## THERMAL SCIENCE

International Scientific Journal

### CHEMICAL REACTION EFFECTS ON UNSTEADY MHD FREE CONVECTIVE FLOW IN A ROTATING POROUS MEDIUM WITH MASS TRANSFER

**ABSTRACT**

An investigation of unsteady MHD free convective flow and mass transfer during the motion of a viscous incompressible fluid through a porous medium, bounded by an infinite vertical porous surface, in a rotating system is presented. The porous plane surface and the porous medium are assumed to rotate in a solid body rotation. The vertical surface is subjected to uniform constant suction perpendicular to it and the temperature at this surface fluctuates in time about a non-zero constant mean. Analytical expressions for the velocity, temperature and concentration fields are obtained using the perturbation technique. The effects of R (rotation parameter), k0 (permeability parameter), M (Hartmann number) and w (frequency parameter) on the flow characteristics are discussed. It is observed that the primary velocity component decreases with the increase in either of the rotation parameter R, the permeability parameter k0, or the Hartmann number M. It is also noted that the primary skin friction increases whenever there is an increase in the Grashof number Gr or the modified Grashof number Gm. It is clear that the heat transfer coefficient in terms of the Nusselt number decreases in the case of both air and water when there is an increase in the Hartmann number M. It is observed that the magnitude of the secondary velocity profiles increases whenever there is an increase in either of the Grashof number or the modified Grashof number for mass transfer or the permeability of the porous media. Concentration profiles decreases with an increase in the Schmidt number.

**KEYWORDS**

PAPER SUBMITTED: 2011-10-04

PAPER REVISED: 2012-04-18

PAPER ACCEPTED: 2012-09-04

**THERMAL SCIENCE** YEAR

**2014**, VOLUME

**18**, ISSUE

**Supplement 2**, PAGES [S515 - S526]

- Malathy, T. and Srinivas, S., Pulsating flow of a hydro magnetic fluid between permeable beds, International Communications in Heat and Mass Transfer, 35 (2008 ): pp 681-688.
- Singh, K. D., Influence of moving magnetic field on three dimensional Couette flow, ZAMP, 55: (2004) pp 894-902.
- Das, S.S., Satapathy, A., Das, J.K. and Panda, J.P, Mass transfer effects on MHD flow and heat transfer past a vertical porous plate through a porous medium under oscillatory suction and heat source, International Journal of Heat and Mass Transfer, 52: (2009) pp 5962-5969.
- Muthucumaraswamy, R. and Ganesh, P., Unsteady flow past an impulsively started vertical plate with heat and mass transfer, International Journal of heat and mass transfer, 31: (2003) pp 1051-1059.
- Acharya, M., Dash, G.C. and Singh, L.P., Magnetic field effects on the free convection and mass transfer flow through porous medium with constant suction and constant heat flux, Indian J. Pure Appl. Math., 31(1): (2000) pp 1-18.
- Chaudhary, C. and Arpita, J., Combined heat and mass transfer effects on MHD free convection flow past an oscillating plate embedded in porous medium, Rom. Journ. Phys., 52: (2007) pp 505-524, Bucharest.
- S. Dinarvand, M.M. Rashidi, A reliable treatment of homotopy analysis method for two-dimensional viscous flow in a rectangular domain bounded by two moving porous walls, Nonlinear Analysis: Real World Applications 11 (2010) pp 1502-1512.
- Muthuraj, R. and Srinivas, S., A note on heat transfer to MHD oscillatory flow in an asymmetric wavy channel, International Communications in Heat and Mass Transfer, 37 (2010) pp 1255-1260.
- Muthucumaraswamy, R., Manivannan, K. and Thangaraj,V., Chemical reaction effects on infinite vertical plate with uniform heat flux and variable mass diffusion, International Review of Pure and Applied Mathematics, 3: (2007) pp 263-272.
- Singh, K.D. and Verma, G.N., Three dimensional oscillatory flow through a porous medium with periodic permeability, Z. Angew. Math. Mech., 75: (1995) pp 599-604.
- Gersten, K. and Gross, J.F., Flow and heat transfer along a plane wall with periodic solution, Journal of Applied Mathematics and Physics, 25: (1974) pp 200- 205.
- Singh, K.D., Three dimensional couette flow with transpiration cooling, Z. Angew. Maths. Phys.,50: (1999) pp 661-668.
- Gupta, G.D. and Johari, R., MHD three dimensional flow past a porous plate, Indian J. Pure Appl. Math., 32(3): (2001) pp 377-386.
- Singh, K.D., Rakesh, S. and Khem, C., Three dimensional fluctuating flow and heat transfer through a porous medium with variable permeability, ZAMM, 80 : (2000) pp 473-480.
- M.M. Rashidi, S.M. Sadri, Solution of the Laminar Viscous Flow in a Semi-Porous Channel in the Presence of a Uniform Magnetic Field by Using the Differential Transform Method, Int. J. Contemp. Math. Sciences 5 (15) (2010) pp 711-720.
- M.M. Rashidi, E. Erfani, A new analytical study of MHD stagnation-point flow in porous media with heat transfer, Computers and Fluids 40 (2011) pp 172-178.
- Jain, N.C. and Gupta, P.,Three dimensional free convection Couette flow with transpiration cooling, Journal of Zhejiang Univ. Science A, 7(3): (2006) pp 340-346.
- Singh, K.D. and Rakesh, S., MHD three dimensional Couette flow with transpiration cooling, Z. Angew. Math. Mech., 81(10): (2001) pp 715-720.
- Singh, K.D., Gorla, M.G. and Raj, H., Periodic solution of oscillatory Couette flow through porous medium in rotating system, Indian J. Pure Appl. Math., 36(3): (2005) pp 151-159.
- Raptis, A. and Perdikis, C., Oscillatory flow through a porous medium by the presence of free convective flow, International Journal Engineering. Sciences, 23(1) (1985) pp 51-55.
- Mahato, P.K. and Maiti, D.K., Unsteady free convective flow and mass transfer in a rotating porous medium, Indian Journal of Technology, 26: (1988) pp 255-259.
- Perry, E.D., 1963, Chemical Engineers Handbook, (4th Edn.), McGraw-Hill Book Company, New York.