Exploring the dynamics of natural convective Prandtl fluid flow subjected to induced magnetic field

Abstract

In the present study, Prandtl fluid flows naturally under the action of buoyancy in a vertical microchannel. The channel proliferates the fluid to the surrounding through small pores in the channel. Fluid flow properties are explored and heat transfer analysis is carried out theoretically via mathematical modeling using fluid dynamic conservative laws. Magnetohydrodynamics effect is also made a part of the study so that the induced magnetic field impact can be investigated. The mathematical form of the conservative laws leads to a differential system nonlinear in nature. The complexity of the mathematical system demands its solution to be carried out numerically. For this purpose, the finite difference-based Keller box method is utilized. Interpretation of the results is carried out in the form of graphs and tables of numerical values of the skin friction coefficient and the Nusselt number. The results show that the Prandtl number coupled with the suction velocity parameter results in an exponential growth in the heat transfer rate in Prandtl fluid. Graphical representations confirm the fact that skin friction coefficient peaks when the value of Hartmann number is minimum and that of Grashof number is maximum.