Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface
M. Sajid1**, K. Mahmood2, Z. Abbas3
1The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014, Trieste, Italy 2Department of Mathematics, Riphah International University, Islamabad 44000, Pakistan 3Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface
M. Sajid1**, K. Mahmood2, Z. Abbas3
1The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014, Trieste, Italy 2Department of Mathematics, Riphah International University, Islamabad 44000, Pakistan 3Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
摘要We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface. The power law non-Newtonian fluid is considered as a lubricant. The lubrication layer is thin and assumed to have a variable thickness. The transformed nonlinear ordinary differential equation governing the flow is linearized using quasilinearization. The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order Runge–Kutta method. The results are discussed to see the influence of pertinent parameters. The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.
Abstract:We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface. The power law non-Newtonian fluid is considered as a lubricant. The lubrication layer is thin and assumed to have a variable thickness. The transformed nonlinear ordinary differential equation governing the flow is linearized using quasilinearization. The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order Runge–Kutta method. The results are discussed to see the influence of pertinent parameters. The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.
M. Sajid1**, K. Mahmood2, Z. Abbas3. Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface[J]. 中国物理快报, 2012, 29(2): 24702-024702.
M. Sajid, K. Mahmood, Z. Abbas. Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface. Chin. Phys. Lett., 2012, 29(2): 24702-024702.
[1] Navier H M L C 1823 Memoires deI'Academie Roylae des Sciences de I'Institute de France 6 389
[2] Maxwell J C 1879 Phil. Trans. R. Soc. London 170 231
[3] Beavers G S and Joseph D D 1967 J. Fluid Mech. 30 197
[4] Ebert W A and Sparrow E M 1965 J. Basic Eng. 87 1018
[5] Sparrow E M et al 1971 Int. J. Heat Mass Transfer 14 993
[6] Sparrow E M et al 1971 Phys. Fluids 14 1312
[7] Wang C Y 2003 Z. Angew Math. Phys. 54 184
[8] Milavcic M et al 2004 Z. Angew Math. Phys. 55 235
[9] Wang C Y 2002 Chem. Engg. Sci. 57 3745
[10] Ariel P D 2007 Comp. Math. Appl. 54 1169
[11] Sajid M et al 2009 J. Porous Media 12 911
[12] Thompson P A and Troian S M 1997 Nature 389 360
[13] Mathews M T and Hill J M 2007 Acta Mech. 191 195
[14] Sajid M et al 2010 Int. J. Modern Phys. B 30 5939
[15] Santra B et al 2007 Acta Mech. 194 1
[16] Na T Y 1979 Computational Methods in Engineering Boundary Value Problems (New York: Academic)
[17] Andersson H I et al 2006 Int. J. Heat Fluid Flow. 27 329
[18] Joseph D D 1980 Phys. Fluids. 23 2356