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MHD mixed convection stagnation point flow of an upper convected Maxwell fluid on a vertical surface with an induced magnetic field
K. Jafar1 - R. Nazar2 - A. Ishak2 - I. Pop3
1 Faculty of Engineering and Built Environments, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
2 School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia 43600 UKM Bangi, Selangor, Malaysia
3 Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania
Abstract
The present analysis considers the steady laminar magnetohydrodynamic (MHD) mixed convection flow of an electrically conducting upper convected Maxwell fluid near the stagnation point on a semi-infinite vertical flat plate with a variable magnetic field H applied parallel to and far away from the plate. Using a similarity transformation, the governing system of partial differential equations is first transformed to a system of ordinary differential equations, which is then solved numerically using an implicit finite-difference scheme known as the Keller-box method. Numerical results are obtained for the velocity and temperature profiles as well as for the skin friction coefficient and local Nusselt number, for various values of the mixed convection parameter λ, magnetic parameter M, elastic parameter (Deborah number) K, reciprocal magnetic Prandtl number γ and the Prandtl number Pr. The effects of these parameters on the momentum and thermal boundary layer characteristics and the induced magnetic field are also included into the analysis. The results indicate the existence of dual solutions for all values of λ for the buoyancy assisting flow, and up to a critical λc for the buoyancy opposing flow. The critical value λc depends on the value of the magnetic parameter \M as well as the elastic parameter K. A reduction of both the skin friction coefficient f′′(0) and the local Nusselt number −θ′(0) with the increase of the magnetic parameter M is observed for the buoyancy assisting flows. Tables 4, Figs 10, Refs 23.