Hydromagnetic free convective flow in vertical cylinder due to point/line heat source/sink

The current study is to explore the phenomena of the hydromagnetic free convective flow of an electrically conducting and incompressible viscous fluid through an impermeable vertical cylinder, with the point heat source under the influence of the transversely applied magnetic field of uniform strength in the radial direction. The free convection phenomenon in the working fluid occurs due to the presence of the point/line heat source as it appears in many real-world mechanisms. The main motive of this analytical study is thus to examine the effect of point and line heat source on this buoyancy-dominated developing flow. The governing equations thus framed for the prescribed flow namely energy and momentum, simplify to steady linear differential equations in the physical setup assumed in this investigation. These equations, in non-dimensional forms, have been solved, in turn, employed simultaneous ordinary differential equations (ODEs) theory. The resulting closed form solutions for the physical variables, namely fluid temperature and fluid velocity have been presented in terms of Bessel, modified Bessel, and Regularized Hypergeometric functions. Additionally, skin friction coefficient, Nusselt number, and mass flow rate are numerically discussed for the involved parameters. There arises a number of pertinent physical parameters in our analysis: Heat source, Hartman number, and point heat source whose influence on the developing velocity and some temperature profiles have been illustrated through a number of plots. Major outcomes show that the enhancement in Hartmann number motivates a reduction in the velocity profile for the point and line heat source cases. In addition, the fluid motion rises due to the line and point heat source, and the velocity and temperature profiles have a higher value in the case of the line heat source as compared to the point heat source.