ORIGINAL PAPER

Span-Wise Fluctuating MHD Convective Flow of a Viscoelastic Fluid through a Porous Medium in a Hot Vertical Channel with Thermal Radiation

1

Applied Mathematics, Wexlow, Lower Kaithu, Shimla-171003, India

Online publication date: 2016-09-10

Publication date: 2016-08-01

International Journal of Applied Mechanics and Engineering 2016;21(3):667-681

KEYWORDS

ABSTRACT

An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e.,
T*(y*,z*,t*)=T1+(T2−T1)cos(πz*d−ω*t*)$T^* \left( {y^* ,z^* ,t^* } \right) = T_1 + \left( {T_2} - {T_ 1} \right)\cos \left( {{{\pi z^* } \over d} - \omega ^* t^* } \right)$
. A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.

REFERENCES (52)

3.

Raptis A.A. (1983): Unsteady free convection flow through a porous medium. – Int. J. Engineering. Sci., vol.21, pp.345.

4.

5.

Raptis A.A. and Perdikis C.P. (1985): Oscillatory flow through a porous medium by the presence of free convective flow. – Int. J. Engineering. Sci., vol.23, pp.51-55.

6.

7.

Parsuma T.G., Murthy M.V.R., Ramachryulu N.C.P. and Rao G.V. (2010): Unsteady flow of a viscoelastic fluid through a porous media between two impermeable parallel plates. – J. of Emerging Trends in Engineering and Applied Sciences, vol.1, No.2, pp.220-224.

8.

9.

Rajgopal K.R. (1983): On Stoke’s problem for non-Netonian fluid. – Acta Mech., vol.48 pp.223-239.

10.

11.

Pillai K.M.C., Sai K.S., Swamy N.S., Natraja H.R., Tiwari S.B. and Rao B.N. (2004): Heat transfer in a viscoelastic boundary layer flow through porous medium. – Comput. Mech. vol.34, pp.27-37.

12.

13.

Hossain M.A. and Takhar H.S. (1996): Radiation effect on mixed convection along a vertical plate with uniform surface temperature. – Heat and Mass Transfer, vol.31, pp.243-248.

14.

15.

Rajgopal K., Veena P.H. and Pravin V.K. (2006): Oscillatory motion of an electrically conducting visco-elastic fluid over a stretching sheet in saturated porous medium with suction/blowing. – Mathematical Problem in Engineering, vol.1, pp.1-14.

16.

17.

Singh K.D. (2011): Exact solution of an oscillatory MHD flow in a channel filled with porous medium. – Int. J. Applied Mechanics and Engineering, vol.16, pp.277-283.

18.

19.

Rahman M.M. and Sarkar M.S.A. (2004): Unsteady MHD flow of visco-elastic Oldroyd fluid under time varying body force through a rectangular channel. – Bulletin of Calcutta Mathematical Society, vol.96, pp.463-470.

20.

21.

Singh A.K. and Singh N.P. (1996): MHD flow of a dusty visco-elastic liquid through a porous medium between two inclined parallel plates. – Proceeding of National Academy of Sciences India, vol.66A, pp.143.

22.

23.

Attia Hazem Ali and Karem Mahmoud Ewis (2010): Unsteady MHD Couette flow with heat transfer of a viscoelastic fluid under exponential decaying pressure gradient. – Tankang J. Sci. And Engng., vol.13, pp.359-364.

24.

25.

Choudhary R. and Das U.J. (2012): Heat transfer to MHD oscillatory viscoelastic flow in a channel filled with porous medium. – Physics Research International, 101155/2012/879537.

26.

27.

Makinde O.D. and Mhone P.Y. (2005): Heat transfer to MHD oscillatory flow in a channel filled with porous medium. – Rom. Journ. Phys., vol.50, pp.931-938.

28.

29.

Singh K.D. (2012): Viscoelastic mixed convection MHD oscillatory flow through a porous medium filled in a vertical channel. – Int. J. of Phy. And Math. Sci., vol.3, pp.194-205.

30.

31.

Singh K.D. (2013): Effect of slip condition on viscoelastic MHD oscillatory forced convection flow in a vertical channel with heat radiation. – Int. J. of Appl. Mech. and Engng., vol.18, No.4, pp.1237-1248.

32.

33.

Malikov G.K., Lovanov D.L., Malikov K.Y., Lisienko G.V., Viskanta R. and Fedorov A.G. (2001): Direct flame impingement heating for rapid thermal materials processing. – Int. J. Heat and Mass Transfer, vol.44, pp.1751-1758.

34.

35.

Fedorov A.G., Lee K.H. and Viskanta R. (1998): Inverse optimal design of the radiant heating in materials processing and manufacturing. – J. Materials Engineering and Performance, vol.7, pp.719-726.

36.

37.

Lentes F.T. and Siedow N. (1999): Three-dimensional radiative heat transfer in glass cooling processes. – Glass Sci. Technology: Glastechnische Berichte, vol.72, No.6, pp.188-196.

38.

39.

Singh K.D. (1992): Unsteady free convection flow past a hot vertical porous plate with variable temperature. – Proc. Indian Natn. Sci. Acad., vol.58, pp.537-544.

40.

41.

Singh K.D. and Khem Chand (2000): Unsteady free convective MHD flow past a vertical porous plate with variable temperature. – Proc. Nat. Acad. Sci. India, vol.70, pp.49-58.

42.

43.

Sumathi K., Anuradha S. and Arunachalam T. (2011): Heat and mass transfer in an unsteady three dimensional mixed convection flow past an infinite vertical porous plate with cosinusoidally fluctuating temperature. – International J. Engineering Science and Technology, vol.3, pp.8569-8578.

44.

45.

Kumar R. and Singh K.D. (2011): Unsteady MHD flow of radiating and reacting fluid past a vertical porous plate with cosinusoidally fluctuating temperature. – International J. Appl. Math. and Mech., vol.7, pp.19-35.

46.

47.

Coleman B.D. and Noll W. (1960): An approximation theorem for functional, with applications in continuum mechanics. – Archive for Rational Mechanics and Analysis, vol.6, pp.355-370.

48.

49.

Markovitz H. and Coleman B.D. (1964): Incompressible second order fluids. – Advances in Applied Mechanics, vol.8, pp.69-101.

50.

51.

Raptis A.A., Perdikis C. and Leontitsis K. (2003): Effects of radiation in an optically thin gray gas flowing past a vertical infinite plate in the presence of a magnetic field. – Heat and Mass Transfer, vol.39, pp.771-773. 10.1007/s00231-002-0317-8.

52.

Share

RELATED ARTICLE

You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.