Effects of Hall Current on Hydromagnetic Free Convection Flow with Heat and Mass Transfer of a Heat Absorbing Fluid Past an Impulsively Moving Vertical Plate with Ramped Temperature

Effects of Hall Current on Hydromagnetic Free Convection Flow with Heat and Mass Transfer of a Heat Absorbing Fluid Past an Impulsively Moving Vertical Plate with Ramped Temperature

Seth G.S. Sarkar S. Mahato G.K. 

Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India

Page: 
85-95
|
DOI: 
https://doi.org/10.18280/ijht.310111
Received: 
N/A
|
Accepted: 
N/A
|
Published: 
30 June 2013
| Citation

OPEN ACCESS

Abstract: 

Effects of Hall current on unsteady hydromagnetic free convection flow with heat and mass transfer of an electrically conducting, viscous, incompressible and time dependent heat absorbing fluid past an impulsively moving vertical plate in a porous medium, in the presence of thermal diffusion is studied. Exact solution of governing equations is obtained in closed form by Laplace Transform technique. Exact solution is also obtained in case of unit Prandtl number and unit Schmidt number. Expressions for skin friction due to primary and secondary flows and Nusselt number for both ramped temperature and isothermal plates are also derived. Expression for Sherwood number is also derived. The numerical values of primary and secondary fluid velocities, fluid temperature, and fluid concentration are displayed graphically whereas that of skin friction and Nusselt number are presented in tabular form for various values of pertinent flow parameters. Free convection flow with heat and mass transfer near a ramped temperature plate is compared with free convection flow with heat and mass transfer near an isothermal plate.

  References

[1] Bejan, A. (1993) Convection Heat Transfer, p. 176. 2nd ed., Wiley, New York

[2] Gebhart, B., Pera, L.The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion (1971) International Journal of Heat and Mass Transfer, 14 (12), pp. 2025-2050. doi: 10.1016/0017-9310(71)90026-3

[3] Pera, L., Gebhart, B. Natural convection boundary layer flow over horizontal and slightly inclined surfaces (1973) International Journal of Heat and Mass Transfer, 16 (6), pp. 1131-1136,IN7-IN8,1137-1146. doi: 10.1016/0017-9310(73)90126-9

[4] Chen, T.S., Yuh, C.F., Moutsoglou, A. Combined heat and mass transfer in mixed convection along vertical and inclined plates (1980) International Journal of Heat and Mass Transfer, 23 (4), pp. 527-537. doi: 10.1016/0017-9310(80)90094-0

[5] Raptis, A.A.Free convection and mass transfer effects on the oscillatory flow past an infinite moving vertical isothermal plate with constant suction and heat sources (1982) Astrophysics and Space Science: An International Journal of Astronomy, Astrophysics and Space Science, 86 (1), pp. 43-53. doi: 10.1007/BF00651828

[6] Bejan, A., Khair, K.R. Heat and mass transfer by natural convection in a porous medium (1985) International Journal of Heat and Mass Transfer, 28 (5), pp. 909-918. doi: 10.1016/0017-9310(85)90272-8

[7] Jang, J.Y., Chang, W.J. Buoyancy-induced inclined boundary layer flow in a porous medium resulting from combined heat and mass buoyancy effects (1988) International Communications in Heat and Mass Transfer, 15 (1), pp. 17-30. doi: 10.1016/0735-1933(88)90003-6

[8] Trevisan, O.V., Bejan, A. Mass and heat transfer by natural convection in a vertical slot filled with porous medium (1986) International Journal of Heat and Mass Transfer, 29 (3), pp. 403-415. doi: 10.1016/0017-9310(86)90210-3

[9] Lai, F.C., Kulacki, F.A. Non-darcy mixed convection along a vertical wall in a saturated porous medium (1991) Journal of Heat Transfer, 113 (1), pp. 252-255. doi: 10.1115/1.2910537

[10] Nakayama, A., Hossain, M.A. An integral treatment for combined heat and mass transfer by natural convection in a porous medium (1995) International Journal of Heat and Mass Transfer, 38 (4), pp. 761-765. doi: 10.1016/0017-9310(95)93012-7

[11] Yih, K.A. The effect of transpiration on coupled heat and mass transfer in mixed convection over a vertical plate embedded in a saturated porous medium (1997) International Communications in Heat and Mass Transfer, 24 (2), pp. 265-275. doi: 10.1016/S0735-1933(97)00012-2

[12] Chamkha, A.J., Takhar, H.S., Soundalgekar, V.M. Radiation effects on free convection flow past a semi-infinite vertical plate with mass transfer (2001) Chemical Engineering Journal, 84 (3), pp. 335-342. doi: 10.1016/S1385-8947(00)00378-8

[13] Ganesan, P., Palani, G. Natural convection effects on impulsively started inclined plate with heat and mass transfer (2003) Heat and Mass Transfer/Waerme- und Stoffuebertragung, 39 (4), pp. 277-283. http://www.springer.com.ezproxy3.lhl.uab.edu/sgw/cda/frontpage/0,11855,1-40109-70-1034617-0,00.html doi: 10.1007/s00231-002-0380-1

[14] Hossain, M.A., Mandal, A.C. Mass transfer effects on the unsteady hydromagnetic free convection flow past an accelerated vertical porous plate (1985) Journal of Physics D: Applied Physics, 18 (7), art. no. 003, pp. L63-L69. doi: 10.1088/0022-3727/18/7/003

[15] Jha, B.K.MHD free-convection and mass-transform flow through a porous medium (1991) Astrophysics and Space Science, 175 (2), pp. 283-289.doi: 10.1007/BF00644290

[16] Elbashbeshy, E.M.A. Heat and mass transfer along a vertical plate with variable surface tension and concentration in the presence of the magnetic field (1997) International Journal of Engineering Science, 35 (5), pp. 515-522. 

[17] Chen, C.-H. Combined heat and mass transfer in MHD free convection from a vertical surface with Ohmic heating and viscous dissipation (2004) International Journal of Engineering Science, 42 (7), pp. 699-713.doi: 10.1016/j.ijengsci.2003.09.002

[18] Ibrahim, F.S., Hassanien, I.A., Bakr, A.A. Unsteady magnetohydrodynamic micropolar fluid flow and heat transfer over a vertical porous plate through a porous medium in the presence of thermal and mass diffusion with a constant heat source (2004) Canadian Journal of Physics, 82 (10), pp. 775-790. doi: 10.1139/P04-021

[19] Makinde, O.D., Sibanda, P. Magnetohydrodynamic mixed-convective flow and heat and mass transfer past a vertical plate in a porous medium with constant wall suction (2008) Journal of Heat Transfer, 130 (11), pp. 1-8. http://asmedl.aip.org.ezproxy3.lhl.uab.edu/getpdf/servlet/GetPDFServlet?filetype=pdf&id=JHTRAO000130000011112602000001&idtype=cvips&prog=normal doi: 10.1115/1.2955471

[20] Makinde, O.D. On MHD boundary-layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux (2009) International Journal of Numerical Methods for Heat and Fluid Flow, 19 (3-4), pp. 546-554. doi: 10.1108/09615530910938434

[21] Sharma, P.R., Singh, G., Chamkha, A.J. Steady mixed convection flow of water at 4°c along a non-isothermal vertical moving plate with transverse magnetic field (2012) Int. J. Ind. Math., 4 (3), p. 16. Article ID: IJIM-00260

[22] Olajuwon, B.I. Convection heat and mass transfer in a hydromagnetic flow of a second grade fluid in the presence of thermal radiation and thermal diffusion (2011) International Communications in Heat and Mass Transfer, 38 (3), pp. 377-382.doi: 10.1016/j.icheatmasstransfer.2010.11.006

[23] Eldabe, N.T.M., Elbashbeshy, E.M.A., Hasanin, W.S.A., Elsaid, E.M. Unsteady motion of MHD viscous incompressible fluid with heat and mass transfer through porous medium near a moving vertical plate (2011) Int. J. Energy and Tech., 3 (35), pp. 1-11.

[24] Vajravelu, K., Nayfeh, J. Hydromagnetic convection at a cone and a wedge (1992) International Communications in Heat and Mass Transfer, 19 (5), pp. 701-710. doi: 10.1016/0735-1933(92)90052-J

[25] Crepeau, J.C., Clarksean, R. Similarity solutions of natural convection with internal heat generation (1997) Journal of Heat Transfer, 119 (1), pp. 183-185. doi: 10.1115/1.2824086

[26] Mckenzie, D.P., Roberts, J.M., Weiss, N.O. Convection in the earth's mantle: Towards a numerical simulation (1974) Journal of Fluid Mechanics, 62 (3), pp. 465-538. doi: 10.1017/S0022112074000784

[27] Baker Jr., Louis, Faw, Richard E., Kulacki, Francis A. Postaccident heat removal - 1. heat transfer within an internally heated, nonboiling liquid layer. (1976) Nuclear Science and Engineering, 61 (2), pp. 222-230. doi: 10.13182/NSE76-A27355

[28] Delichatsios, M.A. (1988) Air Entrainment into Buoyant Jet Flames and Pool Fires in Dinenno, pp. 306-314. P. J, et al. The SFPA Handbook of Fire Protection Engineering, NFPA Publications, M. A. Quincy 

[29] Westphal, B.R., Keiser, D.D., Rigg, R.H., Loug, D.V. Production of metal waste forms from spent nuclear fuel treatment (1994) DOE Spent Nuclear Fuel Conference, pp. 288-294.Salt Lake City, UT

[30] Sparrow, E.M., Cess, R.D. The effect of a magnetic field on free convection heat transfer (1961) International Journal of Heat and Mass Transfer, 3(4), pp. 267-274. doi: 10.1016/0017-9310(61)90042-4

[31] Chamkha, A.J., Khaled, A.-R.A. Hydromagnetic combined heat and mass transfer by natural convection from a permeable surface embedded in a fluid-saturated porous medium (2000) International Journal of Numerical Methods for Heat and Fluid Flow, 10 (5), pp. 455-476. 

[32] Chamkha, A.J., Khaled, A.A. Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption (2001) Heat and Mass Transfer/Waerme- und Stoffuebertragung, 37 (2-3), pp. 117-123.doi: 10.1007/s002310000131

[33] Kamel, M.H. Unsteady MHD convection through porous medium with combined heat and mass transfer with heat source/sink (2001) Energy Conversion and Management, 42 (4), pp. 393-405. doi: 10.1016/S0196-8904(00)00067-4

[34] Chamkha, A.J. Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption (2004) International Journal of Engineering Science, 42 (2), pp. 217-230. doi: 10.1016/S0020-7225(03)00285-4

[35] Hayday, A.A., Bowlus, D.A., McGraw, R.A. Free convection from a vertical flat plate with step discontinuities in surface temperature (1967) Journal of Heat Transfer, 89 (3), pp. 244-249. doi: 10.1115/1.3614371

[36] Kelleher, M. Free convection from a vertical plate with discontinuous wall temperature (1971) Journal of Heat Transfer, 93 (4), pp. 349-356. doi: 10.1115/1.3449830

[37] Kao, T.-T. Laminar free convective heat transfer response along a vertical flat plate with step jump in surface temperature (1975) Letters in Heat and Mass Transfer, 2 (5), pp. 419-428. doi: 10.1016/0094-4548(75)90008-9

[38] Lee, S., Yovanovich, M.M. Laminar natural convection from a vertical plate with a step change in wall temperature (1991) Journal of Heat Transfer, 113 (2), pp. 501-504. doi: 10.1115/1.2910591

[39] Chandran, P., Sacheti, N.C., Singh, A.K. Natural convection near a vertical plate with ramped wall temperature (2005) Heat and Mass Transfer/Waerme- und Stoffuebertragung, 41 (5), pp. 459-464. doi: 10.1007/s00231-004-0568-7

[40] Seth, G.S., Ansari, M.S. MHD Natural convection flow past an impulsively moving vertical plate with ramped wall temperature in the presence of thermal diffusion with heat absorption (2010) Int. J. Appl. Mech. Eng., 15, pp. 199-215.

[41] Seth, G.S., Nandkeolyar, R., Ansari, M.S. Effect of rotation on unsteady hydromagnetic natural convection flow past an impulsively moving vertical plate with ramped temperature in a porous medium with thermal diffusion and heat absorption (2011) Int. J. Appl. Math. Mech., 7, pp. 52-69. 

[42] Takhar, H.S., Ram, P.C. Free convection in hydromagnetic flows of a viscous heat-generating fluid with wall temperature oscillation and Hall currents (1991) Astrophysics and Space Science, 183 (2), pp. 193-198. doi: 10.1007/BF00637718

[43] Seth, G.S., Mahato, G.K., Sarkar, S. Effects of hall current on hydromagnetic natural convection flow of a heat absorbing fluid past an impulsively moving vertical plate with ramped temperature (2012) Int. J. Of Appl. Math. Res., 1 (4), pp. 462-486. 

[44] Meyer, R.C. Reducing aerodynamic heat transfer rates by magnetohydrodynamic techniques (1958) J. Aero/Space Sci., 25, pp. 561-572. 

[45] Cramer, K.R., Pai, S.I. (1973) Magnetofluid Dynamics for Engineers and Applied Plysicists. McGraw Hill Book Company, New York