Significance of time‐dependent magnetohydrodynamic transient free convective flow in vertical annuli: An analytical approach with the finite Hankel transform

Abstract

AbstractAn analytical study is accomplished by using the Finite Hankel Transform Technique for the variation of the temperature and the velocity profile with several nondimensional parameters. In this problem, an electrically conducting fluid has been considered in the vertical concentric annulus, with a perpendicular radial magnetic field. Furthermore, a closed and exact type of expression for the velocity and the temperature are received in the form of Bessel functions of both kinds (first and second). The impact of emerging parameters in this model, such as time, Hartmann number, Prandtl number, and the annular gap between the cylinders, is discussed through graphs, whereas the numerical values of the skin friction, mass flux, and the Nusselt number are given in the tabular form. As a consequence of this, it is detected that the velocity and temperature distributions are increasing continuously with an enhanced time scale. Eventually, it gains its steady state very quickly. Moreover, the impact of the Prandtl number and the Hartmann number leads to a decrease in the velocity profiles.