Analytical and numerical solution of the longitudinal porous fin with multiple power‐law‐dependent thermal properties and magnetic effects

Abstract

The present study is concentrated on the application of electric and magnetic fields on the longitudinal porous fin with power‐law‐dependent heat transfer coefficient, surface emissivity, and heat generation. The porosity parameter controls the amount of empty spaces or voids in the porous fin and its practical value lies in the range 0 ∠ ϕ ∠ 1. In industrial application, the heat transfer coefficient is governed by a power law and its specific value defines a certain heat transfer process. The heat generation and surface emissivity of the longitudinal porous fin are assumed to be varied according to the power law and the whole fin is under the influence of an external electric field. The resulting nonlinear equation is solved by the classical Adimian decomposition method (ADM) and the obtained solutions are verified further by the finite difference method (FDM). It has been found that both ADM and FDM are in good agreement for lower values of thermophysical parameters. The effects of power index of heat generation, surface emissivity, and heat transfer coefficient parameter on the temperature distribution, heat flux, and efficiency are analyzed at different values of the porosity parameter comprehensively.

Performance analysis of a longitudinal fin under the influence of magnetic field using differential transform method with Pade approximant

“…In all of the above-mentioned research, thermal conductivity is assumed to be either constant or linearly temperature-dependent. But, in several investigations, it is taken to be a nonlinear function of temperature namely power-law thermal conductivity [31,32] and exponential function of temperature [33,34]. Detailed scrutiny of the referenced research articles confirms that the thermal distribution in a convective-radiative longitudinal fin exposed to a magnetic field with exponentially temperature-dependent thermal conductivity has not yet been addressed.…”