×

Group theoretic method for unsteady free convection flow of a micropolar fluid along a vertical plate in a thermally stratified medium. (English) Zbl 1145.76414

Summary: The group theoretic approach is applied for solving the problem of unsteady natural convection flow of micropolar fluid along a vertical flat plate in a thermally stratified medium. The application of two-parameter transformation group reduces the number of independent variables in the governing system consisting of partial differential equations and a set of auxiliary conditions from three to only one independent variable, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. Numerical solution of the velocity, microrotation and heat transfer have been obtained. The possible forms of the ambient temperature variation with position and time are derived.

MSC:

76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
76R10 Free convection
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Eringen, A., Theory of micropolar fluids, J. Math. Mech., 16, 1 (1966)
[2] Eringen, A., Theory of thermomicrofluids, J. Math. Anal. Appl., 9, 480 (1972) · Zbl 0241.76012
[3] Wilson, A. J., Boundary layers in micropolar liquids, Proc. of the Cambridge Philos. Soc., 67, 46 (1970)
[4] Peddieson, J.; McNitt, R. P., Boundary layer theory for a micropolar fluid, Recent Adv. Eng. Sci., 5, 405 (1970)
[5] Ahmadi, G., Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, Int. J. Eng. Sci., 14, 639 (1976) · Zbl 0329.76041
[6] Hassanien, I. A.; Gorla, R. S.R., Boundary layer flow of micropolar fluid near an axisymmetric stagnation point on a moving cylinder, Int. J. Eng. Sci., 28, 323 (1990)
[7] Gorla, R. S.R., Mixed convection in a micropolar fluid from a vertical surface with uniform heat flux, Int. J. Eng. Sci., 30, 319 (1992)
[8] Hassanien, I. A.; Gorla, R. S.R.; Mohammadien, A. A., Boundary layer heat transfer in a micropolar fluid over a flat plate with vectored surface mass transfer, Appl. Mech. Eng., 3, 25 (1998) · Zbl 0916.76003
[9] Hassanien, I. A.; Ibrahim, F. S.; Gorla, R. S.R., Mixed convection boundary layer flow of a micropolar fluid on a horizontal plate, Chem. Eng. Comm., 170, 117 (1998)
[10] Mulolani, I.; Rahman, M., Similarity analysis for natural convection from a vertical plate with distributed wall concentration, Int. J. Math. Math. Sci., 23, 319 (2000) · Zbl 0963.76083
[11] Birkhoff, G., Hydrodynamics (1960), Princeton University Press: Princeton University Press Priceton, New Jersey
[12] Moran, M. J.; Gaggioli, R. A., Reduction of the number of variables in systems of partial differential equations with auxiliary conditions, SIAM J. Appl. Math., 16, 202 (1968) · Zbl 0157.40602
[13] Hassanien, I. A.; Salama, A. A.; Hosham, H. A., Group theoretic method analysis for unsteady boundary layer flow near a stagnation point, TJM, 9, 639 (2005) · Zbl 1160.70335
[14] Moran, M. J.; Gaggioli, R. A., A new systematic formalism for similarity analysis, J. Eng. Math., 3, 151 (1969) · Zbl 0176.08601
[15] Hassanien, I. A.; Baker, A. Y.; Gorla, R. S.R., Natural convection boundary layer flow of a micropolar fluid along a vertical plate in a thermally stratified medium, Appl. Mech. Eng., 1, 381 (1996) · Zbl 0886.76088
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.