This work presents an investigation on the effect of particle deposition and adhesion on the thermal behaviour of convective-radiative porous fin heat sink using Differential Transform method (DTM). The numerical solutions of the developed thermal models are also used to study the influence of thermal conductivity, porosity, convection and radiation factors on the thermal distribution and efficiency of the fin. The analysis reveals the impact of particles or thermal fouling on the surface of the fin, which causes a rise in the temperature uniformity and distribution in the fin while reducing the rate of heat transfer from the fin. Moreover, the study also establishes that the heat transfer rate decreases due to particle deposition on the fin which depends on the particle size, particle density and cooling air flow rate. The fin efficiency decreases with increasing value of the fouled Biot, Darcy and radiation numbers, and thermo-geometric parameter. Furthermore, the analysis shows that the efficiency of the fouled porous fin is always greater than the efficiency of the clean porous fin. The result of this study shows an excellent agreement with the established results of Runge-Kutta with shooting method.
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