Application of Alternate Direction Implicit Technique to an Unsteady MHD Flow over a Semi-Infinite Vertical Plate with Viscous Dissipation
- February 6, 2021
- Posted by: RSIS Team
- Categories: IJRIAS, Mathematics
International Journal of Research and Innovation in Applied Science (IJRIAS) | Volume V, Issue XII, December 2020 | ISSN 2454–6186
A. KAUSHIK
Department of Mathematics, MAIT, Delhi, India
Abstract- An unsteady MHD flow of a viscous incompressible fluid over a semi-infinite plate with variable surface temperature in the presence of heat source is studied. The governing equations of the flow are converted into dimensionless form and the resulting non-linear differential equations are solved numerically using Alternating –Direction-Implicit (ADI) Technique. Flow parameters are obtained and are presented graphically. It was observed that the fluid velocity decreases with increase in magnetic field.
Keywords—Magnetohydodynamic fluid, semi infinite vertical plate, Alternating Direction Implicit technique, variable surface temperature.
1. INTRODUCTION
In engineering and technology, there are numerous applications of the study of transient natural convection flows over vertical plates. These studies are frequently used in heat transfer around different types of electronic and electrical devices, nuclear reactors etc. Extensive research is done for the study of free convection flows over vertical plates under variable conditions. Various techniques such as integral method [1], finite difference scheme [2],[3]. Crank Nicholson implicit scheme [4] etc are employed for these studies of the convection flows.
Alternate Direction Implicit scheme is an effective tool for the solution of problems expressed by elliptic and parabolic partial differential equations. In recent years, many researchers have employed this scheme for the solution of variety of problems. Cheng and Wang[5] applied this method to study forced convection in micropolar fluid flow over a wavy surface. Wang and Cheng [6] studied the flow through a sinusoidally curved converging–diverging channel and analyzed the skin-friction and Nusselt number for the flow for variable wavy geometry, Reynolds number and Prandtl number. In the presence of a transverse magnetic field, Wang and Chen[7] studied mixed convection boundary layer flow past an inclined wavy plate and presented numerical solution for the flow for different values of magnetic field, buoyancy, wavy geometry and material parameters. Navarro et al [8] presented numerical simulations of two dimensional incompressible fluid flows under the influence of a magnetic field at low magnetic Reynolds number. Hakeem et al [9] employed alternating direction implicit method to study natural convection cooling of thermally active plates kept at the center of an air filled cavity, taking two different boundary conditions applied on the cavity walls.
Nejad et al [10] studied mixed convection flow of electrically conducting power law fluids along a vertical wavy surface under the influence of a transverse magnetic field. They have discussed the effects of flow structure and dominant convection mode on the overall parameters of flow and heat transfer and investigated the alterations in boundary layers with magnetic field. Kiyasatfar and Pourmahmoud [11] studied viscous dissipation and joule heating effects in the presence of transverse magnetic field for electrically conducting non-Newtonian fluids through square microchannels. For different values of flow index and dimensionless shear rate parameter of modified power-law fluids, they
