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The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k {displaystyle k} , λ {displaystyle lambda } , or κ {displaystyle kappa } . The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k {displaystyle k} , λ {displaystyle lambda } , or κ {displaystyle kappa } . Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for insulating materials like Styrofoam. Correspondingly, materials of high thermal conductivity are widely used in heat sink applications and materials of low thermal conductivity are used as thermal insulation. The reciprocal of thermal conductivity is called thermal resistivity. The defining equation for thermal conductivity is q = − k ∇ T {displaystyle mathbf {q} =-k abla T} , where q {displaystyle mathbf {q} } is the heat flux, k {displaystyle k} is the thermal conductivity, and ∇ T {displaystyle abla T} is the temperature gradient. This is known as Fourier's Law for heat conduction. Although commonly expressed as a scalar, the most general form of thermal conductivity is a second-rank tensor. However, the tensorial description only becomes necessary in materials which are anisotropic. Consider a solid material placed between two environments of different temperatures. Let T 1 {displaystyle T_{1}} be the temperature at x = 0 {displaystyle x=0} and T 2 {displaystyle T_{2}} be the temperature at x = L {displaystyle x=L} , and suppose T 2 > T 1 {displaystyle T_{2}>T_{1}} . A possible realization of this scenario is a building on a cold winter day: the solid material in this case would be the building wall, separating the cold outdoor environment from the warm indoor environment. According to the second law of thermodynamics, heat will flow from the hot environment to the cold one in an attempt to equalize the temperature difference. This is quantified in terms of a heat flux q {displaystyle q} , which gives the rate, per unit area, at which heat flows in a given direction (in this case the x-direction). In many materials, q {displaystyle q} is observed to be directly proportional to the temperature difference and inversely proportional to the separation: The constant of proportionality k {displaystyle k} is the thermal conductivity; it is a physical property of the material. In the present scenario, since T 2 > T 1 {displaystyle T_{2}>T_{1}} heat flows in the minus x-direction and q {displaystyle q} is negative, which in turn means that k > 0 {displaystyle k>0} . In general, k {displaystyle k} is always defined to be positive. The same definition of k {displaystyle k} can also be extended to gases and liquids, provided other modes of energy transport, such as convection and radiation, are eliminated. For simplicity, we have assumed here that the k {displaystyle k} does not vary significantly as temperature is varied from T 1 {displaystyle T_{1}} to T 2 {displaystyle T_{2}} . Cases in which the temperature variation of k {displaystyle k} is non-negligible must be addressed using the more general definition of k {displaystyle k} discussed below.

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