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Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation. (English) Zbl 1145.76469

Summary: An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] Sakiadis, B.C., Boundary layer behavior on continuous solid surface: I - boundary layer equations for two dimensional and axisymmetric flow, Aiche. j., 7, 26-28, (1961)
[2] Sakiadis, B.C., Boundary layer behavior on continuous solid surface: II - boundary layer on a continuous flat surface, Aiche. j., 7, 221-225, (1961)
[3] Crane, L.J., Flow past a stretching sheet, Zamp, 21, 645-647, (1970)
[4] Tsou, F.K.; Sparrow, E.M.; Goldstein, R.J., Flow and heat transfer in the boundary layer on a continuous moving surface, Int. J. heat mass transfer, 10, 219-223, (1967)
[5] Gupta, P.S.; Gupta, A.S., Heat and mass transfer on a stretching sheet with suction or blowing, Canda. J. chem. engng., 55, 744-746, (1977)
[6] Grubka, L.J.; Bobba, K.M., Heat transfer characteristics of a continuous stretching surface with variable temperature, ASME J. heat transfer, 107, 248-250, (1985)
[7] Rajagopal, K.R.; Na, T.Y.; Gupta, A.S., Flow of a viscoelastic fluid over a stretching sheet, Rheol. acta, 23, 213-215, (1984)
[8] Andersson, H.I., MHD flow of a viscoelastic fluid past a stretching surface, Acta mech., 95, 227-230, (1992) · Zbl 0753.76192
[9] Chiam, T.C., Heat transfer with variable conductivity in a stagnation-point flow towards a stretching sheet, Int. commun. heat mass transfer, 23, 239-248, (1996)
[10] Chiam, T.C., Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet, Acta mech., 129, 63-72, (1998) · Zbl 0914.76026
[11] Chen, C.K.; Char, M.I., Heat transfer of a continuous stretching surface with suction or blowing, J. math. anal. appl., 135, 568-580, (1988) · Zbl 0652.76062
[12] Vajravelu, K.; Rollins, D., Heat transfer in electrically conducting fluid over a stretching surface, Int. J. non-linear mech., 27, 2, 265-277, (1992) · Zbl 0775.76218
[13] Vajravelu, K.; Nayfeh, J., Convective heat transfer at a stretching sheet, Acta mech., 96, 47-54, (1993) · Zbl 0775.76179
[14] Sarpakaya, T., Flow of non-Newtonian fluids in a magnetic field, Aiche j., 7, 324-328, (1961)
[15] Siddappa, B.; Subhas, A., Non-Newtonian flow past a stretching plate, Zamp, 36, 890-892, (1985) · Zbl 0591.76011
[16] Lawrence, P.S.; Rao, B.N., The non-uniqueness of the MHD flow of a viscoelastic fluid past a stretching sheet, Acta mech., 112, 223-228, (1995) · Zbl 0856.76097
[17] Abel, M.S.; Joshi, A.; Sonth, R.M., Heat transfer in MHD viscoelastic fluid flow over a stretching surface, Zamm, 81, 691-698, (2001) · Zbl 0997.80010
[18] Cortell, R., Flow and heat transfer of an electrically conducing fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field, Int. J. heat mass transfer, 49, 1851-1856, (2006) · Zbl 1189.76778
[19] Kays, W.M.; Grawford, M.E., Convection heat and mass transfer, (1980), Pergamon Oxford
[20] Subhas, A.; Prasad, K.V.; Mahaboob, Ali, Buoyancy force and thermal radiation effects in MHD boundary layer viscoelastic flow over continuously moving stretching surface, Int. J. therm. sci., 44, 465-476, (2005)
[21] Abo-Eladahab, Emad M.; El Aziz, Mohamed A., Blowing/suction effect on hydromagnetic heat transfer by mixed convection from an inclined continuously stretching surface with internal heat generation/absorption, Int. J. therm. sci., 43, 709-719, (2004)
[22] Raptis, A., Technical note: flow of a micropolar fluid past continuously moving plate by the presence of radiation, Int. J. heat mass transfer, 41, 2865-2866, (1998) · Zbl 0922.76050
[23] Raptis, A., Radiation and viscoelastic flow, Int. comm. heat mass transfer, 26, 6, 889-895, (1999)
[24] Raptis, A.; Perdikis, C., Viscoelastic flow by the presence of radiation, Zamm, 78, 277-279, (1998) · Zbl 0901.76002
[25] Siddheshwar, P.G.; Mahabaleshwar, U.S., Effect of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet, Int. J. non-linear mech., 40, 807-820, (2005) · Zbl 1349.76906
[26] Khan, S.K., Heat transfer in a viscoelastic fluid flow over a stretching surface with heat source/sink, suction/blowing and radiation, Int. J. heat mass transfer, 49, 628-639, (2006) · Zbl 1189.76055
[27] Beard, D.W.; Walters, K., Elastico-viscous boundary-layer flows I. two-dimensional flow heat stagnation point, Proc. Cambridge philos. soc., 60, 667-674, (1964) · Zbl 0123.41601
[28] Rajagopal, K.R., On the boundary conditions for fluids of the differential type, (), 273-278 · Zbl 0846.35107
[29] Chang, W.D., The non-uniqueness of the flow of a viscoelastic fluid over a stretching sheet, Quart. appl. math., 47, 20, 365-366, (1989) · Zbl 0683.76012
[30] Rao, B.N., Technical note: flow of a fluid of second grade over a stretching sheet, Int. J. non-linear mech., 93, 53-61, (1992)
[31] Brewster, M.Q., Thermal radiative transfer properties, (1972), John Wiley and Sons
[32] Subhas, A.; Veena, P., Viscoelastic fluid flow and heat transfer in a porous medium over a stretching sheet, Int. J. nonlinear mech., 33, 531-540, (1998) · Zbl 0907.76007
[33] Abramowitz, M.; Stegun, L.A., Handbook of mathematical functions, 55, (1972), National Bureau of Standards/Amer. Math. Soc. Providence, RI · Zbl 0543.33001
[34] Ali, M.E., On thermal boundary layer on a power-law stretched surface with suction and injection, Int. J. heat fluid flow, 16, 4, 280-290, (1995)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.