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Flow and heat transfer of an electrically conducting third-grade fluid past an infinite plate with partial slip. (English) Zbl 1258.76025

Summary: The effects of partial slip on the steady flow and heat transfer of an electrically conducting, incompressible, third grade fluid past a horizontal plate subject to uniform suction and blowing is investigated. Two distinct heat transfer problems are studied. In the first case, the plate is assumed to be at a higher temperature than the fluid; and in the second case, the plate is assumed to be insulated. The momentum equation is characterized by a highly nonlinear boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. Numerical solutions for the governing nonlinear equations are obtained over the entire range of physical parameters. The effects of slip, magnetic parameter, non-Newtonian fluid characteristics on the velocity and temperature fields are discussed in detail and shown graphically. It is interesting to find that the velocity and the thermal boundary layers decrease with an increase in the slip, and as the slip increases to infinity, the flow behaves as though it were inviscid.

MSC:

76A05 Non-Newtonian fluids
76W05 Magnetohydrodynamics and electrohydrodynamics
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] Blasius H (1908) Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z Math Phys 56:1–37 · JFM 39.0803.02
[2] Prandtl L Über Flüssigkeitsbewegungen bei sehr kleiner Reibung. In: Verhandlg III Int Math Cong, Heidelberg, August 1904 · JFM 36.0800.02
[3] Griffith AA, Meredith FW The possible improvement in aircraft performance due to the use of boundary layer suction. In: Aero Res Coun, Report No 2315 (1936)
[4] Fazio R (1992) The Blasius problem formulated as a free boundary value problem. Acta Mech 95:1–7 · Zbl 0753.76051 · doi:10.1007/BF01170800
[5] He J (1999) Approximate analytical solution of Blasius equation. Commun Nonlinear Sci Numer Simul 4:75–78 · Zbl 0932.34005 · doi:10.1016/S1007-5704(99)90063-1
[6] Lin J (1999) A new approximate iteration solution of Blasius equation. Commun Nonlinear Sci Numer Simul 4:91–94 · Zbl 0928.34012 · doi:10.1016/S1007-5704(99)90017-5
[7] Liao SJ (1999) An explicit, totally analytic approximation of Blasius viscous flow problems. Int J Non-Linear Mech 34:759–778 · Zbl 1342.74180 · doi:10.1016/S0020-7462(98)00056-0
[8] Liao SJ (1999) A uniformly valid analytic solution of 2D viscous flow past a semi infinite flat plate. J Fluid Mech 385:101–128 · Zbl 0931.76017 · doi:10.1017/S0022112099004292
[9] Fang T, Guo F, Lee CF (2006) A note on the extended Blasius equation. Appl Math Lett 19:613–617 · Zbl 1126.34301 · doi:10.1016/j.aml.2005.08.010
[10] Benlahsen M, Guedda M, Kersner R (2008) The generalized Blasius equation revised. Math Comput Model 47:1063–1076 · Zbl 1144.76307 · doi:10.1016/j.mcm.2007.06.019
[11] Kaloni PN (1966) Fluctuating flow of an elastico-viscous fluid past porous plate. Phys Fluids 10:1344–1346 · Zbl 0147.44104 · doi:10.1063/1.1762282
[12] Soundalgekar VM, Puri P (1969) On fluctuating flow of an elastico-viscous fluid past an infinite plate with variable suction. J Fluid Mech 35:561–573 · Zbl 0164.55603 · doi:10.1017/S0022112069001297
[13] Frater KR, (1970) On the solution of some boundary value problems arising in elastico-viscous fluid mechanics. Z Angew Math Phys 21:134–137 · Zbl 0185.54102 · doi:10.1007/BF01594990
[14] Rajagopal KR, Gupta AS (1984) An exact solution for the flow of a non-Newtonian fluid past an infinite porous plate. Meccanica 19:158–160 · Zbl 0552.76008 · doi:10.1007/BF01560464
[15] Rajagopal KR, Szeri AZ, Troy W (1986) An existence theorem for the flow of a non-Newtonian fluid past an infinite porous plate. Int J Non-Linear Mech 21:279–289 · Zbl 0599.76013 · doi:10.1016/0020-7462(86)90035-1
[16] Cortell R (1993) Numerical solutions for the flow of a fluid of grade three past an infinite porous plate. Int J Non-Linear Mech 28:623–626 · Zbl 0795.76004 · doi:10.1016/0020-7462(93)90023-E
[17] Maneschy CE, Massoudi M, Ghoneimy A (1993) Heat transfer analysis of a non-Newtonian fluid past a porous plate. Int J Non-Linear Mech 28:131–143 · Zbl 0776.76007 · doi:10.1016/0020-7462(93)90052-M
[18] Ariel PD (1994) The flow of a viscoelastic fluid past a porous plate. Acta Mech 107:199–204 · Zbl 0846.76008 · doi:10.1007/BF01201829
[19] Ariel PD (2007) Transient flow of third grade fluid over a moving plate. Int J Comput Methods Eng Mech 8:107–113 · Zbl 1136.76005 · doi:10.1080/15502280701246737
[20] Chan Man Fong CF, Kaloni PN, De Kee D (1996) Comments on the solutions of boundary value problems in non-Newtonian fluid mechanics. Acta Mech 115:231–237 · Zbl 0859.76006 · doi:10.1007/BF01187440
[21] Mansutti D, Pontrelli G, Rajagopal KR (1993) Steady flows of non-Newtonian fluids past a porous plate with suction or injection. Int J Numer Methods Fluids 17:927–941 · Zbl 0797.76003 · doi:10.1002/fld.1650171102
[22] Hayat T, Farooq MA, Javed T, Sajid M (2009) Partial slip effects on the flow and heat transfer characteristics in a third grade fluid. Nonlinear Anal Real World Appl 10(2):745–755. doi: 10.1016/j.nonrwa.2007.11.001 · Zbl 1167.76308 · doi:10.1016/j.nonrwa.2007.11.001
[23] Sajid M, Mahmood R, Hayat T (2008) Finite element solution for flow of a third grade fluid past a horizontal porous plate with partial slip. Comput Math Appl 56(5):1236–1244. doi: 10.1016/j.camwa.2008.02.025 · Zbl 1155.76359 · doi:10.1016/j.camwa.2008.02.025
[24] Truesdell C, Noll W (2004) The nonlinear field theories of mechanics, 3rd edn. Springer, Berlin · Zbl 1068.74002
[25] Rivlin RS, Ericksen JL (1955) Stress deformation relation for isotropic materials. J Ratl Mech Anal 4:323–425
[26] Fosdick RL, Rajagopal KR (1980) Thermodynamics and stability of fluids of third grade. Proc R Soc Lond, Ser A 369:351–377 · Zbl 0441.76002 · doi:10.1098/rspa.1980.0005
[27] Navier CLMH (1827) Sur les lois du mouvement des fluides. Mem Acad R Sci Inst Fr 6:389–440
[28] Sahoo B, Sharma HG (2007) MHD flow and heat transfer from a continuous surface in a uniform free stream of a non-Newtonian fluid. Appl Math Mech 28:1467–1477 · Zbl 1231.34015 · doi:10.1007/s10483-007-1106-z
[29] Sahoo B, Sharma HG (2007) Effects of partial slip on the steady Von Karman flow and heat transfer of a non-Newtonian fluid. Bull Braz Math Soc 38:595–609 · Zbl 1133.76003 · doi:10.1007/s00574-007-0063-0
[30] Sahoo B (2009) Hiemenz flow and heat transfer of a non-Newtonian fluid. Commun Nonlinear Sci Numer Simul 14:811–826 · doi:10.1016/j.cnsns.2007.12.002
[31] Sahoo B (2009) Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet. Cent Eur J Phys. doi: 10.2478/s11534-009-0105-x
[32] Broyden CG (1965) A class of methods for solving nonlinear simultaneous equations. Math Comput 19:577–593 · Zbl 0131.13905 · doi:10.1090/S0025-5718-1965-0198670-6
[33] Broyden CG (2000) On the discovery of the ”good Broyden method”. Math Program Ser B 87:209–213 · Zbl 0970.90002 · doi:10.1007/s101070050111
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