Industrial Application of Heat and Mass Diffusion in Thermal Management and Chemical Process Systems Using the Homotopy Perturbation Method

Abstract

Transient heat and mass diffusion are fundamental transport mechanisms governing the performance of thermal management systems, electronic cooling devices, polymer processing, membrane separation, drying operations, and chemical processing systems. This study investigates the transient diffusion of heat and chemical species from a suddenly heated and concentrated vertical surface using the CP Amadi Heat and Mass Diffusion Model. The governing dimensional equations are transformed into dimensionless form using the Prandtl number (Pr) and the Lewis number (Le) adopted in the model. We construct a Homotopy Perturbation Method (HPM) to obtain a semi-analytical approximation for the temperature and concentration fields. In addition, we independently derive an exact similarity solution in the terms of the complementary error function and use it as the benchmark for assessing the accuracy of the HPM solution. For Pr, Le and the third-order HPM approximation satisfies the wall and far-field boundary conditions and produces maximum normalized absolute errors of approximately 10% for temperature and 8% for concentration over 0 to 1 at t=1. The corresponding Nusselt and Sherwood numbers obtained from the third-order HPM approximation differ from the exact values by approximately 10.78%. Unlike the increasing trend previously reported, the exact solution shows that both heat and mass transfer rates decrease with time according to a t^(-0.5) dependence. The results establish the exact erfc solution as a rigorous benchmark and provide a transparent assessment of the applicability and limitations of HPM to transient heat and mass diffusion problems.