×

The effects of variable fluid properties and magnetic field on the flow of non-Newtonian fluid film on an unsteady stretching sheet through a porous medium. (English) Zbl 1161.76005

The authors investigate the effects of variable viscosity and thermal diffusivity on biviscous non-Newtonian MHD flow thorough a porous medium past an unsteady stretching surface. A transverse uniform magnetic field has been imposed. The governing boundary-layer equations have been reduced to ordinary nonlinear coupled differential equations by using similarity transformations. The variation in viscosity is taken in exponential form, and a linear form is assumed for thermal diffusivity. The coupled nonlinear differential equations have been solved by Chebyshev pseudospectral method. The results compare well with existing data, and the conclusions are interesting.

MSC:

76A05 Non-Newtonian fluids
76S05 Flows in porous media; filtration; seepage
76W05 Magnetohydrodynamics and electrohydrodynamics
76A20 Thin fluid films
76M22 Spectral methods applied to problems in fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Moreau, Magnetohydrodynamics (1990) · doi:10.1007/978-94-015-7883-7
[2] Crane, Flow past a stretching plate, Zeitschrift fur Angewandte Mathematik and Physik 21 pp 645– (1970)
[3] McCormack, Physical Fluid Dynamics (1973) · Zbl 0289.76001
[4] Vleggaar, Laminar boundary-layer behavior on continuous accelerating surfaces, Chemical Engineering Science 32 pp 1517– (1977)
[5] Gupta, Heat and mass transfer on a stretching sheet with suction or blowing, Canadian Journal of Chemical Engineering 55 pp 744– (1977)
[6] Carragher, Heat transfer on a continuous stretching sheet, Zeitschrift fur Angewandte Mathematik and Mechanik 62 pp 564– (1982)
[7] Rajagopal, Flow of a viscoelastic fluid over a stretching sheet, Rheological Acta 23 pp 213– (1984)
[8] Grubka, Heat transfer characteristics of a continuous stretching surface with variable temperature, ASME Journal of Heat Transfer 107 pp 248– (1985)
[9] Jeng, Momentum and heat transfer on a continuous moving surface, ASME Journal of Heat Transfer 108 pp 532– (1986)
[10] Dutta, Cooling of a stretching sheet in a viscous flow, Industrial and Engineering Chemistry Research 26 pp 333– (1987) · Zbl 0619.76002
[11] Chen, Heat transfer of a continuous stretching surface with suction or blowing, Journal of Mathematical Analysis and Applications 135 pp 568– (1988) · Zbl 0652.76062
[12] Laha, Heat transfer characteristics of the flow of an incompressible viscous fluid over a stretching sheet, Wärme- und Stoffübertrag 24 pp 151– (1989)
[13] Dandapat, Flow and heat transfer in a viscoelastic fluid over a stretching sheet, International Journal of Non-linear Mechanics 24 pp 215– (1989) · Zbl 0693.76015
[14] Andersson, Flow of a power-law fluid over a stretching sheet, Stability Application and Analysis in Continuous Media 1 pp 339– (1991)
[15] Afzal, Heat transfer from a stretching surface, International Journal of Heat and Mass Transfer 36 pp 1128– (1993) · Zbl 0764.76011
[16] Wang, Liquid film on an unsteady stretching surface, Quarterly of Applied Mathematics XLVIII pp 601– (1990) · Zbl 0714.76036
[17] Ali, On the thermal boundary on a power-law stretched surface with suction or injection, International Journal of Heat and Fluid Flow 16 pp 280– (1995)
[18] Andersson, Flow of a power-law fluid film on an unsteady stretching surface, Journal of Non-Newtonian Fluid Mechanics 62 pp 1– (1996)
[19] Chiam, Magnetohydrodynamic heat transfer over a nonisothermal stretching sheet, Acta Mechanica 122 pp 169– (1997) · Zbl 0878.76082
[20] Andersson, Heat transfer in a liquid film on an unsteady stretching surface, International Journal of Heat and Mass Transfer 43 pp 69– (2000) · Zbl 1042.76507
[21] Chen, Mixed convection cooling of a heated, continuously stretching surface, Heat and Mass Transfer 36 pp 79– (2000)
[22] Chen, Heat transfer in a power-law fluid film over a unsteady stretching sheet, Heat and Mass Transfer 39 pp 791– (2003)
[23] Dandapat, Thermocapillarity in a liquid film on an unsteady stretching surface, International Journal of Heat and Mass Transfer 46 pp 3009– (2003) · Zbl 1048.76502 · doi:10.1016/S0017-9310(03)00078-4
[24] Dandapat, The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet, International Journal of Heat and Mass Transfer 50 pp 991– (2007) · Zbl 1124.80317
[25] Hassanien, Flow and heat transfer on continuous stretching flat surface moving in a parallel free steam with variable properties, Zeitschrift fur Angewandte Mathematik and Mechanik 79 (11) pp 786– (1999) · Zbl 0959.76019
[26] Elbarbary, Chebyshev finite difference method for the effect of variable viscosity on magneto-micropolar fluid flow with radiation, International Communications in Heat and Mass Transfer 31 pp 409– (2004)
[27] Elbarbary, Chebyshev finite difference method for the effects of variable viscosity and variable thermal conductivity on heat transfer from moving surfaces with radiation, International Journal of Thermal Science 43 pp 889– (2004)
[28] Elbarbary, Flow and heat transfer of a micropolar fluid in an axisymmetric stagnation flow on a cylinder with variable properties and suction, Acta Mechanica 176 pp 213– (2005) · Zbl 1105.76006
[29] Seddeek, The effect of an axial magnetic field on the flow and heat transfer about a fluid underlying the axisymmetric spreading surface with temperature dependent viscosity and thermal diffusivity, Computational Mechanics 39 (4) pp 401– (2007) · Zbl 1175.76162
[30] Salem, Thermal-diffusion and diffusion-thermo effects on convective heat and mass transfer in a visco-elastic fluid flow through a porous medium over a stretching sheet, Communications in Numerical Methods in Engineering 22 pp 955– (2006) · Zbl 1370.76166
[31] Anjali Devi, Effects of chemical reaction, heat and mass transfer on non-linear MHD flow over an accelerating surface with heat source and thermal stratification in the presence of suction or injection, Communications in Numerical Methods in Engineering 19 pp 513– (2003) · Zbl 1112.76499
[32] Zhu, Numerical simulation of two-dimensional transient water driven non-Newtonian fluid flow in porous media, Communications in Numerical Methods in Engineering 18 pp 229– (2002) · Zbl 1154.76354
[33] Hazem, Hydromagnetic flow and heat transfer of a conducting Casson fluid in a rectangular channel, Communications in Numerical Methods in Engineering 22 pp 251– (2006) · Zbl 1098.76074
[34] Nakamura, Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis, Journal of Biomechanical 110 pp 137– (1988)
[35] Slattery, Momentum, Energy and Mass Transfer in Continua (1972)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.