An Unsteady Free Convection Slip Flow along a Vertical Plate Embedded in a Porous Medium with Effects of Hall Current and Thermal Radiation | Open Access Journals

ISSN ONLINE(2319-8753)PRINT(2347-6710)

An Unsteady Free Convection Slip Flow along a Vertical Plate Embedded in a Porous Medium with Effects of Hall Current and Thermal Radiation

S.Anuradha1, D.Subbulakshmi2
  1. Professor & Head, PG & Research Department of Mathematics, Hindusthan College of Arts & Science, Coimbatore, Tamilnadu, India1
  2. Assistant Professor, Department of Mathematics, Dr.NGP Institute of Technology, Coimbatore, Tamilnadu, India2
Related article at Pubmed, Scholar Google

Visit for more related articles at International Journal of Innovative Research in Science, Engineering and Technology

Abstract

An unsteady free convection slip flow with Heat and Mass transfer effect of viscous incompressible fluid through a porous medium in a rotating system with Hall Effect, thermal radiation and chemical reaction have been studied. The plate moves with constant velocity U0 in its own plane. A perturbation technique is used to obtain the expressions for velocity, temperature and concentration. Expressions for Skin friction, Nusselt number and Sherwood number are also derived

Keywords

Hall current, Thermal radiation, porous medium, chemical reaction

INTRODUCTION

Magneto hydrodynamic (MHD) free convection flow through porous media are very important particularly in the fields of petroleum technology for the flow of oil through porous rocks, in chemical engineering for the purification and filtration processes and in the cases like drug permeation through human skin. Free convection arises in the fluid when temperature and concentration changes cause density variation leading to buoyancy forces acting on the fluid elements. The mass transfer differences affect the rate of heat transfer. Recently, it is of great interest to study the effect of magnetic field on the temperature distribution and heat transfer when the fluid is not only an electrical conductor but also when it is capable of emitting and absorbing thermal radiation. The radiative free convective flows are encountered in countless industrial and environment processes e.g. heating and cooling chambers, fossil fuel combustion energy processes, evaporation from large open water reservoirs, astrophysical flows, solar power technology and space vehicle reentry. The radiative heat transfer plays an important role in manufacturing industries for the design of reliable equipment. This chapter deals with the effects of hall current, thermal radiation, chemical reaction, soret number etc., on an unsteady, rotating, free convection slip flow past an infinite vertical porous plate, embedded in a porous medium, with constant heat and mass flux at the plate. The analytical expressions for the velocity, temperature and concentration are obtained using perturbation technique. The effects on velocity, temperature and concentration are discussed through graphs.

II. RELATED WORK

Sivaiah et al. [1] and Das and Jana [2] have studied heat and mass transfer effects on MHD free convection flow past a vertical plate with different boundary conditions. Chaudhary and Jain [3] have also studied combined heat and mass transfer effects on MHD free convection flow past an oscillating plate. Aboeldahab et al. [4] and Shit [5] studied the effects of Hall currents on MHD free convection flow with mass transfer. Acharya et al. [6] studied the magnetic effects on the free convection and mass transfer flow through porous medium. The no slip boundary condition is valid only when particles close to the surface do not move with the flow; however this is only true macroscopically. Effect of Hall currents, with slip conditions at the boundary have been studied by Abbas and Asghar [7] and Jain and Gupta [8]. Jain and Singh [9], have observed Hall and thermal radiative effects on an unsteady rotating free convection slip flow. Anjalidevi and Kandasamy [11] investigated the effect of chemical reaction on the flow in the presence of heat transfer and magnetic field. Chemical reaction effects on heat and mass transf er in laminar boundary layer flow have been studied by several scholars e.g. Kandasamy et al. [12], Afify [10], Takhar et al. [14] and Mansour et al. [13] etc.

III. MATHEMATICAL FORMULATION

image
image
image

V. RESULTS AND CONCLUSION

Increasing values of Sc, Pr, Kr results in decrease in velocity. Figure 6, velocity (u) profiles are plotted against z. We fix t = 1, Kr=0.2, Pr=0.71 and Sc = 0.61. It is observed that on increasing K, Gr, Gc and So, velocity increases. Temperature profiles are plotted against z in Figure 4 by fixing t = 1. From the figure we observe that as we increase the radiation our temperature drops as heat is being radiated while the effect of absorption is obvious, the temperature rises. Also, increase is H, which is source parameter, decreases the temperature. In Figure 5, effects of different parameters are studied on concentration (C), profiles are plotted against z fixing t = 1. We observe that on increasing the Schmidt number (Sc) our concentration drops, while concentration rises on increasing the Soret number (So) and H. It’s interesting to note that when we increase R concentration decreases.
image
image

References

[1] Sivaiah, M., Nagarajan, A.S. and Reddy, P.S., “Heat and mass transfer effects on MHD free convective flow past a vertical porous plate”, The ICFAI University J. of computational Mathematics Vol II no.2, pp.14-21, 2009.

[2] Das, K. and Jana, S., “Heat and mass transfer effects on unsteady MHD free convection flow near a moving vertical plate in a porous medium” Bull. Sco. Math. Vol 17, pp 15-32, 2010.

[3] Chaudhary, R.C. and Jain, A.,” Combined heat and mass transfer effects on MHD free convection flow past oscillating plate embedded in aporous medium”. Rom. J. Phys.Vol 52 no (5-7),pp 505-524, 2007.

[4] Aboeldahabn, E. M and Ebarbary, Elsayed, M. E.,” Hall current effect on Magnetohydrodynamic free convection flow past a semi infinite vertical plate with mass transfer” Int. J. of Eng. Sci. 39 (14), pp.1641-1652., 2001

[5] Shit, G.C.,”Halll effects on MHD free convection flow and mass transfer over a stretching sheet” Int. J. of Appl. Math. And Mech. 5 (8), pp22- 38. 2009

[6] Acharya, M., Dash, G.C. and Singh, L.P”Magnetic field effects on the free convection and mass transfer flow through a porous medium with constant suction and constant heat flux” Ind. J. Pure, Appl. Math. Vol 31,pp 1-18. 2000.

[7] Abbas, Z. and Asghar, S.,” Effect of Hall current and heat transfer on the flow in a porous medium with slip conditions” J. of porous media, 10 (1), pp 35-50. 2007.

[8] Jain, N.C. and Gupta; P.,” Hall effects on unsteady free convection slip flow in a rotating fluid along a porous vertical surface bounded by a porous medium.”, Int. J. of Appl. Mech. And Eng. 12 (3), pp 609-627., 2007

[9] Jain, N.C., and Singh H.,”Hall and thermal radiation effects on an unsteady rotating free convection slip flow along a porous vertical moving plate” Int. J. of Appl. Mech. And Eng. 17 (1), pp 53-70, 2012

[10] Afify A A “ Effects of radiation and chemical reaction on MHD free convective flow past a vertical isothermal cone”, Canadian Journal of Physics 82, pp4 47-458,2004

[11] Anjalidevi S P, Kandasamy R “Effects of chemical reaction heat and mass transfer on MHD flow past a semi-infinite plate”, Z. Angew. Mathematics andMechanics 80,pp 697-701,2000.

[12] Kandasamy R, Periasamy K, Sivagnana Prabhu K K ,”Effects of chemical reactions heat and mass transfer along a wedge with heat source in the presence of suction/injection” International Journal of Heat Mass Transfer 48,pp 1 388-1393,2005.

[13] Mansour M A, El-Anssary N F, Aly A M,”Effects of chemical reaction and viscous dissipation on MHD natural convection flows saturated in porousmedia”, International Journal of Applied Mathematics and Mechanics 4(2),pp 60-76.2008

[14] Takhar H S, Chamkha A J , Nath G (2000),”Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species” ternational Journal of Engineering and Science 38,pp 1303-1306,2000.

[15] England, W.G. and Emery, A.F.,”Thermal radiation Effects on the laminar free convection boundary layer of an absorbing on the laminar free convection boundary layer of an absorbing gas”, J. Heat Transf. 91, pp 37-44,, 1969.

[16] Choudhary D et.,al., “Effects of hall current and thermal radiation on an unsteady free convection slip flow along a vertical plate embedded in
a porous medium with constant heat and mass flux”, Applied Mathematics and Physics, V- 1,No 2, pp.11-26.2013.