Numerical Treatment of Casson Fluid Free Convective Flow Past An Infinite Vertical Plate Filled in Magnetic Field in Presence Of Thermal Radiation: A Finite Element Technique

Abstract

The combined effects of hall current, thermal radiation on an unsteady MHD free convection casson fluid flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical plate are investigated in presence of heat transfer. Numerical solutions of the non-linear coupled governing equations is obtained by finite element technique. The expressions for primary fluid velocity, secondary fluid velocity and fluid temperature, skin friction due to primary and secondary velocity fields and rate of heat transfer coefficient due to temperature at the plate are obtained and discussed with the help of different material parameters like Grashof number for heat transfer, Casson fluid parameter, Magnetic field parameter, hall parameter, thermal radiation parameter, Prandtl number. Finally, it is seen that the numerical results of the present study conform very well to those of previous studies reported in available scientific literatures.

Keywords

• Hall current,Casson fluid,MHD,Thermal Radiation,Finite element method

References

1. [1] Baltacıoğlu, A.K., Civalek, O., Akgöz, B., Demir, F., Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution. International Journal of Pressure Vessels and Piping, 88, 290-300, 2011.
2. [2] Shu, C., Chew, Y.T., Richards, B.E., Generalized differential and integral quadrature and their application to solve boundary layer equations. International Journal for Numerical Methods in Fluids, 1995.
3. [3] Civalek, O., Korkmaz, A., Demir, C., Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges. Advances in Engineering Software, 41, 557-560, 2010.
4. [4] Ramana Murthy, M.V., Srinivasa Raju, R., Anand Rao, J., Heat and mass transfer effects on MHD natural convective flow past an infinite vertical porous plate with thermal radiation and Hall current. Procedia Engineering Journal, 127, 1330-1337, 2015.
5. [5] Rao, V.S., Babu, L.A., Raju, R.S., Finite element analysis of radiation and mass transfer flow past semi-infinite moving vertical plate with viscous dissipation. Journal of Applied Fluid Mechanics, 6, 321-329, 2013.
6. [6] Srinivasa Raju, R., Combined influence of thermal diffusion and diffusion thermo on unsteady hydromagnetic free convective fluid flow past an infinite vertical porous plate in presence of chemical reaction. Journal of Institution of Engineers: Series C, 97(4), 505-515, 2016.
7. [7] Srinivasa Raju, R., Effects Of Soret And Dufour On Natural Convective Fluid Flow Past A Vertical Plate Embedded In Porous Medium In Presence Of Thermal Radiation Via FEM, Journal of the Korean Society for Industrial and Applied Mathematics, 20(4), 309-332, 2016.
8. [8] Srinivasa Raju, R., Anitha, G., Jitthender Reddy, G., Influence of Transpiration and Hall effects on unsteady MHD free convection fluid flow over an infinite vertical plate. International Journal of Control Theory and Applications, 9(23), 455-462, 2016.

9. [9] Srinivasa Raju, R., Anil Kumar, M., Dharmendar Reddy, Y., Unsteady MHD Free Convective Flow Past A Vertical Porous Plate With Variable Suction. ARPN Journal of Engineering and Applied Sciences, 11(23), 13608-13616, 2016.
10. [10] Sailaja, S.V., Shanker, B., Srinivasa Raju, R., Double Diffusive Effects On MHD Mixed Convection Casson Fluid Flow Towards A Vertically Inclined Plate Filled In Porous Medium In Presence Of Biot Number: A Finite Element Technique, Journal of Nanofluids, 2016 (In press).
11. [11] Sarpkaya, T., Flow of non-Newtonian fluids in a magnetic field. American Institute of Chemical Engineering, 7, 324-328, 1961.
12. [12] Mukhopadhyay, S., De, P.R., Bhattacharyya, K., Layek, G.C., Casson fluid flow over an unsteady stretching surface. Ain Shams Engineering Journal, 4, 933-938, 2013.
13. [13] Mukhopadhyaya, S., Moindala, I.C., Hayat, T., MHD boundary layer flow of Casson fluid passing through an exponentially stretching permeable surface with thermal radiation. Chinese Physics Letters, 23, 104701, 2014.
14. [14] Raju, C.S.K., Sandeep, N., Sugunamma, V., Babu, M.J., Reddy, J.V.R., Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface. Engineering Science and Technology, International Journal, 19(1), 45-52, 2016.
15. [15] Das, M., Mahato, R., Nandkeolyar, R., Newtonian heating effect on unsteady hydro-magnetic Casson fluid flow past a flat plate with heat and mass transfer. Alexandria Engineering Journal, 2015, http://dx.doi/10.1016/j.aej.2015.07.007.
16. [16] Mahanta, G., Shaw, S., 3D Casson fluid flow past a porous linearly stretching sheet with convective boundary condition. Alexandria Engineering Journal, 2015.
17. [17] Seddeek, Md., Emad Aboeldahab, M., Radiation effects on unsteady MHD free convection with hall current near an infinite vertical porous plate. International Journal of Applied Mathematics and Mechanics, 26(4), 249-255, 2001.
18. [18] Dash, R. K., Mehta, K. N., Jayaraman, G., Casson Fluid Flow in a Pipe Filled with a Homogeneous Porous Medium. International Journal of Engineering Science, 34, 1145-1156, 1996.
19. [19] Cogley, A. C., Vincenty, W. E., Gilles, S. E., Differential approximation for radiation in a non-gray gas near equilibrium, AIAA Journal, 6, 551-553, 1968.
20. [20] Schlichting, H., Boundary Layer Theory. McGraw–Hill New York, 1968.
21. [21] Bhargava, R., Rana, P., Finite element solution to mixed convection in MHD flow of micropolar fluid along a moving vertical cylinder with variable conductivity. International Journal of Applied Mathematics and Mechanics, 7, 29-51, 2011.
22. [22] Lin, Y. Y., Lo, S. P., Finite element modeling for chemical mechanical polishing process under different back pressures. J. Mat. Proc. Tech., 140(1-3), 646-652, 2003.
23. [23] Dettmer, W., Peric, D., A computational framework for fluid-rigid body interaction, finite element formulation and applications, Computer Methods in Applied Mechanics in Engineering, 195(13-16), 1633-1666, 2006.
24. [24] Hansbo, A., Hansbo, P., A finite element method for the simulation of strong and weak discontinuities in solid mechanics, Computer Methods in Applied Mechanics in Engineering, 193(33-35), 3523-3540, 2004.
25. [25] Bathe, K. J., Finite Element Procedures. Prentice–Hall New Jersey, 1996.
26. [26] Reddy, J. N., An Introduction to the Finite Element Method. McGraw–Hill New York, 1985.
27. [27] Nirmal, C. S., Rallath, H., Singh, A. K., An exact solution for unsteady MHD free convection flow with constant heat flux. International Journal Communications in Heat Mass Transfer, 21, 131-315, 1994.