{"id":21131,"date":"2019-02-24T07:53:49","date_gmt":"2019-02-24T07:53:49","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=21131"},"modified":"2023-04-26T17:44:27","modified_gmt":"2023-04-26T17:44:27","slug":"heat-losses","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/heat-losses\/","title":{"rendered":"Heat Losses"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"su-quote su-quote-style-default\"><div   id="8n9s8rpp6h"    class=\"su-quote-inner su-u-clearfix su-u-trim\">\n<p><strong>Heat losses<\/strong> from hotter objects occur by three mechanisms (either individually or in combination):<\/p>\n<ul>\n<li><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\"><strong>Heat Conduction<\/strong><\/a><strong>.<\/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. When an object is at a different temperature from another body or its surroundings<\/li>\n<li><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/\"><strong>Heat Convection<\/strong><\/a><strong>.<\/strong> Heat convection depends on the motion of mass 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 title=\"Thermal Radiation \u2013 Radiant Heat\" 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<p><strong>Thermal insulators<\/strong>\u00a0have\u00a0<strong>very low thermal conductivity.<\/strong> Their low thermal conductivity is based on the alternation of gas pocket and solid material that causes the heat must be transferred through many interfaces causing a rapid decrease in heat transfer coefficient.<\/p>\n<p>As was written, many heat transfer processes involve composite systems and even involve a combination of <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\">conduction<\/a> and <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/\">convection<\/a>. It is often convenient to work with an<strong><a title=\"Overall Heat Transfer Coefficient \u2013 U-factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/overall-heat-transfer-coefficient-u-factor\/\"> overall heat transfer coefficient<\/a>, <\/strong>known as a <strong>U-factor<\/strong> with these composite systems.<\/p>\n<\/div><\/div>\n<p>While <a title=\"Internal Energy \u2013 Thermal Energy\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/what-is-energy-physics\/internal-energy-thermal-energy\/\"><strong>thermal energy <\/strong><\/a>refers to the total energy of all the molecules within the object, <a title=\"Heat in Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/first-law-of-thermodynamics\/heat-in-thermodynamics\/\"><strong>heat<\/strong><\/a> is the amount of energy <strong>flowing<\/strong> spontaneously from one body to another due to their temperature difference. <strong>Heat<\/strong> is a form of energy, but it is <strong>energy in transit<\/strong>. Heat is not a property of a system. However, the transfer of energy as heat occurs at the molecular level due to a <strong>temperature difference<\/strong>. When a <strong><a title=\"What is Temperature \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-temperature-physics\/\">temperature<\/a> difference<\/strong> does exist, heat flows spontaneously <strong>from the warmer system to the colder system<\/strong>, never the reverse. This direction of <a title=\"Thermodynamic Processes\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-processes\/\">thermodynamic processes<\/a> is given by the<a title=\"Second Law of Thermodynamics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/laws-of-thermodynamics\/second-law-of-thermodynamics\/\"> second law of thermodynamics<\/a>.<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Zeroth-Law-of-Thermodynamics-heat.png\"><img loading=\"lazy\" class=\"size-medium wp-image-16452 aligncenter\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Zeroth-Law-of-Thermodynamics-heat-300x158.png\" alt=\"zeroth-law-of-thermodynamics-heat\" width=\"300\" height=\"158\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Zeroth-Law-of-Thermodynamics-heat-300x158.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/01\/Zeroth-Law-of-Thermodynamics-heat.png 387w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>As a result, any object hotter than the surroundings must continuously lose a part of its thermal energy. This is a natural behavior of all objects. When the <strong>flow of heat stops<\/strong>, they are said to be at the <strong>same temperature<\/strong>, and they\u00a0are then said to be in <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-temperature-physics\/thermal-equilibrium\/\"><strong>thermal equilibrium<\/strong><\/a>. <strong>Heat losses<\/strong> from hotter objects occur by three mechanisms (either individually or in combination):<\/p>\n<ul>\n<li><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\"><strong>Heat Conduction<\/strong><\/a><strong>.<\/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. When an object is at a different temperature from another body or its surroundings<\/li>\n<li><a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/\"><strong>Heat Convection<\/strong><\/a><strong>.<\/strong> Heat convection depends on the 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 title=\"Thermal Radiation \u2013 Radiant Heat\" 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<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Heat Losses &#8211; Clothing<\/h2>\n<p>The purpose of clothing is similar. The insulating properties of clothing come from the <strong>insulating properties of air<\/strong>. Gases possess poor <a title=\"Thermal Conductivity of Fluids \u2013 Gases and Liquids\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/thermal-conductivity-of-fluids-gases-and-liquids\/\">thermal conduction<\/a> properties compared to liquids and solids and thus make a good insulation material if they can be trapped (e.g., in a foam-like structure). Air and other gases are generally good insulators. But the main benefit is in the <strong>absence of convection<\/strong>. Without clothes, our bodies in still air would heat the air in direct contact with the skin and soon become reasonably comfortable because air is a very good insulator. It must be added. Also, in this case, air will be flowing due to <a title=\"Natural Convection \u2013 Free Convection\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/natural-convection-free-convection\/\">natural convection<\/a>. In <strong>natural convection<\/strong>, the air surrounding a body receives heat and, by <strong>thermal expansion,<\/strong> becomes less dense and rises. Thermal expansion of air plays a crucial role. In other words, heavier (more dense) components will fall while lighter (less dense) components rise, leading to bulk air movement.<\/p>\n<p>In the wind, the warm air surrounding our body would be replaced by cold air, thus increasing the temperature difference and the <strong>heat loss<\/strong> from the body. Clothes constitute a barrier to this moving air, and the main benefit is in the absence of large-scale convection. Moreover, clothes are made from materials that are generally good insulators. Many insulating materials (e.g., wool) function simply by having many <strong>gas-filled pockets,<\/strong> which significantly decrease the material&#8217;s thermal conductivity. Alternation of gas pocket and solid material causes heat to transfer through many interfaces, causing a rapid decrease in heat transfer coefficient.<\/p>\n<h2>Heat Losses &#8211; Thermal Insulation<\/h2>\n<figure id=\"attachment_21154\" aria-describedby=\"caption-attachment-21154\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/expanded-polystyrene-thermal-insulation.png\"><img loading=\"lazy\" class=\"size-medium wp-image-21154\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/expanded-polystyrene-thermal-insulation-300x180.png\" alt=\"expanded polystyrene - thermal insulation\" width=\"300\" height=\"180\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/expanded-polystyrene-thermal-insulation-300x180.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/expanded-polystyrene-thermal-insulation.png 656w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-21154\" class=\"wp-caption-text\">Expanded polystyrene insulation<\/figcaption><\/figure>\n<p>To minimize <strong>heat losses<\/strong> in industry and also in the construction of buildings, <strong>thermal insulation<\/strong> is widely used. The purpose of thermal insulation is to reduce the<a title=\"Overall Heat Transfer Coefficient \u2013 U-factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/overall-heat-transfer-coefficient-u-factor\/\"> overall heat transfer coefficient<\/a> by adding material with low <a title=\"Thermal Conductivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/\">thermal conductivity<\/a>. \u00a0<strong>Thermal insulation<\/strong> in buildings is an important factor in achieving thermal comfort for occupants. Thermal insulation reduces unwanted <strong>heat loss<\/strong> and also reduces unwanted <strong>heat gain<\/strong>. Therefore thermal insulation can decrease the energy demands of heating and cooling systems. It must be added that no material can completely prevent heat losses, and heat losses can only be minimized.<\/p>\n<p>Similarly, as for clothing, thermal insulation is based on low thermal conductivity materials and geometry (e.g., double-pane windows). The insulating properties of these materials come from the insulating properties of air. Many insulating materials (e.g., glass wool) function simply by having a large number of <strong>gas-filled pockets<\/strong> which <strong>prevent large-scale convection<\/strong>. The geometry of these materials also plays a crucial role. For example, \u00a0increasing the width of the air layer, such as using two panes of glass separated by an air gap, will reduce the heat loss more than simply increasing the glass thickness since the thermal conductivity of air is much less than that for glass.<\/p>\n<h2>Example &#8211; Heat Loss through a Wall<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/heat-loss-through-wall-example-calculation.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-21148\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/heat-loss-through-wall-example-calculation-169x300.png\" alt=\"heat loss through wall - example - calculation\" width=\"169\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/heat-loss-through-wall-example-calculation-169x300.png 169w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/heat-loss-through-wall-example-calculation.png 536w\" sizes=\"(max-width: 169px) 100vw, 169px\" \/><\/a>A major source of <strong>heat loss<\/strong> from a house is through walls. Calculate the rate of <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> through a wall 3 m x 10 m in the area (A = 30 m<sup>2<\/sup>). The wall is 15 cm thick (L<sub>1<\/sub>), and it is made of bricks with <a title=\"Thermal Conductivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/\">thermal conductivity<\/a> of k<sub>1<\/sub> = 1.0 W\/m.K (poor thermal insulator). Assume that the indoor and the outdoor <a title=\"What is Temperature \u2013 Physics\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/thermodynamics\/thermodynamic-properties\/what-is-temperature-physics\/\">temperatures<\/a> are 22\u00b0C and -8\u00b0C, and the <a title=\"Convective Heat Transfer Coefficient\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/convective-heat-transfer-coefficient\/\">convection heat transfer coefficients<\/a> on the inner and the outer sides are h<sub>1<\/sub> = 10 W\/m<sup>2<\/sup>K and h<sub>2<\/sub> = 30 W\/m<sup>2<\/sup>K, respectively. Note that these convection coefficients strongly depend on ambient and interior conditions (wind, humidity, etc.).<\/p>\n<ol>\n<li>Calculate the heat flux (<a title=\"Heat Losses\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/heat-losses\/\"><strong>heat loss<\/strong><\/a>) through this non-insulated wall.<\/li>\n<li>Now assume <strong>thermal insulation<\/strong> on the outer side of this wall. Use expanded <strong>polystyrene insulation <\/strong>10 cm thick (L<sub>2<\/sub>) with the thermal conductivity of k<sub>2<\/sub> = 0.03 W\/m.K and calculate the heat flux (<a title=\"Heat Losses\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/heat-losses\/\"><strong>heat loss<\/strong><\/a>) through this composite wall.<\/li>\n<\/ol>\n<p><strong>Solution:<\/strong><\/p>\n<p>As was written, many heat transfer processes involve composite systems and even involve a combination of <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/\">conduction<\/a> and <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/\">convection<\/a>. With these composite systems, it is often convenient to work with an<strong><a title=\"Overall Heat Transfer Coefficient \u2013 U-factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/overall-heat-transfer-coefficient-u-factor\/\"> overall heat transfer coefficient<\/a>, <\/strong>known as a <strong>U-factor<\/strong>. The U-factor is defined by an expression analogous to <a title=\"Newton\u2019s Law of Cooling\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/newtons-law-of-cooling\/\"><strong>Newton\u2019s law of cooling<\/strong><\/a>:<\/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 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.<\/p>\n<ol>\n<li><strong>bare wall<\/strong><\/li>\n<\/ol>\n<p>Assuming one-dimensional heat transfer through the plane wall and disregarding radiation, the <strong>overall heat transfer coefficient<\/strong> can be calculated as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/overall-heat-transfer-coefficient-heat-loss-calculation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-21160\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/overall-heat-transfer-coefficient-heat-loss-calculation.png\" alt=\"overall heat transfer coefficient - heat loss calculation\" width=\"343\" height=\"200\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/overall-heat-transfer-coefficient-heat-loss-calculation.png 343w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/overall-heat-transfer-coefficient-heat-loss-calculation-300x175.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/a><\/p>\n<p>The <strong>overall heat transfer coefficient <\/strong>is then:<\/p>\n<p>U = 1 \/ (1\/10 + 0.15\/1 + 1\/30) = 3.53 W\/m<sup>2<\/sup>K<\/p>\n<p>The heat flux can be then calculated simply as:<\/p>\n<p>q = 3.53 [W\/m<sup>2<\/sup>K] x 30 [K] = 105.9 W\/m<sup>2<\/sup><\/p>\n<p>The total heat loss through this wall will be:<\/p>\n<p>q<sub>loss<\/sub> = q . A = 105.9 [W\/m<sup>2<\/sup>] x 30 [m<sup>2<\/sup>] = 3177W<\/p>\n<ol start=\"2\">\n<li><strong>composite wall with thermal insulation<\/strong><\/li>\n<\/ol>\n<p>Assuming one-dimensional heat transfer through the plane composite wall, no thermal contact resistance, and disregarding radiation, the <strong>overall heat transfer coefficient<\/strong> can be calculated as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/overall-heat-transfer-coefficient-thermal-insulation-calculation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-21159\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/overall-heat-transfer-coefficient-thermal-insulation-calculation.png\" alt=\"overall heat transfer coefficient - thermal insulation calculation\" width=\"423\" height=\"211\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/overall-heat-transfer-coefficient-thermal-insulation-calculation.png 423w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/overall-heat-transfer-coefficient-thermal-insulation-calculation-300x150.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/a><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/thermal-insulation-expanded-polystyrene.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-21147\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/thermal-insulation-expanded-polystyrene-167x300.png\" alt=\"thermal insulation - expanded polystyrene\" width=\"167\" height=\"300\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/thermal-insulation-expanded-polystyrene-167x300.png 167w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/thermal-insulation-expanded-polystyrene.png 532w\" sizes=\"(max-width: 167px) 100vw, 167px\" \/><\/a>The <strong>overall heat transfer coefficient <\/strong>is then:<\/p>\n<p>U = 1 \/ (1\/10 + 0.15\/1 + 0.1\/0.03 + 1\/30) = 0.276 W\/m<sup>2<\/sup>K<\/p>\n<p>The heat flux can be then calculated simply as:<\/p>\n<p>q = 0.276 [W\/m<sup>2<\/sup>K] x 30 [K] = 8.28 W\/m<sup>2<\/sup><\/p>\n<p>The total heat loss through this wall will be:<\/p>\n<p>q<sub>loss<\/sub> = q . A = 8.28 [W\/m<sup>2<\/sup>] x 30 [m<sup>2<\/sup>] = 248 W<\/p>\n<p>As can be seen, adding a thermal insulator causes a significant decrease in heat losses. It must be added that adding the next layer of the thermal insulator does not cause such high savings. This can be better seen from the thermal resistance method, which can be used to calculate the heat transfer through <strong>composite walls<\/strong>. The rate of steady heat transfer between two surfaces is equal to the temperature difference divided by the total <a title=\"Thermal Resistance \u2013 Thermal Resistivity\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-resistance-thermal-resistivity\/\">thermal resistance<\/a> between those two surfaces.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20128\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/thermal-resistance-equation.png\" 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<h2>Example &#8211; Heat Loss through a Window<\/h2>\n<p><strong><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/Example-Heat-Flux-Thermal-Conduction.png?36a14b\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-20047\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/Example-Heat-Flux-Thermal-Conduction-300x280.png?36a14b\" alt=\"Example - Heat Flux - Thermal Conduction\" width=\"300\" height=\"280\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/Example-Heat-Flux-Thermal-Conduction-300x280.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/Example-Heat-Flux-Thermal-Conduction-52x50.png 52w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/Example-Heat-Flux-Thermal-Conduction.png 660w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>Heat loss through windows<\/strong><\/p>\n<p>A major source of heat loss from a house is through the windows. Calculate the rate of heat\u00a0flux through a glass window 1.5 m x<strong>\u00a0<\/strong>1.0 m in area and 3.0 mm thick if the temperatures at the inner and outer surfaces are 14.0\u00b0C and 13.0\u00b0C, respectively. Calculate the heat flux through this window.<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>At this point, we know the temperatures on the surfaces of the material, and these temperatures are also given by conditions inside the house and outside the house. In this case, heat flows by conduction through the glass from the higher inside temperature to the lower outside temperature. We use the heat conduction equation:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/Heat-loss-through-window-equation.png?36a14b\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-20027\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2017\/10\/Heat-loss-through-window-equation.png?36a14b\" alt=\"Heat loss through window - equation\" width=\"259\" height=\"145\" \/><\/a><\/p>\n<p>We assume that the thermal conductivity of a common glass is k = 0.96 W\/m.K.<\/p>\n<p>The heat flux will then be:<\/p>\n<p>q = 0.96 [W\/m.K] x\u00a01 [K] \/ 3.0 x\u00a010<sup>-3<\/sup>\u00a0[m] =\u00a0320 W\/m<sup>2<\/sup><\/p>\n<p>The total heat loss through this window will be:<\/p>\n<p>q<sub>loss<\/sub>\u00a0= q . A = 320 x 1.5 x 1.0 = 480W<\/p>\n<p>It must be added that 15\u00b0C is not very warm for the living room of a house. But this temperature does not correspond to the interior temperature but corresponds to the surface temperature. Due to the finite convective heat transfer coefficient, there is always a considerable temperature drop between the interior and window surface temperatures. Note that both convection coefficients strongly depend on ambient and interior conditions (wind, humidity, etc.).<\/p>\n<p>See also: <a title=\"Convective Heat Transfer Coefficient\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/convection-convective-heat-transfer\/convective-heat-transfer-coefficient\/\">Convective Heat Transfer Coefficient<\/a><\/p>\n<p>Similarly, as for clothing, thermal insulation is based on low thermal conductivity materials and geometry (e.g., double-pane windows). The insulating properties of these materials come from the insulating properties of air. Many insulating materials (e.g., wool) function simply by having a large number of <strong>gas-filled pockets<\/strong> which <strong>prevent large-scale convection<\/strong>. The geometry of these materials also plays a crucial role. For example, increasing the width of the air layer, such as using two panes of glass separated by an air gap, will reduce the heat loss more than simply increasing the glass thickness since the thermal conductivity of air is much less than that for glass.<\/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>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, MA (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, Springer; 4th edition, 1994, ISBN: 978-0412985317<\/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>D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.<\/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>While thermal energy refers to the total energy of all the molecules within the object, heat is the amount of energy flowing spontaneously from one body to another due to their temperature difference. Heat is a form of energy, but it is energy in transit. Heat is not a property of a system. However, the &#8230; <a title=\"Heat Losses\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/heat-losses\/\" aria-label=\"More on Heat Losses\">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\/21131"}],"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=21131"}],"version-history":[{"count":4,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/21131\/revisions"}],"predecessor-version":[{"id":37459,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/21131\/revisions\/37459"}],"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=21131"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}