# THERMAL DIFFUSION AND RADIATION EFFECTS ON UNSTEADY MHD FREE CONVECTION HEAT AND MASS TRANSFER FLOW PAST A LINEARLY ACCELERATED VERTICAL POROUS PLATE WITH VARIABLE TEMPERATURE AND MASS DIFFUSION

• Venkateswarlu, M. (DEPARTMENT OF MATHEMATICS, V. R. SIDDHARTHA ENGINEERING COLLEGE) ;
• Ramana Reddy, G.V. (DEPARTMENT OF MATHEMATICS, K. L UNIVERSITY) ;
• Lakshmi, D.V. (DEPARTMENT OF MATHEMATICS, BAPATLA WOMEN'S ENGINEERING COLLEGE)
• Accepted : 2014.08.19
• Published : 2014.09.25

#### Abstract

The objective of the present study is to investigate thermal diffusion and radiation effects on unsteady MHD flow past a linearly accelerated vertical porous plate with variable temperature and also with variable mass diffusion in presence of heat source or sink under the influence of applied transverse magnetic field. The fluid considered here is a gray, absorbing/emitting radiation but a non-scattering medium. At time t > 0, the plate is linearly accelerated with a velocity $u=u_0t$ in its own plane. And at the same time, plate temperature and concentration levels near the plate raised linearly with time t. The dimensionless governing equations involved in the present analysis are solved using the closed analytical method. The velocity, temperature, concentration, skin-friction, the rate or heat transfer and the rate of mass transfer are studied through graphs in terms of different physical parameters like magnetic field parameter (M), radiation parameter (R), Schmidt parameter (Sc), Soret number (So), Heat source parameter (S), Prandtl number (Pr), thermal Grashof number (Gr), mass Grashof number (Gm) and time (t).

#### References

1. E. Pohlhausen: Der Warmeaustrausch Zwischen Festen Korpen und Flussigkeiten mit Kleiner Reibung und kleiner Warmeleitung. ZAMM, 1(1921), pp.115-121. https://doi.org/10.1002/zamm.19210010205
2. S. Ostrach: An analysis of laminar free convection flow and heat transfer along a flat plate parallel to the direction of the generating body force, NACA report TR-1111(1953), pp.63-79.
3. R. Siegel: Transient free convection from a vertical flat plate, J. Heat Transfer, 80(1958), pp.347-359.
4. B.Gebhart: Transient natural convection from vertical elements, J. Heat Transfer, 83C (1961), pp.61-70.
5. T. Watanabe and I. Pop: Thermal boundary layers in magneto hydrodynamic flow over a flat plate in the presence of transverse magnetic field, Acta. Mech, 105(1994), pp. 233-238. https://doi.org/10.1007/BF01183954
6. I. Michiyochi, I. Takahashi and A. Serizawa: Natural convection heat transfer from a horizontal circular cylinder to mercury under a magnetic field, Int. J. Heat and Mass Transfer, 19(1976), pp.1021-1029. https://doi.org/10.1016/0017-9310(76)90185-X
7. K. Vajravelu and J. Nayfeh: Hydrodynamics convection at a cone and a wedge, Int. Commun in.Heat and Mass Transfer, 19(1992), pp. 701-710. https://doi.org/10.1016/0735-1933(92)90052-J
8. E. M. Sparrow and R.D. Cess: The effect of a magnetic field on free convection heat transfer, Int. J. Heat and Mass Transfer, 4(1961), pp.267-274.
9. N. Riley: Magnetohydrodynamic free convection about a semi-infinite vertical plate in strong cross-fiel, J. Appl. Math. Phys. (ZAMP), 27(1976), pp. 621-631. https://doi.org/10.1007/BF01591174
10. E. V. Somers: Theoretical considerations of combined thermal and mass transfer from vertical flat plate, J. Appl. Mech, 23(1956), pp. 295-301.
11. W. G. Mathers, A. J. Madden and E.L. Piret: Simultaneous heat and mass transfer in free convection, India. Engg. Chem, 49(1956), pp.961-968.
12. B. Gebhart and L. Pera: The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion, Int. J. Heat and Mass Transfer, 14(1971), pp. 2025-2050. https://doi.org/10.1016/0017-9310(71)90026-3
13. V. M. Soundalgekar and P.D.Wavre: Unsteady free convection flow past an infinite vertical plate with constant suction and mass transfer, J. Heat and Mass transfer, 19(1977), pp. 1363-1373.
14. G. D. Callahan and W.J. Manner: Transient free convection with mass transfer on an isothermal vertical flat plate, Int. J. Heat and Mass Transfer, 19(1976), pp.165-174. https://doi.org/10.1016/0017-9310(76)90109-5
15. V. M. Soundalgekar and P. Ganesan: Finite-Difference analysis of transient free convection with mass transfer on an isothermal vertical flat plate, Int. J. Eng. Sci, 19(1981), pp. 757-770. https://doi.org/10.1016/0020-7225(81)90109-9
16. E. M. A. Elbashbeshy: Heat and mass transfer along a vertical plate with variable surface temperature and concentration in the presence of magnetic field, Int. J. Engg. Sci, 34(1970), pp.515-522.
17. E. M. Aboeldahab and E.M.E. Elbarbary: Hall current effect on magneto-hydrodynamic free convective flow past a semi-infinite vertical plate with mass transfer, Int. J.Eng. Sci, 39(2001), pp.1641-1652. https://doi.org/10.1016/S0020-7225(01)00020-9
18. C. H. Chen: Heat and mass transfer in MHD flow by natural convection from a permeable inclined surface with variable wall temperature and concentration, Acta. Mech, 172(2004), pp.219-235. https://doi.org/10.1007/s00707-004-0155-5
19. H. S. Takhar, P. Ganesan, K. Ekambavahar and V. M. Soundalgekar: Transient free convection past a semi-infinite vertical plate with variable surface temperature, Int. J. Numerical Methods, Heat Fluid Flow, 7(1997), pp. 280-296. https://doi.org/10.1108/09615539710165804
20. P. Ganesan and H. P. Rani: Unsteady free convection MHD flow past a vertical cylinder with mass transfer, Int. J. Ther. Sci, 39(2000), pp. 265-272. https://doi.org/10.1016/S1290-0729(00)00244-1
21. M. A. Abd El- Naby, M. E. E. Elbarbary and Y. A. Nader: Finite difference solution of radiation effects on free convection flow over a vertical plate with variable surface temperature, J. Appl. Math, 2(2003), pp.65-86.
22. A. J. Chamkha, H. S. Takhar and V.M. Soundalgekar: Radiation effects on free convection flow past a semiinfinite vertical plate with mass transfer, Chem. Engg. J, 84(2001), pp. 335 - 342. https://doi.org/10.1016/S1385-8947(00)00378-8
23. P. Ganesan and P. Loganadan: Radiation and mass transfer effects on flow of an incompressible viscous fluid past a moving cylinder, Int. J. Heat Mass and Transfer, 45(2002), pp.4281-4288. https://doi.org/10.1016/S0017-9310(02)00140-0
24. B. Gebhart: Effect of viscous dissipation in natural convection, J. Fluid Mech, 14(1962) pp.225-232. https://doi.org/10.1017/S0022112062001196
25. H. S. Takhar, R. S. R. Gorla and V. M. Soundalgekar: Radiation effects on MHD free convection flow of a radiation gas past a semi-infinite vertical plate, Int. J. Numerical Methods Heat Fluid Flow, 6(1996), pp. 77-83.
26. B. Gebhart and J. Mollendraf: Viscous dissipation in external natural convection flows, Fluid. Mech, 38(1969), pp. 97-107. https://doi.org/10.1017/S0022112069000061
27. V. M. Soundalgekar: Viscous dissipation effects on unsteady free convective flow past an infinite, vertical porous plate with constant suction, Int. J. Heat and Mass Transfer, 15(1972), pp. 1253-1261. https://doi.org/10.1016/0017-9310(72)90189-5
28. C. Israel-Cookey, A. Ogulu and V.B. Omubo-Pepple: Influence of viscous dissipation on unsteady MHD free convection flow past an infinite heated vertical plate in porous medium with time-dependent suction, Int. J. Heat and Mass Transfer, 46(2003), pp. 2305-2311. https://doi.org/10.1016/S0017-9310(02)00544-6
29. M. Y. Gokhale and F. M. Al Samman: Effects of mass transfer on the transient free convection flow of a dissipative fluid along a semi-infinite vertical plate with constant heat flux, Int. J. Heat and Mass Transfer, 46(2003), pp. 999-1011. https://doi.org/10.1016/S0017-9310(02)00367-8
30. G. V. Ramana Reddy, A. Madan Mohan Rao and Ch. V. Ramana Murthy: Effects of radiation and mass transfer on MHD free convective dissipative fluid in the presence of heat source/sink, Mathematics Applied in Science and Technology, 2(2010), pp. 45-56.
31. G. V. RamanaReddy, G. Sudershan Reddy and K. Jayarami Reddy: Chemical and radiation absorption effects on MHD convective heat and mass transfer flow past a semi-infinite vertical moving porous plate with time dependent suction, International journal of mathematical archive, 3(2012), pp 2974-2982.
32. M. Turkyilmazoglu and I. Pop: Heat and mass transfer of unsteady natural convection flow of some nanofluids past a vertical infinite flat plate with radiation effect, International Journal of Heat and Mass Transfer, 59(2013), pp. 167-171. https://doi.org/10.1016/j.ijheatmasstransfer.2012.12.009
33. K.Gangadhar and N. Bhaskar Reddy: Chemically reacting MHD boundarylayer flow of heat and mass transfer over a moving vertical plate in a porous medium with suction, Journal of Applied Fluid Mechanics,6(2013), pp.107-114.

#### Cited by

1. SORET, HALL CURRENT, ROTATION, CHEMICAL REACTION AND THERMAL RADIATION EFFECTS ON UNSTEADY MHD HEAT AND MASS TRANSFER NATURAL CONVECTION FLOW PAST AN ACCELERATED VERTICAL PLATE vol.20, pp.3, 2016, https://doi.org/10.12941/jksiam.2016.20.203
2. INFLUENCE OF SLIP CONDITION ON RADIATIVE MHD FLOW OF A VISCOUS FLUID IN A PARALLEL POROUS PLATE CHANNEL IN PRESENCE OF HEAT ABSORPTION AND CHEMICAL REACTION vol.20, pp.4, 2016, https://doi.org/10.12941/jksiam.2016.20.333
3. HEAT AND MASS TRANSFER EFFECTS ON MHD NATURAL CONVECTION FLOW PAST AN INFINITE INCLINED PLATE WITH RAMPED TEMPERATURE vol.20, pp.4, 2016, https://doi.org/10.12941/jksiam.2016.20.355
4. Unsteady MHD Flow of Radiating and Rotating Fluid with Hall Current and Thermal Diffusion Past a Moving Plate in a Porous Medium vol.389, pp.1662-9507, 2018, https://doi.org/10.4028/www.scientific.net/DDF.389.71