Unsteady MHD free convection flow between two heated vertical parallel plates in the presence of a uniform magnetic field

Amarjyoti Goswami¹ , Mrinmoy Goswami² , Krishna Gopal Singha³

1. Dept. of Electronics and Communication Engineering, Kaziranga University, Jorhat, Assam, India.
2. Dept. of Mathematics, Kaziranga University, Jorhat, Assam, India.
3. Dept. of Mathematics, Karanga Girls’ Higher Secondary School, Jorhat, Assam, India.

Correspondence should be addressed to: mrinmoygoswami1977@yahoo.in .

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.2 , pp.86-94, Apr-2020

Online published on Apr 30, 2020

Copyright © Amarjyoti Goswami, Mrinmoy Goswami, Krishna Gopal Singha . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The problem of unsteady viscous incompressible MHD free convection flow of an electrically conducting fluid between two heated vertical parallel plates in the presence of a uniform magnetic field applied transversely to the flow is considered. The induce field along the lines of motion varies transversely to the flow and the fluid temperature changing with time. An analytical solution for velocity, induced field and the temperature distributions are obtained for small and large Magnetic Reynolds numbers. The skin-friction at the two plates is obtained. Velocity distribution, induced field and skin-friction are plotted graphically against the distance from the plates. It has been observed that with the increase in the Magnetic Reynolds number, at constant Hartmann number, leads to an increase in the skin-friction gradually. But with the increase in Hartmann number, at constant Magnetic Reynolds number, the skin-friction decreases.

Key-Words / Index Term :
Fully developed flow; Conducting fluid; induced field; Skin-friction; Magnetic Reynolds number

References :
[1] Hanratty T J and Campbell J A. “Measurement of wall shear stress”, Fluid Mechanics Measurements. 1st edition, Hemisphere Publishing Corporation, 1983.
[2] Winter KG. “An outline of the techniques available for the measurement of skin friction in turbulent boundary layers”, Progress in Aerospace Sciences, Vol.18, pp.-57 1957,.
[3] Schetz J A. “Direct measurement of skin friction in complex fluid flows”, Applied Mechanics Review, 50, S198 – S203, 1997.
[4] Naughton J W and Sheplak M. “Modern developments in shear stress measurements”, Progress in Aerospace Sciences, Vol. 38, pp.515 –570, 2002.
[5] Pohlhausen, E., ZAMM, Vol.1, pp. 115 ,1921.
[6] Soundalgekar, V.M., Patil, M.R. and Jahagirdar, M.D., “MHD stokes problem for a vertical infinite plate with variable temperature”, Nuclear Engg. and Design, Vol. 64, No.1, pp.39-42, 1981.
[7] Das, K. and Saynal, D.C.,"laminar Conv. flow of cond. fluid between vert. plates", J. Ass. Sci. Soc., 1995.
[8] Borkakati, A.K., and Chakraborty, S.,"Laminar conv. flow of cond. fluid for an inclined magnetic field", Int. Jr. Theo. and Mech., Vol.24, pp.17-34, 1998,.
[9] Gourla, M.G.and Katoch, S.L., “Unsteady free convection MHD flow between heated vertical plates”, Ganita, Vol.42, No.2,pp. 143-153, (1991.
[10] Ostrach, S., NACA. PN, , 3141, 1954.
[11] Ostrach, S.Grenzschi-Chtfurschung (Ed.-II, Gortler), 1958.
[12] Grief, R and Habib, I.S.and Lin, J.C., “Laminar convection of a radiating gas in a vertical channel”, J, Fluid Mech, Vol. 46, pp. 513-520, 1971.
[13] Gupta et. al., Bull. Cal. Math. Soc.,Vol. 61, pp.29, 1969.
[14] Soundalgekar, V. M. and Ramana Murty, T.V., “Heat transfer in MHD flow with pressure gradient, suction and injection”, J. Engg.Math., Vol.14, No.2, pp.155-159, 1980.
[15] Soundalgekar, V. M. and Bhatt. J.P., Bull. Cal. Math. Soc., Vol. 61, pp. 93, 1990.
[16] Kim, Y.J., “Unsteady MHD convection flow of polar fluids past a vertical moving porous plate in a porous medium”, Int. J. Heat and Mass Transfer, Vol. 44 No. 15, pp. 2791-2799, 2001.
[17] Chen, C.H., “Combined heat and mass transfer in MHD free convection from a vertical surface with Ohmic heating and viscous dissipation”, Int. J. Engg. Sci. , Vol. 42, No. 7, pp. 699-713, 2004.
[18] Dahake S.P. and Dubewar A.V., “Effects of Radiation on Magnetohydrodynamic Convection Flow past an Impulsively Started Vertical Plate Submersed in a Porous Medium with Suction”, International Journal of Computer Sciences and Engineering, Vo. 5, Issue-2, pp 1-7, 2017.
[19] Mrinmoy Goswami, Krishna Gopal Singha, Amarjyoti Goswami and P N Deka, “A study of unsteady MHD vertical flow of an incompressible viscous electrically conducting fluid bound by two non-conducting plates in the presence of uniform inclined magnetic field”, Proceedings of World Congress on Engineering, 2018,Vol I ,London UK.
[20] Aruna Sharma, A.V .Dubewar, “MHD Flow between Two Parallel Plates under the Influence of Inclined Magnetic Field by Finite Difference Method”, International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Vol. 8 Issue-12, October 2019.