Mixed convection stagnation point flow past a vertical flat plate with a second order slip: Heat flux case

Abstract Steady mixed convection stagnation point flow past a vertical flat plate with a second order slip when the plate is maintained at a variable heat flux is investigated. By selecting appropriate similarity variables, the partial differential equations are transformed into ordinary (similarity) differential equations, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. It is found that the solutions of the ordinary (similarity) differential equations have two branches, upper and lower branch solutions, in a certain range of the mixed convection and velocity slip parameters. In order to establish which of these solutions are stable and which are not, a stability analysis has been performed. The effects of the mixed convection and velocity slip parameters on the skin friction coefficient, dimensionless wall temperature, and dimensionless velocity and temperature profiles are presented graphically, and discussed in details. It results in that the second order slip affects considerably the flow and heat transfer characteristics.

[1]  Anthony M. J. Davis,et al.  The effect of transpiration on self-similar boundary layer flow over moving surfaces , 2006 .

[2]  Karl Hiemenz,et al.  Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder , 1911 .

[3]  Shigehisa Fukui,et al.  A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems , 1990 .

[4]  Tiegang Fang,et al.  A moving-wall boundary layer flow of a slightly rarefied gas free stream over a moving flat plate , 2005, Appl. Math. Lett..

[5]  C. Wang,et al.  Stagnation flows with slip: Exact solutions of the Navier-Stokes Equations , 2003 .

[6]  Oluwole Daniel Makinde,et al.  Buoyancy Effects on Thermal Boundary Layer Over a Vertical Plate With a Convective Surface Boundary Condition , 2010 .

[7]  Chao-Yang Wang,et al.  Flow due to a stretching boundary with partial slip—an exact solution of the Navier–Stokes equations , 2002 .

[8]  P. Ariel.  Two dimensional stagnation point flow of an elastico‐viscous fluid with partial slip , 2008 .

[9]  Abdul Aziz,et al.  Viscous flow over a shrinking sheet with a second order slip flow model , 2010 .

[10]  I. Pop,et al.  The forced convection flow of a uniform stream over a flat surface with a convective surface boundary condition , 2011 .

[11]  G. Wilks.  COMBINED FORCED AND FREE CONVECTION FLOW ON VERTICAL SURFACES , 1973 .

[12]  H. Schlichting.  Boundary Layer Theory , 1955 .

[13]  I. Pop,et al.  Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media , 2001 .

[14]  Derek B. Ingham,et al.  Mixed Convection Boundary-Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium: Brinkman Model with Slip , 2009 .

[15]  C. Lee,et al.  Exact solutions of incompressible Couette flow with porous walls for slightly rarefied gases , 2006 .

[16]  J. Merkin.  Natural-convection boundary-layer flow on a vertical surface with Newtonian heating , 1994 .

[17]  F. White.  Viscous Fluid Flow , 1974 .

[18]  G. Wilks.  The flow of a uniform stream over a semi-infinite vertical flat plate with uniform surface heat flux , 1974 .

[19]  S. Goldstein.  On backward boundary layers and flow in converging passages , 1965, Journal of Fluid Mechanics.

[20]  C. Wang.  Stagnation slip flow and heat transfer on a moving plate , 2006 .

[21]  Lin Wu,et al.  A slip model for rarefied gas flows at arbitrary Knudsen number , 2008 .

[22]  S. G. Moulic,et al.  Mixed Convection Along a Semi-Infinite Vertical Flat Plate With Uniform Surface Heat Flux , 2009 .

[23]  F. Homann.  Der Einfluß großer Zähigkeit bei der Strömung um den Zylinder und um die Kugel , 1936 .

[24]  C. Wang.  Analysis of viscous flow due to a stretching sheet with surface slip and suction , 2009 .

[25]  B. Armaly,et al.  Mixed Convection in Stagnation Flows Adjacent to Vertical Surfaces , 1988 .

[26]  Ioan Pop,et al.  Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip , 2013 .

[27]  Bahgat Sammakia,et al.  Buoyancy-Induced Flows and Transport , 1988 .

[28]  J. Merkin.  Natural convective boundary-layer flow in a heat generating porous medium with a prescribed wall heat flux , 2009 .

[29]  J. Merkin,et al.  Mixed convection boundary layer similarity solutions: prescribed wall heat flux , 1989 .

[30]  Ephraim M Sparrow,et al.  Combined forced and free convection flow on vertical surfaces , 1970 .

[31]  Abdul Aziz,et al.  A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition , 2009 .

[32]  J. Merkin,et al.  On the free convection boundary layer on a vertical plate with prescribed surface heat flux , 1990 .

[33]  L. S. Yao,et al.  Natural Convection Along a Vertical Wavy Surface With Uniform Heat Flux , 1989 .

[34]  V. Carey,et al.  Transport at large downstream distances in mixed convection flow adjacent to a vertical uniform-heat-flux surface , 1982 .

[35]  H. Andersson.  Slip flow past a stretching surface , 2002 .

[36]  I. Pop,et al.  Mixed convection boundary layer flow over a permeable vertical surface with prescribed wall heat flux , 2008 .

[37]  C. Wang.  Stagnation flow on a cylinder with partial slip—an exact solution of the Navier–Stokes equations , 2007 .