Boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretching vertical surface with prescribed skin friction

Abstract

The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered. The governing partial differential equations were transformed into a system of ordinary differential equations, which were then solved numerically using the shooting method. Results for the stretching velocity, the local Nusselt number, the temperature, and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to 1. Both assisting (heated plate) and opposing (cooled plate) flow regions are considered. It is found that dual solutions exist for both assisting and opposing flows.

Keywords

boundary layer flow / dual solutions / micropolar fluids / mixed convection / skin friction

References

[1] Łukaszewicz G. Micropolar Fluids: Theory and Application, 1999 Basel, Birkhäuser

[2] Shu J.J., Lee J.S. Fundamental solutions for micropolar fluids. J. Eng. Math., 2008, 61, 69.

[3] Eringen A.C. Theory of micropolar fluids. J. Math. Mech., 1966, 16, 1.

[4] Eringen A.C. Theory of thermomicropolar fluids. J. Math. Anal. Appl., 1972, 38, 480.

[5] Peddieson J., McNitt R.P. Boundary layer theory for a micropolar fluid. Recent Adv. Eng. Sci., 1970, 5, 405.

[6] Eringen A.C. Microcontinuum Field Theories II: Fluent Media, 2001 New York, Springer

[7] Crane L.J. Flow past a stretching plane. J. Appl. Math. Phys., 1970, 21, 645.

[8] Magyari E., Keller B. Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J. Phys. D, 1999, 32, 577.

[9] Magyari E., Keller B. Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls. Eur. J. Mech. B Fluids, 2000, 19, 109.

[10] Liao S.J., Pop I. Explicit analytical solution for similarity boundary layer equations. Int. J. Heat Mass Transfer, 2004, 47, 75.

[11] Nazar R., Amin N., Pop I. Unsteady boundary layer flow due to a stretching surface in a rotating fluid. Mech. Res. Commun., 2004, 31, 121.

[12] Ishak A., Nazar R., Pop I. Magnetohydrodynamic (MHD) flow of a micropolar fluid towards a stagnation point on a vertical surface. Comput. Math. Appl., 2008, 56, 3188.

[13] Zheng L.C., Wang L.J., Zhang X.X. Analytic solutions of unsteady boundary flow and heat transfer on a permeable stretching sheet with non-uniform heat source/sink. Commun. Nonlinear Sci. Numer. Simul., 2010, 16, 731.

[14] Zhu J., Zheng L.C., Zhang Z.G. Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet. Appl. Math. Mech., 2010, 31(4): 439.

[15] Nazar R., Amin N., Filip D., Pop I. Stagnation point flow of a micropolar fluid towards a stretching sheet. Int. J. Nonlinear Mech., 2004, 39, 1227.

[16] Abo-Eldahab E.M., El Aziz M.A. Flow and heat transfer in micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with uniform free stream. Appl. Math. Comput., 2005, 162, 881.

[17] Lok Y.Y., Phang P., Amin N., Pop I. Unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface. Int. J. Eng. Sci., 2003, 41, 173.

[18] Hayat T., Javed T., Abbas Z. MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface. Nonlinear Anal. Real World Appl., 2009, 10(3): 1514.

[19] Magyari E., Keller B. Heat transfer characteristics of boundary layer flows induced by a continuous surface stretched with prescribed skin friction. Heat Mass Transfer, 2006, 42, 679.

[20] Sajid M., Hayat T., Pop I. Stretching a plane surface in a viscoelastic fluid with prescribed skin friction. Numer. Methods Partial Differential Equations, 2010, 25(6): 1342.

[21] Rees D.A.S., Bassom A.P. The Blasius boundary-layer flow of a micropolar fluid. Int. J. Eng. Sci., 1996, 34, 113.

[22] Ahmadi G. Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate. Int. J. Eng. Sci., 1976, 14, 639.

[23] Kline K.A. A spin-vorticity relation for unidirectional plane flows of micropolar fluids. Int. J. Eng. Sci., 1977, 15, 131.

[24] Gorla R.S.R. Combined forced and free convection in micropolar boundary layer flow on a vertical flat plate. Int. J. Eng. Sci., 1988, 26, 385.

[25] Rees D.A.S., Pop I. Free convection boundary-layer flow of a micropolar fluid from a vertical flat plate. IMA J. Appl. Math., 1998, 61, 179.

[26] Lok Y.Y., Amin N., Pop I. Steady two-dimensional asymmetric stagnation point flow of a micropolar fluid. J. Appl. Math. Mech., 2003, 83, 594.

[27] Nazar R., Amin N., Pop I. Mixed convection boundary-layer flow from a horizontal circular cylinder in micropolar fluids: case of constant wall temperature. Int. J. Numer. Methods Heat Fluid Flow, 2003, 13, 86.