Visco-Elastic MHD Mixed Convection Flow in a Vertical Channel with Slip Flow Condition and Radiation Heat

Reena Pathak*, Vikram Singh Kapil and Sudershna Sharma

Swami Vivekanand Govt. College Ghumarwin, Distt. Bilaspur, H. P.

*Corresponding Author E-mail: pathakreena8@gmail.com

ABSTRACT:

This paper investigates the problem of oscillating MHD flow of a visco-elastic, incompressible and electrically conducting fluid in a vertical channel with slip condition on one of the wall of the channel. A magnetic field of uniform strength is applied perpendicular to the plates of the channel. The pressure gradient in the channel oscillates periodically with time. Closed form solutions for the velocity, temperature, sin-friction and the rate of heat transfer are obtained. The results are presented graphically for various values of the visco-elastic parameter γ, the Reynolds number Re, Grushof number Gr, Hartmann number M, Prandtl number Pr, slip flow parameter h and radiation parameter N.

KEYWORDS: Visco-elastic, MHD, Slip flow, Radiation.

INTRODUCTION:

The flow and heat transfer behavior of viscoelastic fluid between parallel plates is of special interest in many engineering fields such as chemical process industries, food preservation, petroleum production and power engineering. In view of these applications, the study of boundary layer behavior has been channelized to visco-elastic fluids. The heat transfer in the forced convection flow of a visco-elastic fluid of Walter model was investigated by Rajagopal [1]. Zhang and Yue [2] studied the mechanism for visco-elastic polymer solution percolating through porous media. The problem of MHD flows has wide range of applications in emerging fields due to an elctro-magnetic field, are relevant to many practical applications in geo-physical and astro-physical situations, the metallurgy industry, cooling of continuous strips and filaments drawn through a quiescent field. The role of thermal radiation is of major importance in engineering areas occurring at high temperatures and knowledge of radiative heat transfer becomes very important in nuclear power plants, gas turbines and the various propulsion devices for aircraft, missiles and space vehicles. The problem of slip-flow regime is very important in this era of modern industrialization. It has numerous applications for example in lubrication of mechanical devices where a thin film of lubricant is attached to the surfaces slipping over one another or when the surfaces are coated with special coatings to minimize the friction between them. Makinde and Osalusi [3] analyzed MHD steady flow in a channel with slip at the permeable boundaries. Hayat et al. [4] discussed the radiation effects on MHD flow of Maxwell fluid in a channel with porous medium. Choudhury and Das [5] analyzed the heat transfer to MHD oscillatory viscoelastic flow in a channel filled with porous medium. Abdelkhaled [6] studied the radiative and dissipation effect on unsteady MHD mixed convection laminar boundary layer flow of an electrically conducting viscous micro polar fluid past an infinite vertical plate. Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space was discussed by Hayat et al. [7]. Singh [8] discussed the hydromagnetic forced convection oscillatory slip flow through porous medium in a vertical channel with thermal radiation. Uwanta et al. [9] analysed MHD convection slip flow with radiation and heat deposition in a channel in a porous medium.

REFERENCES:

[1] K. R. Rajagopal, “On Stokes problem foe non-Newtonian fluid “. Acta Mechanica, 48,1983, 233-239.

[2] L. J. Zhang, and X. A. Yue, “Mechanism for visco-elastic polymer solution percolating through porous media”. Journal of Hydrodynamics Series B, 19(2), 2007, 241-248.

[3] O. D. Makinde and E. Osalusi, “MHD steady flow in a channel with slip at the permeable boundaries”. Rom. J. Phys., 51, 2006, 319-328.

[4] T. Hayat, R. Sajjad, Z. Abbas, M. Sajid, and A. A. Hendi, “Radiation effects on MHD flow of Maxwell fluid in a channel with porous medium”. Int. J. Heat Mass Transfer, 54, 2011, 854-862.

[5] R. Choudhury and U. J. Das, “Heat transfer to MHD oscillatory viscoelastic flow in a channel filled with porous medium”. Hindawi Publishing Corporation, 2012.

[6] M.M. Abdelkhaled, “Radiation and dissipation effect on unsteady MHD micropolar flow past an infinite vertical plate in porous medium with time dependent suction”. Indian J. Phys., 82, 2008, 415-434.

[7] T. Hayat, T. Javed and Z. Abbas, “Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space”. Int. J. of Heat and Mass Transfer, 51, 2008, 4528-4534.

[8] K. D. Singh, “Hydromagnetic forced convection oscillatory slip flow through porous medium in a vertical channel with thermal radiation”. Proc. Indian Natn. Sci. Acad., 77, 2011, 19-30.

[9] I. J. Uwanta, M. Sani, and M. O. Ibrahim, “MHD convection slip fluid flow with radiation and heat deposition in a channel in a porous medium”. Int. J. Computer Applications, 36(2), 2011, 41-48.

[10] A. C. Cogley, W. G. Vinvent and S. E. Giles, “Differential approximation for radiative transfer in a non-gray near equilibrium”. American Institute of Aeronautics and Astronautics, 6, 1968, 551-553.

Received on 19.01.2014 Accepted on 01.02.2014

Int. J. Tech. 4(1): Jan.-June. 2014; Page 77-81