Effect of line/point heat source and Hall current with induced magnetic field on free convective flow in vertical walls

Abstract

In this research, the hydromagnetic natural convection of an incompressible fluid with point heat source by considering the influence of Hall current and induced magnetic field between infinite vertical walls is studied. The Laplace transform procedure is utilized to determine the analytical solutions of the acquired mathematical model with the wavelet function. With the derived solution of velocity, induced magnetic field, temperature field, and induced current density, the flow character is investigated with the influence of the physical parameters (namely Hall current, Hartmann number, and point heat source) for the presented boundary conditions. Also, the skin friction and volumetric flow rate are derived through the velocity expression. Numerical and graphical results are introduced to formalize the solution of the model. The valuable result from the investigation is that an increase in the length of the point heat source leads to enhance both components of induced current density, induced magnetic field, and primary velocity profiles. Moreover, it is noticeable that an enhancement in the Hall current has a reverse connection with both components of the induced current density, induced magnetic field, while the direct connection with the primary velocity component. There are numerous engineering applications such as the metal cutting, grinding, welding, laser hardening of metals, and many others in which the calculation of temperature field is modeled as a problem involving a point heat source.