Abstract

Magneto-hydro-dynamic unsteady flow and heat transfer of a third grade fluid between two porous plates with variable viscosity has been investigated. The coupled non-linear partial differential equations governing the flow and heat transfer are reduced to a system of nonlinear algebraic equations using implicit finite difference scheme, and then the system is solved by using damped-Newton method. The effects of various physical parameters on the velocity and temperature field have been studied. One of the important observations obtained is that both velocity and temperature fields increase with an increase in the value of the variable viscosity parameter. The uniqueness of the developed method is that, it is valid for all values of elastic parameters whereas the earlier approximation methods like perturbation and power series methods are valid only for small values of elastic parameters. Further, unlike these methods, presented method does not require a repeated derivation of solution of the governing equation for every change in the boundary conditions.

Keywords

References

[1] T. Hayat, A. Navneed, and M. Sajid, Analytic solution for MHD flow of a third order fluid in a porous channel, Journal of Computational and Applied Mathematics 214(2) (2008) 572–582.
[2] M.E. Erdogan, Plane surface suddenly set in motion in a non Newtonian fluid, Acta Mech. 108 (1995) 179–187.
[3] T. Hayat, A. H. Kara, and E. Momoniat, Exact flow of a third-grade fluid on a porous wall, Int J Non-Linear Mechanics 38(10) (2003) 1533–1537.
[4] R.L. Fosdick and K.R. Rajagopal, Thermodynamics and Stability of fluids of third grade fluid, Proc. Of Royal Society London A. 38(10) (1980) 351–377.
[5] T. Hayat, S. Nadeem, S. Asghar, and A. M. Siddiqui, Fluctuating flow of a third order fluid on a porous plate in a rotating medium, Non-Linear Mechanics 36(6) (2001) 901–916.
[6] P.K. Kaloni and A.M. Siddique, A note on the flow of a visco-elastic fluid between eccentric disc, Non-Newtonian Fluid Mech 26 (1987) 901–916.
[7] P. D. Ariel, Flow of a third grade fluid through a porous at channel, Int.J. of Engineering Science 41(11) (2003) 1267-1285.
[8] I. Nayak, and S. Padhy, Unsteady MHD flow analysis of a third-grade fluid between two porous plates, Journal of the Orissa Mathematical Society 31 (2012) 83–96.
[9] S. S. Okoya, On the transition for a generalized coquette flow of a reactive third grade fluid with viscous dissipation, Int. Comm. in Heat and Mass Transfer 35(2) (2008) 188-196.
[10] B. Sahoo and D. Younghae, Effects of slip on sheet-driven flow and heat transfer of a third grade fluid past a stretching sheet, Int. Comm. in Heat and Mass Transfer 37(8) (2010) 1064–1071.
[11] M. Sajid and T. Hayat, The application of homotopy analysis method to thin film flows of a third order fluid, Chaos, Solutons & Fractals 38(2) (2008) 506–515.
[12] O. D. Makinde and T. Chinyoka, Numerical study of unsteady hydro magnetic generalized couette flow of a reactive third grade fluid with asymmetric convective cooling, Computers and Mathematics with Application 61 (2011) 1167–1179.
[13] B.D. Coleman and W. Noll, An approximation theorem for functional with application in continuum mechanics, Archive for Rational Mechanics and Analysis 6(1) (1965) 355–370.
[14] S.D. Conte and C. De Boor, Elementary Numerical Analysis an Algorithmic Approach, McGraw- Hill Inc. New York (1980).