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Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. (English) Zbl 1228.76008

Summary: The effects of surface slip and heat generation (absorption) on the flow and heat transfer of a non-Newtonian power-law fluid on a continuously moving surface have been examined. The governing nonlinear partial differential equations describing the problem are transformed to nonlinear ordinary differential equations using suitable transformations. The transformed ordinary differential equations are solved numerically using the fourth order Runge-Kutta method with the shooting technique. Graphical solutions for the dimensionless velocity and the dimensionless temperature are presented and discussed for various values of the slip parameter, the heat generation or absorption parameter and the Eckert number. The results show that the local skin-friction coefficient is decreased as the slip parameter increased. Also, it is found that the local Nusselt number is decreased as the slip parameter or the heat generation parameter increased and the heat absorption parameter has the effect of increasing the local Nusselt number.

MSC:

76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
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[1] Schowalter, W.R., The application of boundary layer theory to power-law pseudoplastic fluid: similar solutions, Aiche j., 6, 24-28, (1960)
[2] Acrivos, A.; Shah, M.J.; Petersen, E.E., Momentum and heat transfer in laminar boundary layer flows of non-Newtonian fluids past external surfaces, Aiche j., 6, 312-317, (1960)
[3] Kapur, J.N.; Srivastava, R.C., Similar solutions of the boundary layer equations for power-law fluids, Z. angew. math. phys., 14, 383-388, (1963) · Zbl 0113.40502
[4] Lee, S.Y.; Ames, W.F., Similarity solutions for non-Newtonian fluids, American inst. chemical. engs. J., 12, 700-708, (1966)
[5] Berkovskii, B.M., A class of self-similar boundary layer problems for rheological power-law fluids, Int. chem. eng., 6, 187-201, (1966)
[6] Hansen, A.G.; Na, R.Y., Similarity solutions of laminar incompressible boundary layer equations of non-Newtonian fluids, Trans. ASME, J. basic eng., 40, 71-74, (1968)
[7] Fox, V.G.; Erickson, L.E.; Fan, L.T., The laminar boundary layer on a moving continuous flat sheet immersed in a non-Newtonian fluid, Aiche j., 15, 327-333, (1969)
[8] Howell, T.G.; Jengand, D.R.; De Witt, K.J., Momentum and heat transfer on a continuous moving surface in a power law fluid, Int. J. heat mass transfer, 40, 1853-1861, (1997) · Zbl 0915.76005
[9] Akçay, M.; Adil yükselen, M., Drag reduction of a non-Newtonian fluid by fluid injection on a moving wall, Arch. appl. mech., 69, 215-225, (1999) · Zbl 0933.76004
[10] Mahmoud, M.A.A.; Mahmoud, M.A.-E., Analytical solutions of hydromagnetic boundary-layer flow of a non-Newtonian power-law fluid past a continuously moving surface, Acta mech., 181, 83-89, (2006) · Zbl 1096.76062
[11] Hassanien, I.A.; Abdulllah, A.A.; Gorla, R.S.R., Flow and heat transfer in a power law fluid over a non isothermal stretching sheet, Math. comput. model., 28, 105-116, (1998) · Zbl 1098.76531
[12] Jadhav, B.P.; Waghmode, B.B., Heat transfer to non-Newtonian power-law fluid past a continuously moving porous flat plate with heat flux, Wärm stoffübertrag., 25, 377-380, (1990) · Zbl 0721.76005
[13] Hassanien, I.A., Flow and heat transfer on a continuous flat surface moving in a parallel free stream of power-law fluid, Appl. math. modelling, 20, 779-784, (1996) · Zbl 0872.76004
[14] Rao, J.H.; Jeng, D.R.; De Witt, K.J., Momentum and heat transfer in a power-law fluid with arbitrary injection/suction at a moving wall, Int. J. heat mass transfer, 42, 2837-2847, (1999) · Zbl 0977.76004
[15] Sahu, A.K.; Mathur, M.N.; Chaturani, P.; Saxena Bharatiya, S., Momentum and heat transfer from a continuous moving surface to a power law fluid, Acta mech., 142, 119-131, (2000) · Zbl 0962.76006
[16] Kumari, M.; Nath, G., MHD boundary-layer flow of a non-Newtonian fluid over a continuously moving surface with a parallel free stream, Acta mech., 146, 139-150, (2001) · Zbl 1008.76099
[17] Ariel, P.D., On the flow of power law fluid over a stretching sheet-techniques and solutions, Acta mech., 156, 13-27, (2002) · Zbl 1013.76007
[18] Chen, C.-H., Convection cooling of a continuously moving surface in manufacturing processes, J. mater. process technol., 138, 332-338, (2003)
[19] Cortell, R., A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet, Appl. math. comput., 168, 557-566, (2005) · Zbl 1081.76059
[20] Mahmoud, M.A.A.; Megahed, A.M., On steady hydromagnetic boundarylayer flow of a non-Newtonian power-law fluid over a continuously moving surface with suction, Chem. eng. comm., 194, 1457-1469, (2007)
[21] Rao, I.J.; Rajagopal, K.R., The effect of the slip boundary condition on the flow of fluids in a channel, Acta mech., 135, 113-126, (1999) · Zbl 0936.76013
[22] Tanner, R.I., Partial wall slip in polymer flow, Ind. eng. chem. res., 33, 2434-2436, (1994)
[23] Roux, C.L., Existence and uniqueness of the flow of second-grade fluids with slip boundary conditions, Arch. ration. mech. anal., 148, 309-356, (1999) · Zbl 0934.76005
[24] Ariel, P.D.; Hayat, T.; Asghar, S., The flow of an elastico-viscous fluid past a stretching sheet with partial slip, Acta mech., 187, 29-35, (2006) · Zbl 1103.76010
[25] Hayat, T.; Khan, M.; Ayub, M., The effect of the slip condition on flows of an Oldroyd 6-constant fluid, Int. comput. appl. math, 202, 402-413, (2007) · Zbl 1147.76550
[26] Mahmoud, M.A.A., Chemical reaction and variable viscosity effects on flow and mass transfer of a non-Newtonian visco-elastic fluid past a stretching surface embedded in a porous medium, Meccanica, 45, 835-846, (2010) · Zbl 1258.76192
[27] Abel, M.S.; Mahesha, N.; Malipatil, S.B., Heat transfer due to MHD slip flow of a second-grade liquid over a stretching sheet through a porous medium with nonuniform heat source/sink, Chem. eng. comm., 1998, 191-213, (2011)
[28] Foraboschi, F.P.; Federico, I.D., Heat transfer in laminar flow of non- Newtonian heat generating fluids, Int. J. heat mass transfer, 7, 315-318, (1964) · Zbl 0128.42902
[29] Mahmoud, M.A.A.; Megahed, A.M., Effects of suction and injection on MHD heat transfer in an electrically conducting fluid at a stretching vertical plate embedded in a porous medium with uniform free stream, Il nuovo cimento b, 121, 9, 923-935, (2006)
[30] Sakiadis, B.C., Boundary-layer behavior on continuous solid surface on a continuous flat surface II, the boundary layer on a continuous flat surface, Aiche j., 7, 221-225, (1961)
[31] Fox, V.G.; Erickson, L.E.; Fan, L.T., Methods for solving the boundary layer equations for moving continuous flat surface with suction and injection, Aiche j., 14, 726-736, (1969)
[32] Chen, C.-H., Forced convection over a continuous sheet with suction or injection moving in a flowing fluid, Acta mech., 138, 1-11, (1999) · Zbl 0943.76072
[33] Jacobi, A.M., Scale analysis approach to the correlation of continuous moving sheet (backward boundary layer) forced convective heat transfer, ASME J. heat transfer, 115, 1058-1061, (1993)
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