Impact of porous medium on natural convection heat transfer in plume generated due to the combined effects of heat source and aligned magnetic field

This study focuses on how the porous medium affects the plume generated due to line heat source when an aligned magnetic field is present. For this study, the momentum equation of the flow model is modified for porous medium by including the porosity term. A mathematical model is developed as coupled partial differential equations in order to study the flow problem. Later, a numerical solution is found for the system of coupled partial differential equations that are transmuted in to ordinary differential equations. For this purpose, the numerical characteristics of the problem are derived employing a shooting approach in combination with the built-in MATLAB tool bvp4c. The graphical illustrations of missing and specified boundary conditions demonstrate the impacts of porosity parameter [Formula: see text], magnetic force parameter S, Prandtl number [Formula: see text] and magnetic Prandtl number [Formula: see text] accompanied by a discussion of their corresponding physical implications. The novelty of this developed problem is proclaimed with justification by its emphasis on the principal characteristics of heat and fluid flow affected predominantly by the presence of a porous medium. The thorough examination of the porosity parameter [Formula: see text] for missing conditions depicts that the temperature and velocity profiles enhance while current density drops for the increasing values of the porosity parameter [Formula: see text]. Whereas, for specified conditions, the skin friction and magnetic flux enhance but heat transfer rate declines with increment in [Formula: see text].