>, the rate of convection heat transfer is observed to be <strong>proportional<\/strong> to the <strong>temperature difference. It is<\/strong>\u00a0conveniently expressed by <strong>Newton\u2019s law of cooling<\/strong>, which states that:<\/p>\n<p><em>The rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings, provided the temperature difference is small, and the nature of radiating surface remains the same.<\/em><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/newtons-law-of-cooling-convection-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20387\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/newtons-law-of-cooling-convection-equation.png\" alt=\"newton's law of cooling - convection equation\" width=\"269\" height=\"137\" \/><\/a><\/p>\n<p>Note that <strong>\u0394T<\/strong> is given by the surface or <strong>wall temperature<\/strong>, <strong>T<sub>wall,<\/sub> <\/strong>and the <strong>bulk temperature<\/strong>, <strong>T<sub>\u221e<\/sub><\/strong>, which is the temperature of the fluid sufficiently far from the surface.<\/p>\n<h2>Convective Heat Transfer Coefficient<\/h2>\n<p>As can be seen, the <strong>constant of proportionality<\/strong> will be crucial in calculations, and it is known as the <strong>convective heat transfer coefficient<\/strong>, <strong>h<\/strong>. The <strong>convective heat transfer coefficient,<\/strong> h, can be defined as:<\/p>\n<p><em>The rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature difference.<\/em><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20388\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-equation.png\" alt=\"convective heat transfer coefficient - equation\" width=\"265\" height=\"167\" \/><\/a><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-examples.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-20389\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-examples.png\" alt=\"convective heat transfer coefficient - examples\" width=\"337\" height=\"277\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-examples.png 337w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-examples-300x247.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/a>The <strong>convective heat transfer coefficient<\/strong> depends on the fluid\u2019s physical properties and the physical situation. The convective heat transfer coefficient is not a property of the fluid. It is an experimentally determined parameter whose value depends on all the variables influencing convection, such as the <strong>surface geometry<\/strong>, the <strong>nature of fluid motion<\/strong>, the <strong>properties of the fluid<\/strong>, and the <strong>bulk fluid velocity<\/strong>.<\/p>\n<p>Typically, the <strong>convective heat transfer coefficient<\/strong> for<a title=\"Laminar Flow \u2013 Viscous Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/laminar-flow-viscous\/\"><strong> laminar flow<\/strong><\/a> is relatively low compared to the <strong>convective heat transfer coefficient<\/strong> for <a title=\"Turbulent Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/turbulent-flow\/\"><strong>turbulent flow<\/strong><\/a>. This is due to turbulent flow having a <strong>thinner stagnant fluid film layer<\/strong> on the heat transfer surface.<\/p>\n<p>It must be noted this <strong>stagnant fluid film layer<\/strong> plays a crucial role in the convective heat transfer coefficient. It is observed that the fluid comes to a<strong> complete stop at the surface<\/strong> and assumes a zero velocity relative to the surface. This phenomenon is known as the no-slip condition, and therefore, <strong>at the surface, <\/strong>energy flow occurs <strong>purely by conduction. <\/strong>But in the next layers, both conduction and diffusion-mass movement occur at the molecular or macroscopic levels. Due to the mass movement, the rate of energy transfer is higher. As was written, <strong>nucleate boiling<\/strong> at the surface effectively disrupts this stagnant layer. Therefore, nucleate boiling significantly increases the ability of a surface to transfer <a title=\"Internal Energy \u2013 Thermal Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/\">thermal energy<\/a> to the bulk fluid.<\/p>\n<p>A similar phenomenon occurs for the temperature. It is observed that the fluid\u2019s temperature at the surface and the surface will have the same <a title=\"What is Temperature \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-temperature-physics\/\">temperature<\/a> at the point of contact. This phenomenon is known as the no-temperature-jump condition, and it is very important for the theory of nucleate boiling<strong>.<\/strong><\/p>\n<p>Values of the <strong>heat transfer coefficient<\/strong>, h, have been measured and tabulated for the commonly encountered fluids and flow situations occurring during heat transfer by convection.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Thermal Resistance - Analogy to Electric Resistance<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">See also: <a title=\"Thermal Resistance \u2013 Thermal Resistivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-resistance-thermal-resistivity\/\">Thermal Resistance<\/a><\/p>\n<p><strong>Thermal resistance<\/strong> is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. The thermal resistance for conduction in a plane wall is defined as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-definition.png?d484e7\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20119\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-definition.png?d484e7\" alt=\"thermal resistance - definition\" width=\"260\" height=\"170\" \/><\/a><\/p>\n<p>The equation above can also be derived for convective heat transfer. For heat flow is <strong>analogous<\/strong>\u00a0to the relation for\u00a0<strong>electric current flow I<\/strong>, expressed as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/analogy-to-electric-resistance.png?d484e7\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20129\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/analogy-to-electric-resistance.png?d484e7\" alt=\"analogy to electric resistance\" width=\"186\" height=\"92\" \/><\/a><\/p>\n<p>where\u00a0<strong>R<sub>e<\/sub>\u00a0= L\/\u03c3<sub>e<\/sub>A<\/strong>\u00a0is the electric resistance and V<sub>1<\/sub>\u00a0\u2013 V<sub>2<\/sub>\u00a0is the voltage difference across the resistance (\u03c3<sub>e<\/sub> is the electrical conductivity). The analogy between both equations is obvious. The rate of heat transfer through a layer corresponds to the electric current, the <strong>thermal resistance<\/strong> corresponds to electrical resistance, and the temperature difference corresponds to the voltage difference across the layer. The temperature difference is the potential or driving function for the heat flow, resulting in the <strong>Fourier equation<\/strong> being written similarly to Ohm\u2019s Law of Electrical Circuit Theory.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-composite-walls.png?d484e7\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20126\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-composite-walls-217x300.png?d484e7\" alt=\"thermal resistance - composite walls\" width=\"217\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-composite-walls-217x300.png 217w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-composite-walls.png 562w\" sizes=\"(max-width: 217px) 100vw, 217px\" \/><\/a>Circuit representations provide a useful\u00a0<strong>tool<\/strong> for conceptualizing and quantifying heat transfer problems. This analogy can also be used for the <strong>thermal resistance<\/strong> of the surface against heat convection. Note that when the convection heat transfer coefficient is very large (h \u2192 infinity), the convection resistance becomes zero and the surface temperature approaches the bulk temperature. This situation is approached in practice at surfaces where intensive boiling and condensation occur.<\/p>\n<p>The heat transfer through the\u00a0<strong>composite wall<\/strong> can be calculated from these resistances. The rate of steady heat transfer between two surfaces is equal to the temperature difference divided by the total thermal resistance between those two surfaces.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-equation.png?d484e7\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20128\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-equation.png?d484e7\" alt=\"thermal resistance - equation\" width=\"601\" height=\"73\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-equation.png 601w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-equation-300x36.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><\/a><\/p>\n<p>The equivalent thermal circuit for the plane wall with convection surface conditions is shown in the figure.<\/p>\n<p>See also:\u00a0<a title=\"Wiedemann\u2013Franz Law \u2013 Lorenz Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/wiedemann-franz-law-lorenz-number\/\"><strong>Wiedemann\u2013Franz Law<\/strong><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span> U-factor - Overall Heat Transfer Coefficient<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Many of the heat transfer processes encountered in industry involve composite systems and even involve a combination of both <a title=\"Thermal Conduction \u2013 Heat Conduction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\">conduction<\/a> and <a title=\"Convection \u2013 Convective Heat Transfer\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/\">convection<\/a>. It is often convenient to work with an<strong> overall heat transfer coefficient, <\/strong>known as a <strong>U-factor <\/strong>with these composite systems. The U-factor is defined by an expression analogous to <strong>Newton\u2019s law of cooling<\/strong>:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/u-factor-overall-heat-transfer-coefficient.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20390\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/u-factor-overall-heat-transfer-coefficient.png\" alt=\"u-factor - overall heat transfer coefficient\" width=\"314\" height=\"136\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/u-factor-overall-heat-transfer-coefficient.png 314w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/u-factor-overall-heat-transfer-coefficient-300x130.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/a><\/p>\n<p>The <strong>overall heat transfer coefficient<\/strong> is related to the<a title=\"Thermal Resistance \u2013 Thermal Resistivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-resistance-thermal-resistivity\/\"> total thermal resistance<\/a> and depends on the geometry of the problem. For example,<a title=\"Heat Transfer\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/\"> heat transfer<\/a> in a<a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\"> steam generator<\/a> involves convection from the bulk of the reactor coolant to the steam generator inner tube surface, conduction through the tube wall, and convection (boiling) from the outer tube surface to the secondary side fluid.<\/p>\n<p>In cases of combined heat transfer for a heat exchanger, there are two values for h. The convective heat transfer coefficient (h) for the fluid film inside the tubes and a convective heat transfer coefficient for the fluid film outside the tubes. The tube wall\u2019s <a title=\"Thermal Conductivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/\">thermal conductivity<\/a> (k) and thickness (\u0394x) must also be accounted for.<\/p>\n<p><strong>Overall Heat Transfer Coefficient &#8211; Plane Wall<\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/U-factor-Overall-Heat-Transfer-Coefficient-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20392\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/U-factor-Overall-Heat-Transfer-Coefficient-example.png\" alt=\"U-factor - Overall Heat Transfer Coefficient\" width=\"821\" height=\"996\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/U-factor-Overall-Heat-Transfer-Coefficient-example.png 821w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/U-factor-Overall-Heat-Transfer-Coefficient-example-247x300.png 247w\" sizes=\"(max-width: 821px) 100vw, 821px\" \/><\/a><\/p>\n<p><strong>Overall Heat Transfer Coefficient &#8211; Cylindrical Tubes<\/strong><\/p>\n<p>Steady heat transfer through multilayered cylindrical or spherical shells can be handled just like multilayered plane walls.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Overall-Heat-Transfer-Coefficient-Cylindrical-Tubes-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20393\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Overall-Heat-Transfer-Coefficient-Cylindrical-Tubes-example.png\" alt=\"Overall Heat Transfer Coefficient - Cylindrical Tubes\" width=\"701\" height=\"585\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Overall-Heat-Transfer-Coefficient-Cylindrical-Tubes-example.png 701w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Overall-Heat-Transfer-Coefficient-Cylindrical-Tubes-example-300x250.png 300w\" sizes=\"(max-width: 701px) 100vw, 701px\" \/><\/a><\/p>\n<\/div><\/div><\/div>\n<h2>Nusselt Number<\/h2>\n<p>The <strong>Nusselt number<\/strong> is a dimensionless number, named after a German engineer Wilhelm Nusselt. The <strong>Nusselt number<\/strong> is closely related to the <a title=\"What is P\u00e9clet Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-peclet-number\/\">P\u00e9clet number<\/a>. Both\u00a0numbers are used to describe the ratio of the <strong>thermal energy convected<\/strong> to the fluid to the <strong>thermal energy conducted<\/strong> within the fluid. <strong>Nusselt number<\/strong> is equal to the dimensionless <strong>temperature gradient<\/strong> at the surface, and it provides a measure of the convection heat transfer occurring at the surface. The conductive component is measured under the same conditions as the heat convection but with stagnant fluid. The <strong>Nusselt number<\/strong> is to the thermal boundary layer what the friction coefficient is to the velocity boundary layer. Thus, the Nusselt number is defined as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Nusselt-Number-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-medium wp-image-20391\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Nusselt-Number-definition-300x270.png\" alt=\"Nusselt Number - definition\" width=\"300\" height=\"270\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Nusselt-Number-definition-300x270.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Nusselt-Number-definition.png 689w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>where:<\/p>\n<p><strong><em>k<\/em><\/strong><strong><em><sub>f<\/sub><\/em><\/strong> is the <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/\"><strong>thermal conductivity<\/strong><\/a> of the fluid [W\/m.K]\n<p><strong><em>L <\/em><\/strong>is the <strong>characteristic length<\/strong><\/p>\n<p><strong><em>h <\/em><\/strong>is the <strong>convective heat transfer coefficient<\/strong> [W\/m<sup>2<\/sup>.K]\n<p>For illustration, consider a fluid layer of thickness <strong>L<\/strong> and temperature difference <strong>\u0394T<\/strong>. Heat transfer through the fluid layer will be by convection when the fluid involves some motion and conduction when the fluid layer is motionless.<\/p>\n<p>In the case of <a title=\"Thermal Conduction \u2013 Heat Conduction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\">conduction<\/a>, the <a title=\"Heat Flux Density \u2013 Thermal Flux\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/heat-flux-density-thermal-flux\/\">heat flux <\/a>can be calculated using <a title=\"Fourier\u2019s Law of Thermal Conduction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/fouriers-law-of-thermal-conduction\/\">Fourier\u2019s law of conduction<\/a>. In the case of convection, the heat flux can be calculated using Newton\u2019s law of cooling. Taking their ratio gives:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/nusselt-number-convection-to-conduction.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20394\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/nusselt-number-convection-to-conduction.png\" alt=\"nusselt number - convection to conduction\" width=\"353\" height=\"227\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/nusselt-number-convection-to-conduction.png 353w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/nusselt-number-convection-to-conduction-300x193.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/a><\/p>\n<p>The preceding equation defines the <strong>Nusselt number<\/strong>. Therefore, the <strong>Nusselt number<\/strong> represents the enhancement of heat transfer through a fluid layer due to <strong>convection relative to conduction <\/strong>across the same fluid layer. A <strong>Nusselt number<\/strong> of <strong>Nu=1<\/strong> for a fluid layer represents heat transfer across the layer by <strong>pure conduction<\/strong>. The larger the <strong>Nusselt number<\/strong>, the more effective the convection. A larger Nusselt number corresponds to more effective convection, with turbulent flow typically in the 100\u20131000 range. The <strong>Nusselt number<\/strong> is usually a function of the <a title=\"Reynolds Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\">Reynolds number<\/a> and the <a title=\"What is Prandtl Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\">Prandtl number<\/a> for turbulent flow.<\/p>\n<h2>Example &#8211; Convective Heat Transfer &#8211; Cladding Surface Temperature<\/h2>\n<p><strong><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Convection-Convective-Heat-Transfer-example.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20406\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Convection-Convective-Heat-Transfer-example-275x300.png\" alt=\"Convection - Convective Heat Transfer\" width=\"275\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Convection-Convective-Heat-Transfer-example-275x300.png 275w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Convection-Convective-Heat-Transfer-example.png 911w\" sizes=\"(max-width: 275px) 100vw, 275px\" \/><\/a>Cladding<\/strong> is the outer layer of the fuel rods, standing between the <strong>reactor coolant<\/strong> and the <a title=\"Nuclear Fuel\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-fuel\/\"><strong>nuclear fuel<\/strong> <\/a>(i.e., <strong>fuel pellets<\/strong>). It is made of corrosion-resistant material with a low absorption cross-section for <a title=\"Thermal Neutron\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/fundamental-particles\/neutron\/thermal-neutron\/\">thermal neutrons<\/a>, usually <strong>zirconium alloy<\/strong>. <strong>Cladding<\/strong> prevents radioactive fission products from escaping the fuel matrix into the reactor coolant and contaminating it. Cladding constitutes one of the barriers in the \u2018<strong>defense-in-depth \u2018<\/strong>approach; therefore, its <strong>coolability<\/strong> is one of the key safety aspects.<\/p>\n<p>Consider the fuel cladding of inner radius <strong>r<\/strong><strong><sub>Zr,2<\/sub><\/strong><strong> = 0.408 cm<\/strong> and outer radius <strong>r<\/strong><strong><sub>Zr,1<\/sub><\/strong><strong> = 0.465 cm<\/strong>. Compared to fuel pellet, there is almost no heat generation in the fuel cladding (cladding is <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/fission\/energy-release-from-fission\/\">slightly heated by radiation<\/a>). All heat generated in the fuel must be transferred via <a title=\"Thermal Conduction \u2013 Heat Conduction\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\"><strong>conduction<\/strong><\/a> through the cladding, and therefore the inner surface is hotter than the outer surface.<\/p>\n<p>Assume that:<\/p>\n<ul>\n<li>the outer diameter of the cladding is: <strong>d = 2 x r<sub>Zr,1<\/sub> = 9,3 mm<\/strong><\/li>\n<li>the pitch of fuel pins is: <strong>p = 13 mm<\/strong><\/li>\n<li>the <a title=\"Thermal Conductivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/\">thermal conductivity<\/a> of <a title=\"Saturated and Subcooled Liquid\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturated-and-subcooled-liquid\/\">saturated water<\/a> at 300\u00b0C is: <strong>k<\/strong><strong><sub>H2O<\/sub><\/strong><strong> = 0.545 W\/m.K<\/strong><\/li>\n<li>the dynamic viscosity of saturated water at 300\u00b0C is: <strong>\u03bc = 0.0000859 N.s\/m<\/strong><strong><sup>2<\/sup><\/strong><\/li>\n<li>the fluid <a title=\"What is Density \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-density-physics\/\">density<\/a> is: <strong>\u03c1 = 714 kg\/m<\/strong><strong><sup>3<\/sup><\/strong><\/li>\n<li>the <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-capacity\/\"><strong>specific heat<\/strong><\/a> is: <strong>c<\/strong><strong><sub>p<\/sub><\/strong><strong> = 5.65 kJ\/kg.K<\/strong><\/li>\n<li>the core flow velocity is constant and equal to <strong>V<\/strong><strong><sub>core<\/sub><\/strong><strong> = 5 m\/s<\/strong><\/li>\n<li>the temperature of reactor coolant at this axial coordinate is: <strong>T<\/strong><strong><sub>bulk<\/sub><\/strong><strong> = 296\u00b0C<\/strong><\/li>\n<li>the linear heat rate of the fuel is <strong>q<\/strong><strong><sub>L<\/sub><\/strong><strong> = 300 W\/cm<\/strong> (F<sub>Q<\/sub> \u2248 2.0) and thus the volumetric heat rate is q<sub>V<\/sub> = 597 x 10<sup>6<\/sup> W\/m<sup>3<\/sup><\/li>\n<\/ul>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Hydraulic-Diameter-Fuel-Channel.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20407\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Hydraulic-Diameter-Fuel-Channel-254x300.png\" alt=\"Hydraulic Diameter - Fuel Channel\" width=\"254\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Hydraulic-Diameter-Fuel-Channel-254x300.png 254w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Hydraulic-Diameter-Fuel-Channel.png 316w\" sizes=\"(max-width: 254px) 100vw, 254px\" \/><\/a>Calculate the <a title=\"What is Prandtl Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\">Prandtl<\/a>, <a title=\"Reynolds Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\">Reynolds<\/a> and Nusselt number for this flow regime (internal forced turbulent flow) inside the rectangular fuel lattice (fuel channel), then calculate the <strong>heat transfer coefficient<\/strong> and finally the <strong>cladding surface temperature<\/strong>, <strong>T<sub>Zr,1<\/sub><\/strong>.<\/p>\n<p>To calculate the <strong>cladding surface temperature<\/strong>, we have to calculate the <strong>Prandtl<\/strong>, <strong>Reynolds,<\/strong> and <strong>Nusselt number<\/strong>\u00a0because the heat transfer for this flow regime can be described by the <strong>Dittus-Boelter equation<\/strong>, which is:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Dittus-Boelter-Equation-Formula.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20409\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Dittus-Boelter-Equation-Formula.png\" alt=\"Dittus-Boelter Equation - Formula\" width=\"556\" height=\"278\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Dittus-Boelter-Equation-Formula.png 556w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Dittus-Boelter-Equation-Formula-300x150.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/a><\/p>\n<h3>Calculation of the Prandtl number<\/h3>\n<p>To calculate the <a title=\"What is Prandtl Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\">Prandtl number<\/a>, we have to know:<\/p>\n<ul>\n<li>the thermal conductivity of saturated water at 300\u00b0C is: <strong>k<\/strong><strong><sub>H2O<\/sub><\/strong><strong> = 0.545 W\/m.K<\/strong><\/li>\n<li>the dynamic viscosity of saturated water at 300\u00b0C is: <strong>\u03bc = 0.0000859 N.s\/m<\/strong><strong><sup>2<\/sup><\/strong><\/li>\n<li>the <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-capacity\/\"><strong>specific heat<\/strong><\/a> is: <strong>c<\/strong><strong><sub>p<\/sub><\/strong><strong> = 5.65 kJ\/kg.K<\/strong><\/li>\n<\/ul>\n<p>Note that all these parameters significantly differ for water at 300\u00b0C from those at 20\u00b0C. Prandtl number for <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-of-water\/\">water<\/a> at 20\u00b0C is around <strong>6.91. <\/strong>Prandtl number for reactor coolant at 300\u00b0C is then:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/prandtl-number-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20411\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/prandtl-number-example.png\" alt=\"prandtl number - example\" width=\"469\" height=\"80\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/prandtl-number-example.png 469w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/prandtl-number-example-300x51.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/a><\/p>\n<h3>Calculation of the Reynolds number<\/h3>\n<p>To calculate the Reynolds number, we have to know:<\/p>\n<ul>\n<li>the outer diameter of the cladding is: <strong>d = 2 x r<sub>Zr,1<\/sub> = 9,3 mm<\/strong> (to calculate the hydraulic diameter)<\/li>\n<li>the pitch of fuel pins is: <strong>p = 13 mm<\/strong> \u00a0(to calculate the hydraulic diameter)<\/li>\n<li>the dynamic viscosity of saturated water at 300\u00b0C is: <strong>\u03bc = 0.0000859 N.s\/m<\/strong><strong><sup>2<\/sup><\/strong><\/li>\n<li>the fluid density is: <strong>\u03c1 = 714 kg\/m<\/strong><strong><sup>3<\/sup><\/strong><\/li>\n<\/ul>\n<p><strong>The hydraulic diameter, D<\/strong><strong><sub>h<\/sub><\/strong>, is a commonly used term when handling flow in <strong>non-circular tubes and channels<\/strong>. The <strong>hydraulic diameter of the fuel channel<\/strong>, <em>D<\/em><em><sub>h<\/sub><\/em>, is equal to 13,85 mm.<\/p>\n<p>See also: <a title=\"Hydraulic Diameter\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/internal-flow\/hydraulic-diameter-2\/\">Hydraulic Diameter<\/a><\/p>\n<p>The <strong>Reynolds number <\/strong>inside the fuel channel is then equal to:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/reynolds-number-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20412\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/reynolds-number-example.png\" alt=\"reynolds number - example\" width=\"593\" height=\"78\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/reynolds-number-example.png 593w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/reynolds-number-example-300x39.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/a><\/p>\n<p>This fully satisfies the <a title=\"Turbulent Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/turbulent-flow\/\"><strong>turbulent conditions<\/strong><\/a>.<\/p>\n<h3>Calculation of the Nusselt number using Dittus-Boelter equation<\/h3>\n<p>For fully developed (hydrodynamically and thermally) turbulent flow in a smooth circular tube, the local <strong>Nusselt number<\/strong> may be obtained from the well-known <strong>Dittus\u0096Boelter equation<\/strong>.<\/p>\n<p>To calculate the <strong>Nusselt number<\/strong>, we have to know:<\/p>\n<ul>\n<li>the <a title=\"Reynolds Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/reynolds-number\/\">Reynolds number<\/a>, which is <strong>Re<sub>Dh<\/sub> = 575600<\/strong><\/li>\n<li>the <a title=\"What is Prandtl Number\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-prandtl-number\/\">Prandtl number<\/a>, which is <strong>Pr = 0.89<\/strong><\/li>\n<\/ul>\n<p>The <strong>Nusselt number <\/strong>for the forced convection inside the fuel channel is then equal to:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/nusselt-number-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20413\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/nusselt-number-example.png\" alt=\"nusselt number - example\" width=\"387\" height=\"58\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/nusselt-number-example.png 387w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/nusselt-number-example-300x45.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/a><\/p>\n<h3>Calculation of the heat transfer coefficient and the cladding surface temperature, T<sub>Zr,1<\/sub><\/h3>\n<p>Detailed knowledge of geometry, fluid parameters, the outer radius of cladding, linear heat rate, convective heat transfer coefficient allows us to calculate the temperature difference <strong>\u2206T <\/strong>between the coolant (T<sub>bulk<\/sub>) and the cladding surface (T<sub>Zr,1<\/sub>).<\/p>\n<p>To calculate the cladding surface temperature, we have to know:<\/p>\n<ul>\n<li>the outer diameter of the cladding is: d = 2 x <strong>r<\/strong><strong><sub>Zr,1<\/sub><\/strong><strong> = 9,3 mm<\/strong><\/li>\n<li>the Nusselt number, which is <strong>Nu<\/strong><strong><sub>Dh<\/sub><\/strong><strong> = 890<\/strong><\/li>\n<li>the hydraulic diameter of the fuel channel is <strong><em>D<\/em><\/strong><strong><em><sub>h<\/sub><\/em><\/strong><strong> = 13,85 mm<\/strong><\/li>\n<li>the thermal conductivity of reactor coolant (300\u00b0C) is: <strong>k<\/strong><strong><sub>H2O<\/sub><\/strong><strong> = 0.545 W\/m.K<\/strong><\/li>\n<li>the bulk temperature of reactor coolant at this axial coordinate is <strong>T<\/strong><strong><sub>bulk<\/sub><\/strong><strong> = 296\u00b0C<\/strong><\/li>\n<li>the linear heat rate of the fuel is: <strong>q<\/strong><strong><sub>L<\/sub><\/strong><strong> = 300 W\/cm <\/strong>(F<sub>Q<\/sub> \u2248 2.0)<\/li>\n<\/ul>\n<p>The convective heat transfer coefficient, <strong>h<\/strong>, is given directly by the definition of Nusselt number:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20410\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-example.png\" alt=\"convective heat transfer coefficient - example\" width=\"619\" height=\"92\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-example.png 619w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/convective-heat-transfer-coefficient-example-300x45.png 300w\" sizes=\"(max-width: 619px) 100vw, 619px\" \/><\/a><\/p>\n<p>Finally, we can calculate the cladding surface temperature (T<sub>Zr,1<\/sub>) simply using <strong>Newton\u2019s Law of Cooling<\/strong>:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Newton-law-of-cooling-example.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20408\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Newton-law-of-cooling-example.png\" alt=\"Newton law of cooling - example\" width=\"377\" height=\"369\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Newton-law-of-cooling-example.png 377w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Newton-law-of-cooling-example-300x294.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Newton-law-of-cooling-example-52x50.png 52w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/11\/Newton-law-of-cooling-example-66x66.png 66w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><\/a><\/p>\n<p>For PWRs at normal operation, there is <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/materials-nuclear-engineering\/properties-steam-what-is-steam\/saturated-and-subcooled-liquid\/\">compressed liquid water<\/a> inside the reactor core, loops, and steam generators. The pressure is maintained at approximately <strong>16MPa<\/strong>. At this pressure, water boils at approximately <strong>350\u00b0C<\/strong>(662\u00b0F). As can be seen, the surface temperature T<sub>Zr,1<\/sub> = 325\u00b0C ensures that even subcooled boiling does not occur. Note that subcooled boiling requires T<sub>Zr,1<\/sub> = T<sub>sat<\/sub>. Since the inlet temperatures of the water are usually about<strong> 290\u00b0C<\/strong> (554\u00b0F), it is obvious this example corresponds to the lower part of the core. At higher core elevations, the bulk temperature may reach up to 330\u00b0C. The temperature difference of 29\u00b0C causes the subcooled boiling may occur (330\u00b0C + 29\u00b0C &gt; 350\u00b0C). On the other hand, <strong>nucleate boiling<\/strong> at the surface effectively disrupts the stagnant layer. Therefore, nucleate boiling significantly increases the ability of a surface to transfer <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/\">thermal energy<\/a> to the bulk fluid. As a result, the convective heat transfer coefficient significantly increases, and therefore at higher elevations, the temperature difference (T<sub>Zr,1<\/sub> &#8211; T<sub>bulk<\/sub>) significantly decreases.<\/p>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Heat Transfer:<\/strong>\n<ol>\n<li>Fundamentals of Heat and Mass Transfer, 7th Edition. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. John Wiley &amp; Sons, Incorporated, 2011. ISBN: 9781118137253.<\/li>\n<li>Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866.<\/li>\n<li>Fundamentals of Heat and Mass Transfer. C. P. Kothandaraman. New Age International, 2006, ISBN: 9788122417722.<\/li>\n<li>U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow. DOE Fundamentals Handbook, Volume 2 of 3. May 2016.<\/li>\n<\/ol>\n<p><strong>Nuclear and Reactor Physics:<\/strong><\/p>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965<\/li>\n<li>Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.<\/li>\n<li>Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.<\/li>\n<\/ol>\n<p><strong><\/strong><strong>Advanced Reactor Physics:<\/strong><\/p>\n<ol>\n<li>K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.<\/li>\n<li>K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.<\/li>\n<li><span style=\"font-weight: 400;\">D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.\u00a0<\/span><\/li>\n<li>E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Heat Transfer<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>In general, convection is either the mass transfer or the heat transfer due to the bulk movement of molecules within fluids such as gases and liquids. Although liquids and gases are generally not very good conductors of heat, they can transfer heat quite rapidly by convection. Convection takes place through advection, diffusion, or both. Convection &#8230; <a title=\"Convection &#8211; Convective Heat Transfer\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/\" aria-label=\"More on Convection &#8211; Convective Heat Transfer\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":19996,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20369"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=20369"}],"version-history":[{"count":5,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20369\/revisions"}],"predecessor-version":[{"id":37258,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/20369\/revisions\/37258"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/19996"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=20369"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}