NUMERICAL SOLUTION OF MHD FLOW OF CASSON FLUID BETWEEN TWO PARALLEL PLATES WITH DISSIPATIONS
M. F. EL-SAYED *
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
H. N. A. ISMAIL
Department of the Basic Science, Faculty of Engineering, Banha University, El-Qlyobaya, Egypt
E. H. ALY
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
N. F. ABDALLA
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
*Author to whom correspondence should be addressed.
Abstract
The influence of Casson viscosity on the steady MHD flow and heat transfer between two parallel plates is studied. In any flow of a Bingham plastic, determination of the yielded and unyielded regions in the flow field leads to discontinuity and numerical difficulties. These are overcome by using the regularized casson model. The fluid is acted upon by an axially uniform pressure gradient and a perpendicularly uniform magnetic field. The plates are stationary and subjected to constant but different temperatures. The effects of Joule and viscous dissipations on the temperature distributions are studied. The difference schemes are used for the nonlinear differential equations. The generalized Thomas algorithm is derived to solve the linearized systems of equations. A second order finite difference scheme is derived to compute the velocity and temperature propotiontial. The effects of the parameters describing the Casson fluid flow and heat transfer behaviors on the velocity and temperature distributions are discussed in detail. It is found that both the velocity and temperature decrease by increasing of the Hartmann and Casson numbers, while they increase by increasing the dimensionless pressure.
Keywords: Casson viscosity, MHD flow, heat transfer, numerical solution, parallel plates