Slip Flow of a Maxwell Fluid Past a Stretching Sheet

Muhammad SAJID, Zaheer ABBAS, Nasir ALI, Tariq JAVED, Iftikhar AHMAD

Abstract


The slip flow rate of a non-Newtonian fluid (Maxwell model) past a stretching sheet is investigated in this paper. The slip condition for the Maxwell fluid is formulated and presented for the first time. The governing nonlinear partial differential equations and boundary conditions are transformed to nonlinear ordinary differential equations and boundary conditions using the well established similarity transformations for a stretching flow. For the numerical solution of the nonlinear problem we first linearize it using quasilinearization. Then the boundary value problem was transformed into 2 initial value problems by employing the method of superposition. The initial value problems were then integrated using a fourth order Runge-Kutta method. The influence of the slip parameter on the velocity components and skin friction coefficient is analyzed through graphical results. The results are valid for all the values of the slip parameter ranging from zero (no-slip) to infinity (full slip). It is also found that numerical results exist for the values less or equal to one of the dimensionless relaxation time parameter.

doi:10.14456/WJST.2014.63

Keywords


Slip condition, Maxwell fluid, stretching flow, quasilinearization, numerical solution

Full Text:

PDF

References


HMLC Navier. Memoire sur les lois du mouvment des fluids. Memoires deI'Academie Roylae des Sciences de I'Institute de France 1823; 6, 389-440.

JC Maxwell. On stresses in rarefied gases arising from inequalities of temperature. Phil. Tran. R. Soc. London 1879; 170, 231-56.

GS Beavers and DD Joseph. Boundary condition at a naturally permeable wall. J. Fluid Mech. 1967; 30, 197-207.

WA Ebert and EM Sparrow. Slip flow and in rectangular and annular ducts. J. Basic Eng. 1965; 87, 1018-24.

EM Sparrow, GS Beavers and LY Hung. Flow about a porous-surfaced rotating disc. Int. J. Heat Mass Tran. 1971; 14, 993-6.

EM Sparrow, GS Beavers and LY Hung. Channel and tube flows with surface mass transfer and velocity slip. Phys. Fluids 1971; 14, 1312-9.

CY Wang. Stagnation flows with slip: Exact solutions of the Navier-Stokes equations. Z. Angew Math. Phys. 2003; 54, 184-9.

M Milavcic and CY Wang. The flow due to a rough rotating disc. Z. Angew Math. Phys. 2004; 55, 235-46.

CY Wang. Flow due to a stretching boundary with partial slip: An exact solutions of the Navier-Stokes equations. Chem. Eng. Sci. 2002; 57, 3745-7.

HI Anderson. Slip flow past a stretching surface. Acta Mech. 2002; 158, 121-5.

PD Ariel. Axisymmetric flow due to a stretching sheet with partial slip. Comput. Math. Appl. 2007; 54, 1169-83.

M Sajid, I Ahmad and T Hayat. Unsteady boundary layer flow due to a stretching sheet in porous medium with partial slip. J. Porous Media 2009; 12, 911-7.

M Sajid, N Ali, Z Abbas and T Javed. Stretching flows with general slip boundary condition. Int. J. Modern Phys. B. 2010; 30, 5939-47.

PD Ariel, T Hayat and S Asghar. The flow of an elastico-viscous fluid past a stretching sheet with partial slip. Acta Mech. 2006; 187, 29-35.

T Hayat, T Javed and Z Abbas. Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space. Int. J. Heat Mass Tran. 2008; 51, 4528-34.

B Sahoo. Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet. Cent. Eur. J. Phys. 2010; 8, 498-508.

B Sahoo. Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet. Appl. Math. Mech. 2010; 31, 159-73.

K Sadeghy, AH Najafi and M Saffaripour. Sakiadis flow of an upper-convected Maxwell fluid. Int. J. Nonlinear Mech. 2005; 40, 1220-8.

Z Abbas, M Sajid and T Hayat. MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel. Theor. Comput. Fluid Dyn. 2006; 20, 229-38.

T Hayat, Z Abbas and M Sajid. Series solution for the upper-convected Maxwell fluid over a porous stretching plate. Phys. Lett. A 2006; 358, 396-403.

T Hayat and M Sajid. Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid. Int. J. Eng. Sci. 2007; 45, 393-401.

T Hayat, Z Abbas and N Ali. MHD flow and mass transfer of an upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species. Phys. Lett. A 2008; 372, 4698-704.

A Alizadeh-Pahlavan, V Aliakbar, F Vakili-Farahani and K Sadeghy. MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method. Comm. Nonlinear Sci. Numer. Simulat. 2009; 14, 473-88.

V Aliakbar, A Alizadeh-Pahlavan and K Sadeghy. The influence of thermal radiation on MHD flow of Maxwellian fluids above stretching sheets. Comm. Nonlinear Sci. Numer. Simulat. 2009; 14, 779-94.

T Hayat, Z Abbas and M Sajid. MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface. Chaos Soliton. Fract. 2009; 39, 840-8.

RK Bhatnagar, G Gupta and KR Rajagopal. Flow of an Oldroyd-B fluid due to a stretching sheet in the presence of a free stream velocity. Int. J. Nonlinear Mech. 1995; 30, 391-405.

M Sajid, Z Abbas, T Javed and N Ali. Boundary layer flow of an Oldroyd-B fluid in the region of stagnation point over a stretching sheet. Can. J. Phys. 2010; 88, 635-40.

TY Na. Computational Methods in Engineering Boundary Value Problems. Academic Press, New York, 1977, p. 94-5.

J Harris. Rheology and Non-Newtonian Flow. Longman, London, 1977, p. 221-3.

H Schlichting. Boundary Layer Theory. 6th ed. McGraw-Hill, New York, 1964, p. 127-31.


Refbacks

  • There are currently no refbacks.




http://wjst.wu.ac.th/public/site/images/admin/image012_400

Online ISSN: 2228-835X

http://wjst.wu.ac.th

Last updated: 20 June 2019