{"id":20056,"date":"2018-10-17T17:54:43","date_gmt":"2018-10-17T17:54:43","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=20056"},"modified":"2023-02-10T13:33:13","modified_gmt":"2023-02-10T13:33:13","slug":"thermal-conductivity","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/thermal-conduction\/thermal-conductivity\/","title":{"rendered":"Thermal Conductivity"},"content":{"rendered":"
The heat transfer characteristics of solid material are measured by a property called the thermal conductivity<\/strong>, k (or \u03bb), measured in W\/m.K<\/strong>. It measures a substance\u2019s ability to transfer heat through a material by conduction.<\/p>\n

Metals,<\/strong> in general, have\u00a0high electrical conductivity<\/strong>\u00a0high thermal conductivity. <\/strong>The thermal conductivities of metals\u00a0originate from<\/strong>\u00a0the fact that their\u00a0outer electrons are delocalized<\/strong>.<\/p>\n

Thermal insulators<\/strong>\u00a0have\u00a0very 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<\/div><\/div>\n

The thermal conductivity<\/strong> of most liquids and solids varies with temperature, and for vapors, it also depends upon pressure. In general:<\/p>\n

\"thermal<\/a><\/p>\n

\"Thermal<\/a>Most materials are very nearly homogeneous. Therefore, we can usually write k = k (T)<\/em><\/strong>. Similar definitions are associated with thermal conductivities in the y- and z-directions (ky<\/sub>, kz<\/sub>), but for an isotropic material, the thermal conductivity is independent of the direction of transfer, kx<\/sub> = ky<\/sub> = kz<\/sub> = k. Note that Fourier\u2019s law<\/strong> applies to all matter, regardless of its state (solid, liquid, or gas). Therefore, it is also defined for liquids and gases.<\/p>\n

The previous equation follows that the conduction heat flux increases with increasing thermal conductivity and increases with increasing temperature differences. In general, the thermal conductivity of a solid is larger than that of a liquid, which is larger than that of a gas. This trend is due largely to differences in intermolecular spacing<\/strong> for the two states of matter. In particular, diamond has the highest hardness and thermal conductivity of any bulk material.<\/p>\n

See also: Thermal Conductivity of Common Materials<\/a><\/p>\n

\"thermal<\/a>

<\/span>Fourier\u2019s law of Thermal Conduction<\/div>
Heat transfer<\/strong> processes can be quantified in terms of appropriate rate equations. The rate equation in this heat transfer mode is based on Fourier\u2019s law of thermal conduction<\/strong>. This law states that the time rate of heat transfer<\/strong> through a material is proportional to<\/strong> the negative gradient in the temperature<\/strong> and the area, at right angles to that gradient, through which the heat flows. Its differential form is:<\/p>\n

\"Fourier\u2019s<\/a><\/p>\n

The proportionality constant obtained in the relation is known as thermal conductivity<\/strong>, k<\/strong> (or \u03bb<\/strong>), of the material. A material that readily transfers energy by conduction is a good thermal conductor and has a high value of k<\/strong>. Fourier\u2019s law<\/strong> is an expression that defines thermal conductivity<\/strong>.<\/p>\n

As can be seen, solve Fourier\u2019s law,<\/strong> we have to involve the temperature difference, the geometry, and the thermal conductivity of the object. This law was first formulated by Joseph Fourier in 1822, who concluded that \u201cthe heat flux resulting from thermal conduction is proportional to the magnitude of the temperature gradient and opposite to it in sign\u201d.<\/p>\n

Similarly, as Fourier\u2019s law<\/strong> determines the heat flux through a slab, it can also determine the temperature difference when q<\/strong> is known. This can be used to calculate the temperature in the center of the fuel pellet, as will be shown in the following sections.<\/div><\/div>

<\/span>Units of Thermal Conductivity<\/div>
In SI units, thermal conductivity<\/strong> is measured in watts per meter-kelvin – W\/(m\u00b7K)<\/strong>. In Imperial units, thermal conductivity is measured in BTU\/(hr\u00b7ft\u22c5\u00b0F)<\/strong>.<\/p>\n

Note that British Thermal Unit<\/a> (unit: BTU) is defined as the amount of heat that must be absorbed by a 1 pound of water to raise its temperature by 1 \u00b0F at the temperature that water has its greatest density (approximately 39 degrees Fahrenheit<\/a>).<\/p>\n

Other units closely related to thermal conductivity are commonly used in the construction and textile industries. The construction industry uses units such as the R-value (resistance)<\/strong>, which is expressed as the thickness of the material normalized to the thermal conductivity. Under uniform conditions, it is the temperature difference ratio across an insulator and the heat flux density through it: R(x) = \u2206T\/q. The higher the R-value, the more a material prevents heat transfer. As can be seen, the resistance is dependent on the thickness of the product.<\/div><\/div>

<\/span>Thermal Conductivity of Chemical Elements<\/div>
\"thermal<\/a><\/div><\/div><\/div>\n
\n

Thermal Conductivity of Fluids (Liquids and Gases)<\/h2>\n

In physics, a fluid <\/a>is a substance that continually deforms (flows) under applied shear stress. Fluids<\/strong> are a subset of the phases of matter and include liquids<\/strong>, gases<\/strong>, plasmas, and, to some extent, plastic solids. Because the intermolecular spacing is much larger and the motion of the molecules is more random for the fluid state than for the solid-state, thermal energy transport<\/strong> is less effective. The thermal conductivity<\/strong> of gases and liquids is generally smaller than that of solids. In liquids, thermal conduction is caused by atomic or molecular diffusion. In gases, thermal conduction is caused by the diffusion of molecules from a higher energy level to a lower level.<\/p>\n

Thermal Conductivity of Gases<\/strong><\/p>\n

\"thermal<\/a>The effect of temperature, pressure and chemical species on the thermal conductivity<\/strong> of a gas may be explained in terms of the kinetic theory of gases<\/strong>. Air and other gases are generally good insulators in the absence of convection. Therefore, many insulating materials (e.g., polystyrene) function simply by having a large number of gas-filled pockets,<\/strong> which prevent large-scale convection<\/strong>. Alternation of gas pocket and solid material causes heat to transfer through many interfaces, causing a rapid decrease in heat transfer coefficient.<\/p>\n

The thermal conductivity of gases<\/strong> is directly proportional to the density of the gas, the mean molecular speed, and especially to the mean free path<\/strong> of a molecule. The mean free path also depends on the diameter of the molecule, with larger molecules more likely to experience collisions than small molecules, which is the average distance traveled by an energy carrier (a molecule) before experiencing a collision. Light gases, such as hydrogen<\/strong> and helium,<\/strong> typically have high thermal conductivity<\/strong>, and dense\u00a0gases such as xenon and dichlorodifluoromethane have low thermal conductivity.<\/p>\n

In general, the thermal conductivity of gases increases with increasing temperature.<\/p>\n

Thermal Conductivity of Liquids<\/strong><\/p>\n

As was written, in liquids, the thermal conduction is caused by atomic or molecular diffusion, but physical mechanisms for explaining the thermal conductivity of liquids are not well understood. Liquids tend to have better thermal conductivity than gases, and the ability to flow makes a liquid suitable for removing excess heat from mechanical components. The heat can be removed by channeling the liquid through a heat exchanger. The coolants used in nuclear reactors include water or liquid metals, such as sodium or lead.<\/p>\n

The thermal conductivity of nonmetallic liquids generally decreases with increasing temperature.<\/p>\n

<\/span> Thermal Conductivity of Sodium<\/div>
Liquid sodium is used as a heat transfer fluid in some types of nuclear reactors<\/strong> because it has the high thermal conductivity<\/strong> and low neutron absorption cross-section required to achieve a high neutron flux in the reactor. The high thermal conductivity properties effectively create a reservoir of heat capacity, which provides thermal inertia against overheating.<\/p>\n

\"thermal<\/a><\/p>\n

Special reference: Thermophysical Properties of Materials For Nuclear Engineering: A Tutorial and Collection of Data. IAEA-THPH, IAEA, Vienna, 2008. ISBN 978\u201392\u20130\u2013106508\u20137.<\/div><\/div>

<\/span> Thermal Conductivity of Water and Steam<\/div>
Water<\/a> and steam<\/a><\/strong> are common fluids used for heat exchange<\/strong> in the primary circuit (from the surface of fuel rods to the coolant flow) and in the secondary circuit. It is used due to its availability<\/strong> and high heat capacity,<\/strong> both for cooling and heating. It is especially effective to transport heat through vaporization<\/strong> and condensation<\/strong> of water because of its very large latent heat of vaporization<\/a><\/strong>.<\/p>\n

A disadvantage is that water-moderated reactors have to use a high-pressure primary circuit<\/strong> to keep water in a liquid state<\/strong> and achieve sufficient thermodynamic efficiency. Water and steam also react with metals commonly found in industries such as steel and copper, oxidized faster by untreated water and steam. In almost all thermal power stations (coal, gas, nuclear), water is used as the working fluid (used in a closed-loop between boiler, steam turbine, and condenser), and the coolant (used to exchange the waste heat to a water body or carry it away by evaporation in a cooling tower).<\/p>\n

Thermal Conductivity of Water<\/strong><\/p>\n

\"thermal<\/a><\/p>\n

Thermal Conductivity of\u00a0Steam<\/strong><\/p>\n

\"thermal<\/a><\/p>\n

See also: Steam Tables<\/a><\/p>\n

Special reference: Thermophysical Properties of Materials For Nuclear Engineering: A Tutorial and Collection of Data. IAEA-THPH, IAEA, Vienna, 2008. ISBN 978\u201392\u20130\u2013106508\u20137.<\/div><\/div>

<\/span> Thermal Conductivity of Helium<\/div>
Helium<\/strong>\u00a0is a chemical element with\u00a0atomic number<\/a>\u00a02,<\/strong>\u00a0which means there are 2 protons and 2 electrons in the atomic structure. The\u00a0chemical symbol<\/strong>\u00a0for Helium is\u00a0He<\/strong>.<\/p>\n

It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas, the first in the noble gas group in the periodic table. Its boiling point is the lowest among all the elements.<\/p>\n

Because of helium\u2019s relatively low molar (atomic) mass, its thermal conductivity, specific heat, and sound speed in the gas phase are all greater than any other gas except hydrogen. For its inertness and high thermal conductivity, neutron transparency, and because it does not form radioactive isotopes under reactor conditions, helium is used as a heat-transfer medium in some gas-cooled nuclear reactors (e.g., High-temperature Gas-cooled Reactors – HTGR).<\/p>\n

\"thermal<\/a><\/p>\n

Special reference: Thermophysical Properties of Materials For Nuclear Engineering: A Tutorial and Collection of Data. IAEA-THPH, IAEA, Vienna, 2008. ISBN 978\u201392\u20130\u2013106508\u20137.<\/span><\/div><\/div><\/div>\n

Thermal Conductivity of Solids<\/h2>\n

Transport of thermal energy in solids may generally be due to two effects:<\/p>\n