: The paper focuses on thermal behaviours of a porous longitudinal rectangular fin under various nonlinear interactions, consisting of thermal conductivity that is dependent on temperature, nonlinear convection, thermal radiation, and magnetohydrodynamic (MHD) interactions. The novelty lies in the simultaneous integration of multiple nonlinear effects (MHD, radiation, nonlinear convection, porosity, and variable conductivity) under realistic boundary conditions, which has not been addressed collectively in previous studies. In this study it is assumed that a realistic boundary configuration will be used i.e. the base of the fin is convectively cooled, and the tip is thermally insulated. The current formulation is based on exponential change of thermal conductivity, power-law convection, radiative heat exchange, and magnetic damping in a porous material, as opposed to the traditional fin models that use constant material properties and linear convection. The nonlinear boundary-value problem thus obtained is numerically solved by MATLAB BVP4C solver with Lobatto IIIA collocation scheme to obtain smooth and physical consistent temperature distributions along the fin. Parametric analysis suggests that with an increase in convection conductivity parameter, base Biot number, porosity, radiation, and magnetic parameters, heat dissipation increases and temperature gradients grow steeper. Conversely, a higher exponential conductivity variation facilitates the axial transfer of heat and decreases the total heat transfer rate. Fin efficiency increases significantly from about 0.40 to 0.65, achieving nearly 60% enhancement due to the combined increase in magnetic parameter and temperature ratio parameter.
Basha et al. (2026) studied this question.