×

Analytical approach to heat and mass transfer in MHD free convection from amoving permeable vertical surface. (English) Zbl 1335.76055

Summary: An analytical study is performed on heat and mass transfer in MHD-free convection from a moving permeable vertical surface and the results are compared with previous works on this phenomenon to test the validity. The coupled equations of boundary layer are transformed from their non-linear form to ordinary form using similarity transformation and then are solved by a newly developed method, homotopy analysis method. Having different base functions, homotopy analysis method provides us with great freedom in choosing the solution of a nonlinear problem. Solving the boundary layer equations, the effects of different parameters such as magnetic field strength parameter (M), Prandtl number (Pr), Schmidt number (Sc), buoyancy ratio and suction/blowing parameter \((f_{w})\) on velocity, temperature, and concentration profiles are taken into consideration. Obtained results show that increment of magnetic field strength parameter (M) leads to decrease in velocity profile.
In their note on the present paper, A. Pantokratoras and T. Fang [Math. Methods Appl. Sci. 38, No. 17, 3706–3710 (2015; Zbl 1335.76060)] point out some errors.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)

Citations:

Zbl 1335.76060
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abdelkhalek, Heat and mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique, International Journal for Communications in Nonlinear Science and Numerical Simulation 14 pp 2091– (2009) · doi:10.1016/j.cnsns.2008.06.001
[2] Joneidi, Analytical treatment on Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching hollow cylinder, International Journal for Numerical Methods in Fluids 5 pp 548– (2010) · Zbl 1423.76339
[3] Sakiadis, Boundary layer behavior on continuous solid flat surfaces, AICHE Journal 7 pp 26– (1961) · doi:10.1002/aic.690070108
[4] Tsou, Flow and heat transfer in the boundary layer on a continuous moving surface, International Journal of Heat and Mass Transfer 10 pp 219– (1967) · doi:10.1016/0017-9310(67)90100-7
[5] Erickson, Heat and mass transfer on a moving continuous flat plate with suction or injection, Industrial and Engineering Chemistry Fundamentals 5 pp 19– (1966) · doi:10.1021/i160017a004
[6] Chen, Buoyancy effects in boundary layer adjacent to a continuous, moving horizontal flat plate, Transactions of ASME Journal of Heat Transfer 102 pp 170– (1980) · doi:10.1115/1.3244232
[7] Chakrabarti, Hydromagnetic flow and heat transfer over a stretching sheet, Quarterly of Applied Mathematics 37 pp 73– (1979) · Zbl 0402.76012 · doi:10.1090/qam/99636
[8] Liao, An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate, Communications in Nonlinear Science and Numerical Simulation 11 pp 326– (2006) · Zbl 1078.76022 · doi:10.1016/j.cnsns.2004.09.004
[9] Sparrow, The effect of a magnetic field on free convection heat transfer, International Journal of Heat And Mas Transfer 4 pp 267– (1961) · doi:10.1016/0017-9310(61)90042-4
[10] Wilks, Magnetohydrodynamic free convection flow about a semi-infinite plate at whose surface the heat flux is uniform, Journal of Applied Mathematical Physics 35 pp 34– (1984) · Zbl 0546.76133 · doi:10.1007/BF00945174
[11] Vajravelu, Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream, International Journal of Engineering Science 35 pp 1237– (1997) · Zbl 0907.76084 · doi:10.1016/S0020-7225(97)00031-1
[12] Xu, Analytic solutions of magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate, Journal of Non-Newton Fluid Mechanics 159 pp 46– (2005) · Zbl 1195.76069 · doi:10.1016/j.jnnfm.2005.05.005
[13] Takhar, MHD asymmetric flow past a semi-infinite moving plate, Acta Mechanics 65 pp 287– (1986) · doi:10.1007/BF01176888
[14] Yih, Free convection effect on MHD coupled heat and mass transfer of a moving permeable vertical surface, International Communication in Heat and Mass Transfer 26 (1) pp 95– (1999) · doi:10.1016/S0735-1933(98)00125-0
[15] Liao, On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet, Journal of Fluid Mechanics 488 pp 189– (2003) · Zbl 1063.76671 · doi:10.1017/S0022112003004865
[16] Liao, On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation 147 pp 499– (2004) · Zbl 1086.35005 · doi:10.1016/S0096-3003(02)00790-7
[17] Liao, A new branch of solutions of boundary-layer flows over an impermeable stretched plate, International Journal of Heat And Mass Transfer 48 (12) pp 2529– (2005) · Zbl 1189.76142 · doi:10.1016/j.ijheatmasstransfer.2005.01.005
[18] Liao, An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate, Communications in Nonlinear Science and Numerical Simulation 11 (3) pp 326– (2006) · Zbl 1078.76022
[19] Liao, Analytic solutions of the temperature distribution in Blasius viscous flow problems, Journal of Fluid Mechanics 453 pp 411– (2002) · Zbl 1007.76014 · doi:10.1017/S0022112001007169
[20] Liao, Explicit analytic solution for similarity boundary layer equations, International Journal of Heat and Mass Transfer 47 (1) pp 75– (2004) · Zbl 1045.76008 · doi:10.1016/S0017-9310(03)00405-8
[21] Bararnia, On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium, Communications in Nonlinear Science and Numerical Simulation 14 pp 2689– (2009) · Zbl 1221.76138 · doi:10.1016/j.cnsns.2008.09.018
[22] Ghotbi, Investigation of a Powerful Analytical method into Natural Convection Boundary Layer Flow, Communications in Nonlinear Science and Numerical Simulation 14 pp 2222– (2009) · Zbl 1221.76145 · doi:10.1016/j.cnsns.2008.07.020
[23] Hayat, Analytic solution for MHD flow of a third order fluid in a porous channel, Journal of Computational and Applied Mathematics 214 pp 572– (2008) · Zbl 1144.76059 · doi:10.1016/j.cam.2007.03.013
[24] Hayat, The effect of the slip condition on flows of an Oldroyd 6-constant fluid, Journal of Computational and Applied Mathematics 202 pp 402– (2007) · Zbl 1147.76550 · doi:10.1016/j.cam.2005.10.042
[25] Hayat, A variational analysis of non-Newtonian flow in a rotating system, International Journal of Computational Flud Dynamics 20 pp 157– (2006) · Zbl 1131.76007 · doi:10.1080/10618560600836080
[26] Hayat, Oscillatory solution in rotating flow of a Johnson-Segalman fluid, Zeitschrift Fur Angewandte Mathematik und Mechanik 85 pp 449– (2005) · Zbl 1071.76063 · doi:10.1002/zamm.200310173
[27] Hayat, Peristaltically induced motion of MHD third grade fluid in a deformable tube, Physica A: Statistical Mechanics and its Applications 370 pp 225– (2006) · doi:10.1016/j.physa.2006.02.029
[28] Hayat, Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet, International Journal of Heat and Mass Transfer 50 pp 75– (2007) · Zbl 1104.80006 · doi:10.1016/j.ijheatmasstransfer.2006.06.045
[29] Grubka, Heat transfer characteristics of a continuous stretching surface with variable temperature, Journal of Heat Transfer 107 pp 248– (1985) · doi:10.1115/1.3247387
[30] Joneidi, Analytical treatment of MHD free convective flow and mass transfer over a stretching sheet with chemical reaction, Journal of the Taiwan Institute of Chemical Engineers 41 pp 35– (2010) · doi:10.1016/j.jtice.2009.05.008
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.