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ArticleOpen Access http://dx.doi.org/10.26855/ea.2022.06.004

The Analytical Solution Via Cole-Hopf Transformation of the Unsteady MHD Equations of Salt Water Flow Subjected to Multiple Transport Effects

Aly M. Abourabia1,*, Sara A. Abdel Moneim2

1Department of Mathematics, Faculty of Science, Menoufiya University, Shebin Elkom, 32511, Egypt.

2Department of Physics, Faculty of Science, Menoufiya University, Shebin Elkom, 32511, Egypt.

*Corresponding author: Aly M. Abourabia

Published: March 04, 2022

Abstract

The purpose of this study is to examine the effect of MHD properties on the unsteady hydro-magnetic natural convection with heat transfer over an impulsively moving vertical plate embedded in salt water. The whole system rotates about an axis normal to the plane of the plate with uniform angular velocity. A variable applied magnetic field and Hall current affect the incompressible and optically thick fluid presented by sea water as the working fluid in our problem. A new manipulation as a single independent variable is introduced to reduce the system of ordinary differential equations by successive eliminations to one nonlinear ODE for the secondary velocity, under simple initial and boundary conditions, which is solved analytically using the Cole-Hopf transformation. Through this study, it was found that the resulting solutions include the non-dimensional temperature, primary and secondary velocities depend on different governing parameters.The results indicate that all these quantities are damped far from the rotating plate at different values of the governing parameters. From the irreversi-ble thermodynamic point of view, the entropy generation and Bejan numbers are estimated and illustrated under the same conditions. The results of this research may find its echo in different vital applications such as heat exchangers, Hall accelerators and power generators.

Keyword

Salt water, Unsteady MHD equations, Cole-Hopf transformation, Heat Transfer, Mechanical Rotation, Thermal radiation, Hall Effect

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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license, which permits non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited and is not modified or adapted.
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How to cite this paper

The Analytical Solution Via Cole-Hopf Transformation of the Unsteady MHD Equations of Salt Water Flow Subjected to Multiple Transport Effects

How to cite this paper: Aly M. Abourabia, Sara A. Abdel Moneim. (2022). The Analytical Solution Via Cole-Hopf Transformation of the Unsteady MHD Equations of Salt Water Flow Subjected to Multiple Transport Effects. Engineering Advances, 2(1), 36-50.

DOI: http://dx.doi.org/10.26855/ea.2022.06.004

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