Unsteady Natural Convection Heat and Mass Transfer of Non-Newtonian Casson Fluid along a Vertical Wavy Surface

Authors: A. Mahdy, Sameh E. Ahmed

Abstract:

Detailed numerical calculations are illustrated in our investigation for unsteady natural convection heat and mass transfer of non-Newtonian Casson fluid along a vertical wavy surface. The surface of the plate is kept at a constant temperature and uniform concentration. To transform the complex wavy surface to a flat plate, a simple coordinate transformation is employed. The resulting partial differential equations are solved using the fully implicit finite difference method with SUR procedure. Flow and heat transfer characteristics are investigated for a wide range of values of the Casson parameter, the dimensionless time parameter, the buoyancy ratio and the amplitude-wavelength parameter. It is found that, the variations of the Casson parameter have significant effects on the fluid motion, heat and mass transfer. Also, the maximum and minimum values of the local Nusselt and Sherwood numbers increase by increase either the Casson parameter or the buoyancy ratio.

Keywords: Casson fluid, wavy surface, mass transfer, transient analysis.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1132100

References:

[1] B.Gebhart, Y. Jaluria, R.L. Mahajan, B. Sammakia, Buoyancy-Induced Flow and Transport, Hemisphere, New York, 1998.
[2] J. Jer-Huan,Y. Wei-Mon, L. Hui-Chung, “Natural convection heat and mass transfer along a vertical wavy surface”, Int. J. Heat Mass Transfer vol. 46 pp. 1075-1083, 2003.
[3] A. Mahdy, “MHD non-Darcian free convection from a vertical wavy surface embedded in porous media in the presence of Soret and Dufour effect”, Int. Commu. Heat Mass Transfer, vol. 36, pp. 1067-1074, 2009.
[4] A. Mahdy, E.A. Sameh, Laminar free convection over a vertical wavy surface embedded in a porous medium saturated with a nanofluid, Transp. Porous Med., vol 91, pp. 423–435, 2012.
[5] E.A. Sameh, M.M. Abd El-Aziz, “Effect of local thermal non-equlibrium on unsteady heat transfer by natural convection of a nanofluid over a vertical wavy surface:, Meccanica vol. 48, pp. 33-43, 2013.
[6] H.I. Andersson and B.S. Dandapat, “Flow of a power-law fluid over a stretching sheet”, Appl. Anal. Continuous Media vol. 1, pp. 339-347, 1992.
[7] I.A. Hassanien, “Flow and heat transfer on a continuous flat surface moving in a parallel free stream of power-law fluid”, Appl. Model vol. 20 pp. 779–784, 1996.
[8] B. Serdar, M. Salih Dokuz, “Three-dimensional stagnation point flow of a second grade fluid towards a moving plate”, Int. J. Eng. Sci. vol. 44, pp. 49–58, 2006.
[9] A.M. Siddiqui, A. Zeb, Q.K. Ghori, A.M. Benharbit, “Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates”, Chaos Solitons Fractals vol. 36, pp. 182–192, 2008.
[10] M. Sajid, I. Ahmad, T. Hayat and M. Ayub, “Unsteady flow and heat transfer of a second grade fluid over a stretching sheet”, Commun. Nonlinear Sci. Numer. Simul. Vol. 14, pp. 96–108, (2009).
[11] M. Mustafa, T. Hayat, I. Pop and A. Aziz, “Unsteady boundary layer flow of a Casson fluid due to an impulsively started moving flat plate”, Heat Transfer – Asian Res. Vol. 40, pp. 563–576, 2011.
[12] K. Bhattacharyya, T. Hayat, A. Alsaedi, “Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer”, Chin. Phys. B vol. 22(2), pp. 024702, 2013 .
[13] Y.C. Fung, Biodynamics circulation. New York Inc: Springer Verlag; 1984.
[14] S. Nadeem, R. Ul Haq, C. Lee, “MHD flow of a Casson fluid over an exponentially shrinking sheet”, Sci. Iran vol. 19(6), pp. 1550–1553, (2012).
[15] A. Kandasamy, R.G. Pai, “Entrance region flow of Casson fluid in a circular tube”, Appl. Mech. Mater vol. 110/116, pp. 698–706, (2012).
[16] N. Casson In: Mill CC, editor. Rheology of dispersed system, vol. 84. Oxford: Pergamon Press; 1959.
[17] W.P. Walwander, T.Y. Chen, D.F. Cala, Biorheology vol. 12, pp. 111, 1975.
[18] G.V. Vinogradov, A.Y. Malkin, Rheology of polymers. Moscow: Mir Publisher; 1979.
[19] R.K. Dash, K.N. Mehta and G. Jayaraman, “Casson fluid flow in a pipe filed with a homogeneous porous medium”, Int. J Eng. Sci. vol. 34(10), pp. 1145–1156, 1996.
[20] N.T.M. Eldabe, M.G.E. Salwa, “Heat transfer of MHD non-Newtonian Casson fluid flow between two rotating cylinders”, J. Phys. Soc. Jpn. Vol. 64, pp. 41–64, 1995.
[21] J. Boyd, J.M. Buick, S. Green, “Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flow using the lattice Boltzmann method”, Phys. Fluids vol. 19, pp. 93–103, 2007.
[22] M. Nakamura, T. Sawada, Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis, ASME J Biomechanical Eng vol. 110, pp. 137–143, 1988.
[23] L.S. Yao, “A note on Prandtl's transposition theorem”, ASME J. Heat Transfer vol. 110, pp. 503-507, 1989.
[24] L.S. Yao, “Natural convection along a wavy surface”, ASME J. Heat Transfer vol. 105, pp. 465-468, 1983.
[25] Bapuji Pullepu, Ali J. Chamkha,, I. Pop, “Unsteady laminar free convection flow past a non-isothermal vertical cone in the presence of a magnetic field”, Chem. Eng. Comm., vol. 199, pp. 354-367, 2012.