Research Article Analysis of Magnetohydrodynamics Flow of Incompressible Fluids over Oscillating Bottom Surface with Heat and Mass Transfer Vincent M. Bulinda , Giterere P. Kang’ethe, and Phineas R. Kiogora Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology, Juja 62000-00200, Kenya Correspondence should be addressed to Vincent M. Bulinda; majorblinda@yahoo.com Received 24 March 2020; Accepted 13 May 2020; Published 1 June 2020 Academic Editor: Vladimir V. Mityushev Copyright © 2020 Vincent M. Bulinda et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Analysis of magnetohydrodynamics flow of incompressible fluids over an oscillating bottom surface with heat and mass transfer is discussed. e flow is free convection in nature. Momentum, energy, and concentration equations are obtained for computation of their respective profiles. e unsteady flow two-dimensional governing equations are solved numerically by the explicit finite difference method of the Forward Time Backward Space scheme. e numerical results show that the applied parameters have significant effects on the fluid flow and heat transfer and have been discussed with the help of graphical illustrations. 1. Introduction e problems of hydromagnetic free convection flow of incompressible fluids over corrugated vibrating surface have drawn considerable attention from several medical re- searchers and engineers, resulting in the enhanced heat transfer performance by increasing the area over which heat transfer takes place. is technology is applied in the design of processing equipment that complies with cheap, envi- ronmental friendly, and energy-saving with high efficiency of mass and heat transfers. Temperature control is important in corrugated structures manufacturing because it helps to ensure a strong bond between the layers of the corrugated surface and indicates moisture content [1]. Fluid flow and heat transfer on corrugated channel laminar in nature were first studied by [2] for transitional and low Reynolds number turbulent flow. Magnetohydro- dynamic free convection flow past an infinite vertical plate oscillating in its plane was studied in the case of an iso- thermal plate [3]. Rizwan et al. [4] investigated MHD natural convection flow enclosure in a corrugated cavity filled with a porous medium with a complete structure of corrugated surface for heat transfer effects in the presence of the uni- form magnetic field. e unsteady flow of second-order thermoviscous incompressible forced oscillations of a fluid bounded by rigid bottom was studied by [5]. Also, Schlichting [6] observed experimentally and numerically that corrugated channels do not have significant effects on heat transfer enhancement if operated in a steady regime. Garg and Maji [7] numerically studied the heat transfer of sinusoidal wavy channels at zero degrees phase shift. A numerical analysis of laminar forced convection in corru- gated-plate channels with a sinusoidal, ellipse, and rounded- vee wall shapes were studied [8]. Furthermore, Gbadeyan et al. [9] investigated Soret and Dufour effects on heat and mass transfer in chemically reacting MHD flow through a wavy channel using amplitude as the perturbation parameter. is work attempts to study the effects of velocities, concentration, and temperature fields on the unsteady flow of incompressible fluid over the heated oscillating bottom for the various material parameters. Hindawi International Journal of Mathematics and Mathematical Sciences Volume 2020, Article ID 4054578, 12 pages https://doi.org/10.1155/2020/4054578