×

Group method analysis of magneto-elastico-viscous flow along a semi-infinite flat plate with heat transfer. (English) Zbl 1161.76605

Summary: The group theoretic method is applied for solving problem of the flow of an elastico-viscous liquid past an infinite flat plate in the presence of a magnetic field normal to the plate. The application of one-parameter transformation group reduces the number of independent variables, by one, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate corresponding conditions. Numerical solution of the velocity field and heat transfer have been obtained. The effect of the magnetic parameter M on velocity field, shear stress, temperature fields and heat transfer has been discussed.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74F05 Thermal effects in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] M.B. Abd-el-Malek, Group method analysis of nonlinear temperature variation across the lake depth, in: Proceedings of the XXI International Colloquium on Group Theoretical Methods in Physics Group, Vol. 21, Goslar, Germany, 15-20 July, 1996; World Scientific, Singapore, 1997, pp. 255-261.; M.B. Abd-el-Malek, Group method analysis of nonlinear temperature variation across the lake depth, in: Proceedings of the XXI International Colloquium on Group Theoretical Methods in Physics Group, Vol. 21, Goslar, Germany, 15-20 July, 1996; World Scientific, Singapore, 1997, pp. 255-261.
[2] Abd-el-Malek, M. B.; Badran, N. A., Group method analysis of unsteady free convective laminar boundary-layer flow on a nonisothermal vertical circular cylinder, Acta Mech, 85, 3-4, 193-206 (1990) · Zbl 0714.76089
[3] Abd-el-Malek, M. B.; Boutros, Y. Z.; Badran, N. A., Group method analysis of unsteady free-convective boundary-layer flow on a nonisothermal vertical flat plate, J. Eng. Math, 24, 4, 343-368 (1990) · Zbl 0716.76062
[4] Abd-el-Malek, M. B.; El-Mansi, S. M.A., Group theoretic methods applied to Burgers’ equation, J. Comput. Appl. Math, 115, 1-2, 1-12 (2000) · Zbl 0942.35157
[5] Baumann, G., Symmetry Analysis of Differential Equations with Mathematica (2000), Springer: Springer Berlin · Zbl 0898.34003
[6] Beard, D. W.; Walters, K., Elastico-viscous boundary layer flows. Part I. Two dimensional flow near a stagnation point, Proc. Cambridge Philos. Soc, 60, 667-674 (1964) · Zbl 0123.41601
[7] Bluman, G. W.; Kumei, S., Symmetries and Differential Equations (1989), Springer: Springer New York · Zbl 0718.35003
[8] Boutros, Y. Z.; Abd-el-Malek, M. B.; El-Awadi, I. A.; El-Mansi, S. M.A., Group method for temperature analysis of thermally stagnant lakes, Acta Mech, 133, 131-144 (1999) · Zbl 0922.76257
[9] Cebeci, T.; Bradshaw, P., Momentum Transfer in Boundary Layers (1977), Hemisphere Publishing Corporation: Hemisphere Publishing Corporation New York · Zbl 0424.76023
[10] Frater, K. R., On the solution of some boundary-value problems arising in elastic-viscous fluid mechanics, Z. Angew. Math. Phys, 21, 134-137 (1970) · Zbl 0185.54102
[11] N.H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 1, CRC Press, Boca Raton, FL, 1994.; N.H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 1, CRC Press, Boca Raton, FL, 1994. · Zbl 0864.35001
[12] Lie, S., Üeber die integration durch bestimmte integration von einer classe linearer partieller differentialgleichungen, Lie Arch, VI, 328-368 (1881) · JFM 13.0298.01
[13] Olver, P. J., Applications of Lie Group to Differential Equations (1986), Springer: Springer New York · Zbl 0656.58039
[14] Ovsiannikov, L. V., Group Analysis of Differential Equations (1982), Academic Press: Academic Press New York · Zbl 0485.58002
[15] Soundalgekar, V. M.; Puri, P., On fluctuating flow of an elastico-viscous fluid past an infinite plate with variable suction, J. Fluid Mech, 35, 561-573 (1969) · Zbl 0164.55603
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.