Lie group analysis of heat flux effect on MHD second slip flow for a slightly rarefied gas past a stretching sheet with heat generation
Ahmed M. Megahed
Reda G. Abdel-Rahman
Abstrakt
The present paper discusses steady MHD second order slip flow and heat transfer for a slightly rarefied gas due to an impermeable stretching sheet with heat flux and internal heat generation. By using the Lie group analysis, new similarity transformations are obtained. Employing these transformations, allows the partial differential equations governing the problem to transform into a system of ordinary differential equations which are later treated numerically using shooting method. Effects of the governing parameters on the dimensionless velocity and dimensionless temperature profiles are outlined graphically. Furthermore, results for the local skin-friction coefficient and the local Nusselt number are presented for some different values of the governing parameters in a tabular form. Also, results show that there is a strong dependency of the dimensionless temperature on the heat flux.
Słowa kluczowe:
Lie group analysis, second order slip, slightly rarefied gas, MHD, heat fluxBibliografia
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Hamad M.A.A., Uddin M.J., Ismail A.I.M. 2012. Investigation of combined heat and mass transfer by Lie group analysis with variable diffusivity taking into account hydrodynamic slip and thermal convective boundary conditions. International Journal of Heat and Mass Transfer, 55: 1355-1362.
Hossam S.H. 2015. Symmetry analysis for MHD viscous flow and heat transfer over a stretching sheet. Applied Mathematics, 6: article ID: 53062,16 pages.
Ibragimov N.C.R.C. 1994. Handbook of Lie group analysis of differential equations. Vol 1: Symmetries, exact solutions and conservation laws. CRC Press, Boca Raton, FL.
Khader M.M., Megahed A.M. 2014. Differential transformation method for the flow and heat transfer due to a permeable stretching surface embedded in a porous medium with a second order slip and viscous dissipation. ASME Journal of Heat Transfer, 136(7): 072602– 072607.
Khader M.M., Megahed A.M. 2014. Numerical solution for the flow and heat transfer due to a permeable stretching surface embedded in a porous medium with a second order slip and viscous dissipation. European Physical Journal Plus, 129: 10.
Khader M.M., Megahed A.M. 2014. Effect of viscous dissipation on the boundary layer flow and heat transfer past a permeable stretching surface embedded in a porous medium with a second-order slip using Chebyshev finite difference method. Transport in Porous Media, 105: 487–501.
Mahmoud M.A.A. 2012. MHD flow and heat transfer in a viscous fluid over a non-isothermal stretching surface with thermal radiation in slip-flow regime. Chemical Engineering Communications, 199: 925-942.
Mekheimer K.S., Husseny S.Z.A., Ali A.T., Abo-Elkhair R.E. 2010. Lie Group Analysis and Similarity Solutions for a Couple Stress Fluid with Heat Transfer. Journal of Advanced Research in Applied Mathematics, 2: 1-17.
Mina B.M., Amin A.M. 2014. Lie group analysis of nonlinear inviscid flows with a free surface under gravity. Journal of Computational and Applied Mathematics, 258: 17-29.
Nandeppanavar M.M, Vajravelu K., Abel M.S., Siddalingappa, M.N. 2012. Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition. International Journal of Thermal Science, 58: 143-150.
Olver P. 1986. Applications of Lie groups to differential equations. Springer-Verlag, New York.
Ramasami E.K. 2006. Lie group analysis of natural convection heat and mass transfer in an inclined porous surface with heat generation. International Journal of Applied Mathematics and Mechanics, 2: 34–40.
Ramasami E.K. 2006. Lie group analysis of natural convection heat and mass transfer in an inclined surface. Nonlinear Analysis: Modelling and Control, 11: 201–212.
Shidlovskiy V.P. 1967. Introduction to the Dynamics of Rarefied Gases. American Elsevier Publishing Company Inc., New York.
Sivasankaran S., Bhuvaneswari M., Kandaswamy P., Stephani H. 1989. Differential Equations: Their Solution Using Symmetries. Cambridge University Press, New York.
Wu L. 2008. A slip model for rarefied gas flows at arbitrary Kundsen Number. Applied Physics Letters, 93: 253103.
Yürüsoy M., Pakdemirli M., Noyan O.F. 2001. Lie group analysis of creeping flow of a second grade fluid. International Journal of Non-Linear Mechanics, 36: 955–960.
Fang T., Yao S., Zhang J., Aziz A. 2010. Viscous flow over a shrinking sheet with second order slip flow model. Communications in Nonlinear Science and Numerical Simulation, 15: 1831-1842.
Hamad M.A.A., Uddin M.J., Ismail A.I.M. 2012. Investigation of combined heat and mass transfer by Lie group analysis with variable diffusivity taking into account hydrodynamic slip and thermal convective boundary conditions. International Journal of Heat and Mass Transfer, 55: 1355-1362.
Hossam S.H. 2015. Symmetry analysis for MHD viscous flow and heat transfer over a stretching sheet. Applied Mathematics, 6: article ID: 53062,16 pages.
Ibragimov N.C.R.C. 1994. Handbook of Lie group analysis of differential equations. Vol 1: Symmetries, exact solutions and conservation laws. CRC Press, Boca Raton, FL.
Khader M.M., Megahed A.M. 2014. Differential transformation method for the flow and heat transfer due to a permeable stretching surface embedded in a porous medium with a second order slip and viscous dissipation. ASME Journal of Heat Transfer, 136(7): 072602– 072607.
Khader M.M., Megahed A.M. 2014. Numerical solution for the flow and heat transfer due to a permeable stretching surface embedded in a porous medium with a second order slip and viscous dissipation. European Physical Journal Plus, 129: 10.
Khader M.M., Megahed A.M. 2014. Effect of viscous dissipation on the boundary layer flow and heat transfer past a permeable stretching surface embedded in a porous medium with a second-order slip using Chebyshev finite difference method. Transport in Porous Media, 105: 487–501.
Mahmoud M.A.A. 2012. MHD flow and heat transfer in a viscous fluid over a non-isothermal stretching surface with thermal radiation in slip-flow regime. Chemical Engineering Communications, 199: 925-942.
Mekheimer K.S., Husseny S.Z.A., Ali A.T., Abo-Elkhair R.E. 2010. Lie Group Analysis and Similarity Solutions for a Couple Stress Fluid with Heat Transfer. Journal of Advanced Research in Applied Mathematics, 2: 1-17.
Mina B.M., Amin A.M. 2014. Lie group analysis of nonlinear inviscid flows with a free surface under gravity. Journal of Computational and Applied Mathematics, 258: 17-29.
Nandeppanavar M.M, Vajravelu K., Abel M.S., Siddalingappa, M.N. 2012. Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition. International Journal of Thermal Science, 58: 143-150.
Olver P. 1986. Applications of Lie groups to differential equations. Springer-Verlag, New York.
Ramasami E.K. 2006. Lie group analysis of natural convection heat and mass transfer in an inclined porous surface with heat generation. International Journal of Applied Mathematics and Mechanics, 2: 34–40.
Ramasami E.K. 2006. Lie group analysis of natural convection heat and mass transfer in an inclined surface. Nonlinear Analysis: Modelling and Control, 11: 201–212.
Shidlovskiy V.P. 1967. Introduction to the Dynamics of Rarefied Gases. American Elsevier Publishing Company Inc., New York.
Sivasankaran S., Bhuvaneswari M., Kandaswamy P., Stephani H. 1989. Differential Equations: Their Solution Using Symmetries. Cambridge University Press, New York.
Wu L. 2008. A slip model for rarefied gas flows at arbitrary Kundsen Number. Applied Physics Letters, 93: 253103.
Yürüsoy M., Pakdemirli M., Noyan O.F. 2001. Lie group analysis of creeping flow of a second grade fluid. International Journal of Non-Linear Mechanics, 36: 955–960.
Megahed, A. M., & Abdel-Rahman, R. G. (2019). Lie group analysis of heat flux effect on MHD second slip flow for a slightly rarefied gas past a stretching sheet with heat generation. Technical Sciences, 22(1), 45–59. https://doi.org/10.31648/ts.4347
Ahmed M. Megahed
Reda G. Abdel-Rahman
