Thermal scrutinization of a triangular porous fin induced by linear and nonlinear temperature-dependent heat generation and magnetic field effect: the case of Darcy model

The present study investigates the use of a triangular-profiled fin to enhance heat transfer. It specifically focuses on the impact of a ternary nanofluid, incorporating Zr, Cu, and Al2O3 nanoparticles in an ethylene glycol base fluid, in the context of heat transfer involving a porous triangular fin. This investigation accounts for both linear and non-linear internal heat generation, the presence of a magnetic field, and radiation effects. The problem at hand involves a second-order ordinary differential equation, which is transformed into a dimensionless form by utilizing dimensionless terms. This transformed ordinary differential equation is then solved using the differential transformation technique, employing a semi-analytical approach. The study systematically examines the influence of various thermal parameters on temperature distribution and fin efficiency, considering that the fin tip is insulated. Notably, an increase in the convective–conduction and porosity parameters is found to decrease the heat transfer rate. Conversely, the use of a ternary nanofluid and the incorporation of a non-linear form of internal heat generation leads to higher heat transfer rates. Through thermal analysis, it is determined that a magnesium alloy and a fin base thickness of 0.75 cm are optimal for achieving enhanced heat transmission in a triangular fin configuration.