Thermal analysis of fully wetted porous longitudinal fin of parabolic profile with variable thermal conductivity and convection–radiation

The thermal performance of a fully wetted porous fin with concave parabolic cross section is explored in this study for variable thermal conductivity. We have considered convective and radiative heat transfer with variations of temperature-dependent surface emissivity, internal heat generation, heat transfer coefficient, and magnetic field effect on the thermal profile of the fin. The heat transfer equation is derived from Darcy's model. Nondimensional governing ordinary differential equation is attempted by Runge–Kutta–Fehlberg technique. Influences of associated parameters on the cooling performance of fin are explored through graphs. From this study, it was found that the rate of heat transfer from the fin whose thermal conductivity varies linearly with temperature is twice than that of the fin with exponential dependency on thermal conductivity in the presence of magnetic effect.