Title: Implicit finite difference solution for the magneto-hydro-dynamic unsteady free convective flow and heat transfer of a third-grade fluid past a porous vertical plate
Authors: Itishree Nayak; Ajit Kumar Nayak; Sudarsan Padhy
Addresses: Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha, India ' Department of CS&IT, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar, Odisha, India ' Institute of Mathematics and Applications, Bhubaneswar, Odisha, India
Abstract: Magneto-hydro-dynamic (MHD) unsteady flow and heat transfer of a third grade fluid passing an infinite vertical porous plate with uniform suction applied at the plate has been studied. The governing nonlinear partial differential equations are reduced to a system of nonlinear algebraic equations using implicit finite difference schemes and then the system is solved using damped-Newton method. The effect of the various physical parameters on the velocity and temperature are studied. One of the important observations is that when the third order elastic parameter increases the velocity decreases, whereas an opposite effect is observed when second order elastic parameter increases. Present method is valid for all values of elastic parameters where as the earlier approximation methods like perturbation and power series methods are valid for small values of elastic parameter. Further the advantage of our method is that it does not require repeated derivation for every change in the boundary conditions.
Keywords: third grade fluids; magnetohydrodynamic flow; free convection; finite difference method; FDM; damped Newton method; magnetohydrodynamics; unsteady flow; free convective flow; heat transfer; porous vertical plates; nonlinear PDEs; partial differential equations; nonlinear algebraic equations; implicit finite difference; velocity; temperature; elastic parameters; perturbation; power series.
International Journal of Mathematical Modelling and Numerical Optimisation, 2016 Vol.7 No.1, pp.4 - 19
Received: 13 Dec 2014
Accepted: 27 Apr 2015
Published online: 23 Jan 2016 *