Thermal Transport Management in a Mixed Convective Flow on a Thermally Conducting Cone With Variable Magnetic Permeability and Joule Heating Effects

Abstract

The fundamental objective of this study is to investigate the thermal transport of mixed convective flow over a thermally conducting vertical cone with combined effects of Joule heating and variable magnetic permeability. The principal novelty of this work is the incorporation of Joule heating effect into mixed convection flow over a thermally conducting cone with variable magnetic permeability, a combined consideration that has not been previously explored in this configuration. This research gap motivates an extensive investigation of the combined effects of variable magnetic permeability and Joule heating on flow and heat transfer characteristics. The governing partial differential equations are formulated into primitive variables and the steady, real and imaginary primitive components are evaluated using implicit finite difference methodology and the Gaussian elimination technique. The resulting numerical solutions provide the fluid velocity, temperature and magnetic-field profiles, which are further used to examine the oscillatory skin friction, heat transfer rate and current density for different appropriate dimensionless parameters, including the modified magnetic Prandtl number, Joule heating parameter, mixed convection parameter, magnetic force parameter and conductivity variation parameter. The results are graphically presented using FORTRAN software and display these results on Tech Plot. It was observed that the velocity and temperature distributions show a visible increase as the value of the Joule heating parameter rises and the magnetic field profile decreases with higher values of $J$. Also, an increase in the Joule heating parameter enhances skin friction and magnetic transfer rates, whereas the heat transfer rates exhibit a declining response. The parametric analysis further demonstrates that magnetic diffusion plays a significant role in regulating the coupled flow and thermal characteristics of the magnetised cone.