Heat conduction in anisotropic solids

Since the overall reaction is not an elementary step but a result of many elementary steps, the relation v = / eff(l — is not valid. 

Though we considered a coupled set of unimolecular reactions (16.5.24) to obtain (16.5.31), the result is more generally valid. Thus, the linear phenomenological law is valid for an overall chemical reaction if A/RT 1 

In an anisotropic solid the flow of heat Jq may not be in the direction of the temperature gradient a temperature gradient in one direction can cause the heat to flow in another direction. The entropy production is 

For anisotropic solids the heat conductivity k is a tensor of the second rank. The empirical Fourier law of heat conduction is then written as 

Fi re 16.3 The method of Curie and Voigt to verify the reciprocal relations for anisotropic heat conduction. An anisotropic solid whose crystal symmetry implies Ki2 — — 21 is placed in contact with two heat reservoirs of temperature T and Tc. If the reciprocal relations are valid then K12 = K2i = 0. If this is true, the isotherms should be perpendicular to the direction xi, i.e. 0 should be 90° 

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In this part we study the stationer heat conduction in anisotropic solid, e.g. in triclinic crystal. We suppose certain energy deposit cr in all the volume elements of the system, and let the heat conduction tensor be temperature dependent. The stationer balance equation is... 

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