Computational study of the aligned magnetic field in a plume generated by the energy line source

Abstract

This present research concerns with the study of two-dimensional, steady, magnetohydrodynamic free convection flow in a plume generated due to horizontal line heat source. The aligned magnetic field is applied at the vertical component of plume. The mathematical model of the governing flow problem is based on coupled nonlinear partial differential equations. Later, the system of partial differential equations is transformed into system of ordinary differential equations by using appropriate form of stream function formulation. For computational results, a Shooting technique along with bvp4c algorithm for MATLAB is employed to estimate the missing conditions in flow model. The effects of variation in Prandtl number., magnetic force parameter S , and magnetic Prandtl number γ on the velocity, current density, and temperature profile are illustrated in graphical manner along with their physical impacts. The novelty of current work is that the magnetic field has its strong impact on the vertical component of plume generated due to heat source. It is observed that, with the increase in the parameter S , the missing conditions, the velocity, current density, and temperature decreased. Whereas, the specified conditions, the skin friction f ″ and magnetic flux ϕ ′ drop while heat transfer rate θ ′ enhanced with increment in parameter S .