Entropy production and dissipation function in heat conduction

Comparing this equation with Eq. (3.284), we find the entropy production term 

represents the heat flow rate. The rate 

Three-dimensional heat conduction in an isotropic solid is 

Jq is the heat flow, V( 1/7 ) is the inverse temperature gradient representing the thermodynamic force for heat conduction, and JJT = Js is the entropy flow. 

The local entropy production for diffusion of several substances per unit volume is 

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Example 3.14 Entropy production and dissipation function in heat conduction Consider one-dimensional heat conduction in an isotropic solid rod. The surface of the rod is insulated and the cross-sectional area is constant (Figure 3.2). Describe the entropy production and the dissipation function for the heat conduction in an isotropic rod. The entropy change of the rod element is... 

Example 3.14 Entropy production and dissipation function in heat conduction... 

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