Heat transfer study through porous fins (Si3N4 and AL) with temperature-dependent heat generation

In this study, three highly accurate and simple analytical methods, Differential Transformation Method (DTM), Collocation Method (CM) and Least Square Method (LS) are applied for predicting the temperature distribution in a porous fin with temperature dependent internal heat generation. The selected porous fin's materials are Si3N4 and AL and generated heat varies linearly with temperature. The heat transfer through porous media is simulated using passage velocity from the Darcy's model. Results reveal that DTM, CM and LS are very effective and accurate in comparison with the numerical results. Moreover the temperature distribution is depended to the Darcy and Rayleigh numbers. In addition the results show that using the AL as a porous fin's substrate leads to higher value of temperature than Si3N4 element. A higher heat generation rate leads to higher fin temperatures since more amount of heat is dissipated to the surrounding.