Boundary Layer Analysis Adjacent to Moving Heated Plate Inside Electrically Conducting Fluid with Heat Source/Sink Ahmed S. Rashed 1* , Ehsan H. Nasr 2 , Magda M. Kassem 1 1 Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt 2 Delta Higher Institute for Engineering and Technology, Mansoura 35681, Egypt Corresponding Author Email: asrashed@zu.edu.eg https://doi.org/10.18280/ijht.380312 ABSTRACT Received: 12 November 2019 Accepted: 24 July 2020 Newtonian steady state flow of fluids with electrical conduction properties was examined adjacent to a moving heated vertical plate subjected to a magnetic field and a heat source/sink. The impact of magnetic parameter, Prandtl number, permeability coefficient, heat source/sink volumetric rate and temperature difference between heated plate and ambient temperature. A reduced system of ODEs was created via group similarity method. The solution led to some important results. Increasing permeability coefficient of the plate material resulted in a significant increase in flow velocity and a slight increase in heat flux but the magnitude of shear stress and temperature distribution decreased. Moreover, increasing the magnetic parameter, M, led to a significant decrease in velocity and a decrease in heat flux, whereas shear stress and temperature distribution increased. Furthermore, increasing Prandtl number, Pr, reduced the velocity significantly and the heat flux slightly. On the other hand, the magnitude of shear stress and temperature distribution increased. In case of using heat source, the increase in its energy rate decreased the heat flux with no significant effect on shear stress. Finally, the increment of temperature difference led to noticeable increase in velocity and a slight increase in heat flux, whereas the shear stress decreased. Keywords: electrically conducting fluids, group method, magnetic parameter, Prandtl number 1. INTRODUCTION For many decades, Newtonian flows attracts many researchers to investigate and study their behaviors. Steady and unsteady fluid dynamics were studied for different cases of operations to model and simulate many engineering applications. Power generators, cooling systems of nuclear reactors and liquid metal flow control are few examples of such applications. Electrically conducting fluids subjected to magnetic field, which are also known as magnetohydrodynamic (MHD) fluids, are important fluids models. Many researchers have studied different cases of MHD fluids using numerous methods. Kataria and Patel [1] studied the effects of heat generation on MHD fluid flow through porous medium past an oscillating vertical plate. Huang and Liu [2], analyzed the features of laminar MHD fluid in a pipe. Liu and Guo [3] examined the fractional Maxwell MHD fluid. Ahmad et al. [4] used a periodically accelerated plate to find a new analytical technique for MHD fluid flow. Ajam et al. [5] used Buongiorno’s model and found a new analytical approximation of MHD resulting from a stretching permeable surface. Chen et al. [6] obtained a solution for fractional viscoelastic MHD fluid using Lie group similarity over a stretching sheet. Khan et al. [7] attained a numerical solution of MHD flow with homogenous heterogeneous reactions. Prasad et al. [8] studied the thermal properties of MHD Casson fluid. Umavathi et al. [9] studied the effect of temperature on MHD flow in a vertical channel. Ahmed et al. [10] investigated the non-Newtonian Maxwell fluid with variable thermal conductivity. Rehman et al. [11] studied MHD flow of Casson fluid in stretching cylinder. Different mathematical methods were exploited to investigate and analyze numerous cases of fluid dynamics. Lie Infinitesimal and group methods [12-14], homotopy method [15-17], finite element [18-20] and finite volume [21-23] are examples for such common methods. Several modeling of MHD fluids have been studied [24, 25]. Inspired by all these researches, the present work provides analytical and numerical solutions for heated moving vertical plate submerged in MHD fluid. The objectives of the recent study are to combine many parameters to the considered flow and investigate their effect on the velocity profile, shear stress, heat distribution and heat flux inside the boundary layer. The considered parameters are magnetic parameter, permeability coefficient, Prandtl number, temperature difference and volumetric heat rate of a heat source/sink. 2. MATHEMATICAL FORMULATION Consider a moving vertical porous plate immersed in MHD fluid with temperature adjacent to plate of   while temperature outside boundary layer is  ∞ . The flow undergoes a constant pressure and subjected to a constant magnetic field of density B0 in y-direction that results in Lorentz force in x- direction (− 0 2 ). The momentum in y-direction has been neglected while the heat diffusion is more significant in y- direction. Based on the previous assumptions, the physical model is depicted in Figure 1 while the governing equations are described as: International Journal of Heat and Technology Vol. 38, No. 3, September, 2020, pp. 682-688 Journal homepage: http://iieta.org/journals/ijht 682