IJEMD-M, 1 (2) (2022), 1 - 10 https://doi.org/10.54938/ijemdm.2022.01.2.27 International Journal of Emerging Multidiciplinaries: Mathematics Research Paper Journal Homepage: www.ijemd.com ISSN: 2790-1998 (print), 2790-3257 (online) Joule and Viscous Dissipation Effects on MHD Boundary Layer Flow over a Stretching Sheet with Variable Thickness Saleem Ahmed 1 , Huma Iram 2 and Asif Mahmood 3* 1 College of Engineering, University of Buraimi, Al Buraimi, Oman 2 Independent author from Islamabad, Pakistan 3 Department of Mathematics, University of Nevada Las Vegas, Las Vegas, USA * Corresponding Author Abstract This paper is aimed to investigate the influence of Joule and viscous dissipation effects on boundary layer flow over a stretching sheet with variable thickness and surface temperature. The said flow is subjected to space dependent magnetic field applied normal to the sheet. Mathematical modeling is done under boundary layer approximations. The governing partial differential equations are transformed into ordinary differential equations via appropriate similarity transformations. The resulting set of nonlinear equations is solved numerically using shooting method. MATLAB software is used to obtain numerical results. The impact of various physical parameters, such as power index, magnetic parame- ter, on velocity and temperature profiles is analyzed. Also, their effects on skin friction coefficient and Nusselt number are presented and discussed. Keywords: Boundary Layer Flow; Heat Transfer Rate; MHD; Skin Friction; Stretching Sheet; Variable Thickness. 1. Introduction The study of fluid flow over a stretching surface is a vital problem discussed in current era as it occurs in different engineering processes such as melt-whirling, wire drawing, production of glass fiber, extrusion, manufacturing of rubber sheets and cooling of huge metallic plates such as an electrolyte [1]-[3]. The first study of boundary layer flow on continuous solid surface was carried out by [4]. Further extension of his work was done by [5] in which the surface velocity is related to the distance from flat surface. Magnetohydrodynamic boundary layer flow is of considerable interest as it is widely used in geothermal applications and industrial technology, high temperature plasmas, MHD power generation systems and liquid metal fluids. Many metallurgical processes depend significantly on the rate of cooling of product. To control cooling rate, the sheets are stretched and passed through electrically conducting fluid in the presence of magnetic field. In view of all these aspects, many researchers have investigated the magnetic field effect on the fluid flow problems. Chakrabarti and Gupta [6], and Jhankal and Kumar [7] worked on heat transfer characteristics over a stretching sheet with hydromagnetic flow. Sparrow and Cess [8] analyzed free convection phenomena with magnetic effects. Afterwards, much emphasis has been given on transversely applied magnetic field on electrically conducting fluids. Chaim [9] carried out his work on transverse magnetic field applied on stretching sheet with suction and blowing effects in the presence of electrically conducting fluid. In real world applications, the stretching sheets are not necessarily flat, rather they can have variable thickness. The stretching sheets with variable thickness are used more frequently in architecture, machine design, nuclear reactor technology, naval structures and acoustical components. Recently, the boundary layer flow on a stretching sheet with variable thickness has been investigated by Fang et al. [10]. Also, Khader and Email addresses: saleem.a@uob.edu.om (S. Ahmed), humairam6@gmail.com (H. Iram), asif.mahmood@unlv.edu (A. Mahmood)