Conservation of Energy and Heat Equation

In order to estimate the heat transfer rates in different parts of the fuel cell, it is necessary to determine the temperature distribution or temperature field in the medium resulting from the heat generations and thermal boundary conditions. The temperature field is determined by solving the heat equation, which is a statement of conservation of energy or the first law of thermodynamics. 

A simplified heat model applicable to many convection problems is derived from conservation of energy based on the following assumptions (i) constant thermal conductivity, k (ii) negligible viscous dissipation, O (iii) negligible compressibility effect and (iv) negligible radiation heat transfer rate. TTie energy equation for such a model is derived as 

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