Heat transfer and thermal analysis in a semi-spherical fin with temperature-variant thermal properties: an application of Probabilists’ Hermite collocation method

Abstract

Finned surfaces are utilized in several industrial and technological applications including radiators in cars, air conditioning systems, and computer CPU heat sink to dissipate heat through convection or radiation. In this regard, the heat transfer enhancement utilizing the fins has received more attention in the scientific field. Motivated by this, the present research explicates temperature variation through a convective-radiative semi-spherical fin (SSF) with internal heating by taking into consideration of linear and nonlinear temperature-dependent heat transfer coefficient and thermal conductivities. Furthermore, the efficiency and heat transfer aspects of the fin are elaborated. The Rosseland approximation is used in this study to analyze radiation heat exchange. The developed energy equation is converted to a nonlinear ordinary differential equation (ODE) using dimensionless terms, and the probabilists’ Hermite collocation method (PHCM) is used to solve this problem. The governing parameters have been varied in their appropriate ranges to illustrate their impact on the thermal profile, and the results have been portrayed graphically. Some notable key findings of the current analysis are that as the scale of the convection–conduction and the radiation number upsurges, the thermal distribution through SSF drops. On the other hand, thermal distribution escalates for heat generation and thermal conductivity parameters.