×

Variable viscosity on magnetohydrodynamic fluid flow and heat transfer over an unsteady stretching surface with Hall effect. (English) Zbl 1195.76438

Summary: The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible, and electrically conducting fluid past a semi-infinite unsteady stretching sheet is analyzed numerically. The problem was studied under the effects of Hall currents, variable viscosity, and variable thermal diffusivity. Using a similarity transformation, the governing fundamental equations are approximated by a system of nonlinear ordinary differential equations. The resultant system of ordinary differential equations is then solved numerically by the successive linearization method together with the Chebyshev pseudospectral method. Details of the velocity and temperature fields as well as the local skin friction and the local Nusselt number for various values of the parameters of the problem are presented. It is noted that the axial velocity decreases with increasing the values of the unsteadiness parameter, variable viscosity parameter, or the Hartmann number, while the transverse velocity increases as the Hartmann number increases. Due to increases in thermal diffusivity parameter, temperature is found to increase.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
80A20 Heat and mass transfer, heat flow (MSC2010)

Software:

Matlab
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Crane LJ: Flow past a stretching plate.Zeitschrift für Angewandte Mathematik und Physik 1970,21(4):645-647. 10.1007/BF01587695 · doi:10.1007/BF01587695
[2] Dutta BK, Roy P, Gupta AS: Temperature field in flow over a stretching sheet with uniform heat flux.International Communications in Heat and Mass Transfer 1985,12(1):89-94. 10.1016/0735-1933(85)90010-7 · doi:10.1016/0735-1933(85)90010-7
[3] Grubka LJ, Bobba KM: Heat transfer characteristic of a continuous surface with variabl temperature.Journal of Heat Transfer 1985, 107: 248-255. 10.1115/1.3247387 · doi:10.1115/1.3247387
[4] Elbashbeshy EMA: Heat transfer over a stretching surface with variable surface a heat flux.Journal of Physics D 1998, 31: 1951-1954. 10.1088/0022-3727/31/16/002 · doi:10.1088/0022-3727/31/16/002
[5] Chen CK, Char MI: Heat transfer of a continuous, stretching surface with suction or blowing.Journal of Mathematical Analysis and Applications 1988,135(2):568-580. 10.1016/0022-247X(88)90172-2 · Zbl 0652.76062 · doi:10.1016/0022-247X(88)90172-2
[6] Gupta PS, Gupta AS: Heat and mass transfer on a stretching sheet with suction and blowing.Canadian Journal of Chemistry 1977, 55: 744-746. 10.1002/cjce.5450550619 · doi:10.1002/cjce.5450550619
[7] Elbashbeshy EMA, Bazid MAA: Heat transfer over an unsteady stretching surface with internal heat generation.Applied Mathematics and Computation 2003,138(2-3):239-245. 10.1016/S0096-3003(02)00106-6 · Zbl 1056.76026 · doi:10.1016/S0096-3003(02)00106-6
[8] Abd El-Aziz M: Radiation effect on the flow and heat transfer over an unsteady stretching sheet.International Communications in Heat and Mass Transfer 2009,36(5):521-524. 10.1016/j.icheatmasstransfer.2009.01.016 · doi:10.1016/j.icheatmasstransfer.2009.01.016
[9] Mukhopadyay S: Effect of thermal radiation on unsteady mixed convection flow and heat treansfer over a porous stretching surface in porous medium.International Journal of Heat and Mass Transfer 2009, 52: 3261-3265. 10.1016/j.ijheatmasstransfer.2008.12.029 · Zbl 1167.80352 · doi:10.1016/j.ijheatmasstransfer.2008.12.029
[10] Shateyi, S.; Motsa, SS, Thermal radiation effects on heat and mass transfer over an unsteady stretching surface, No. 2009, 13 (2009) · Zbl 1191.80029
[11] Seddeek MA: The effect of variable viscosity on hyromagnetic flow and heat transfer past a continuously moving porous boundary with radiation.International Communications in Heat and Mass Transfer 2000,27(7):1037-1047. 10.1016/S0735-1933(00)00183-4 · doi:10.1016/S0735-1933(00)00183-4
[12] Seddeek MA: Effects of radiation and variable viscosity on a MHD free convection flow past a semi-infinite flat plate with an aligned magnetic field in the case of unsteady flow.International Journal of Heat and Mass Transfer 2002, 45: 931-935. 10.1016/S0017-9310(01)00189-2 · Zbl 0991.76578 · doi:10.1016/S0017-9310(01)00189-2
[13] Dandapat BS, Santra B, Vajravelu K: 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 2007,50(5-6):991-996. 10.1016/j.ijheatmasstransfer.2006.08.007 · Zbl 1124.80317 · doi:10.1016/j.ijheatmasstransfer.2006.08.007
[14] Mukhopadhyay S: Unsteady boundary layer flow and heat transfer past a porous stretching sheet in presence of variable viscosity and thermal diffusivity.International Journal of Heat and Mass Transfer 2009,52(21-22):5213-5217. 10.1016/j.ijheatmasstransfer.2009.04.013 · Zbl 1176.80029 · doi:10.1016/j.ijheatmasstransfer.2009.04.013
[15] Mahmoud MAA: Thermal radiation effect on unsteady MHD free convection flow past a vertical plate with temperature-dependent viscosity.Canadian Journal of Chemical Engineering 2009,87(1):47-52. · doi:10.1002/cjce.20135
[16] Tsai R, Huang KH, Huang JS: Flow and heat transfer over an unsteady stretching surface with non-uniform heat source.International Communications in Heat and Mass Transfer 2008,35(10):1340-1343. 10.1016/j.icheatmasstransfer.2008.07.001 · doi:10.1016/j.icheatmasstransfer.2008.07.001
[17] Abo-Eldahab EM, Abd El Aziz M: Hall curent and Ohmic heating effects on mixed convection boundary layer flow of a micropolar fluid from a rotating cone with power-law variation in surface in surface temperature.International Communications in Heat and Mass Transfer 2004,31(5):751-762. 10.1016/S0735-1933(04)00062-4 · doi:10.1016/S0735-1933(04)00062-4
[18] Abo-Eldahab EM, El-Aziz MA, Salem AM, Jaber KK: Hall current effect on MHD mixed convection flow from an inclined continuously stretching surface with blowing/suction and internal heat generation/absorption.Applied Mathematical Modelling 2007,31(9):1829-1846. 10.1016/j.apm.2006.06.017 · Zbl 1167.76381 · doi:10.1016/j.apm.2006.06.017
[19] Salem AM, Abd El-Aziz M: Effect of Hall currents and chemical reaction on hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption.Applied Mathematical Modelling 2008,32(7):1236-1254. 10.1016/j.apm.2007.03.008 · Zbl 1251.76064 · doi:10.1016/j.apm.2007.03.008
[20] Pal D, Mondal H: Effect of variable viscosity on MHD non-Darcy mixed convective heat transfer over a stretching sheet embedded in a porous medium with non-uniform heat source/sink.Communications in Nonlinear Science and Numerical Simulation 2010,15(6):1553-1564. 10.1016/j.cnsns.2009.07.002 · Zbl 1221.76237 · doi:10.1016/j.cnsns.2009.07.002
[21] Abd El-Aziz M: Flow and heat transfer over an unsteady stretching surface with Hall effect.Meccanica 2010,45(1):97-109. 10.1007/s11012-009-9227-x · Zbl 1184.76906 · doi:10.1007/s11012-009-9227-x
[22] Elbashbeshy EMA, Bazid MAA: Heat transfer over an unsteady stretching surface with internal heat generation.Applied Mathematics and Computation 2003,138(2-3):239-245. 10.1016/S0096-3003(02)00106-6 · Zbl 1056.76026 · doi:10.1016/S0096-3003(02)00106-6
[23] Canuto C, Hussaini MY, Quarteroni A, Zang T: Spectral Methods in Fluid Dynamics, Springer Series in Computational Physics. Springer, New York, NY, USA; 1988:xiv+557. · Zbl 0658.76001 · doi:10.1007/978-3-642-84108-8
[24] Don WS, Solomonoff A: Accuracy and speed in computing the Chebyshev collocation derivative.SIAM Journal on Scientific Computing 1995,16(6):1253-1268. 10.1137/0916073 · Zbl 0840.65010 · doi:10.1137/0916073
[25] Trefethen LN: Spectral Methods in MATLAB, Software, Environments, and Tools. Volume 10. SIAM, Philadelphia, Pa, USA; 2000:xviii+165. · Zbl 0953.68643 · doi:10.1137/1.9780898719598
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.