Application of Homotopy Perturbation Method to Analyzing Thermal Behavior of Moving Longitudinal Fins with Various Profiles

The homotopy perturbation method (HPM) was applied to analyze the thermal behavior of longitudinal radiative-convective moving fins with trapezoidal, concave parabolic, and convex profiles. The governing equation was extracted from the energy balance of a longitudinal element of the moving longitudinal radiation-convection fin. In addition, Heat transfer coefficient, thermal conductivity, and surface emissivity were assumed to be temperature-dependent. The HPM was used to solve the governing equation as it was a nonlinear equation. The HPM was validated by comparison to the differential transform method (DTM), finding good agreement. The dimensionless temperature, dimensionless fin tip temperature, heat transfer rate, and fin efficiency were compared in the parametric analysis. Additionally, the effects of changes of various dimensionless parameters such as thermal conductivity, emissivity, convective-conductive parameter, radiative-conductive parameter, and Peclet number on performance of the fins were invsetigated. The results indicated the HPM to be a powerful tool capable of rapidly and accurately solving such nonlinear equations as the energy equation governing longitudinal moving fins. Furthermore, the convex fin had 1% and 2% higher dimensionless tip temperatures than the trapezoidal and concave parabolic fins, respectively. The concave parabolic fin had 7% and 13% higher heat transfer rates and efficiency than the trapezoidal and convex fins, respectively. In addition, the concave parabolic fin is a more economical option than the other two as it is made of less material.