Purpose – The purpose of this paper is to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. The principal question the authors address in this paper is in regard to the applicability of the no‐slip condition at a solid‐liquid boundary. The authors present the effects of slip, magnetohydrodynamics (MHD) and heat transfer for the plane Couette, plane Poiseuille and plane Couette‐Poiseuille flows in a homogeneous and thermodynamically compatible third grade fluid. The problem of a non‐Newtonian plane Couette flow, fully developed plane Poiseuille flow and Couette‐Poiseuille flow are investigated.Design/methodology/approach – The present investigation is an attempt to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. A very effective and higher order numerical schem...

Numerical analysis of steady non‐Newtonian flows with heat transfer analysis, MHD and nonlinear slip effects

Chebyshev finite difference method for heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation

In the present paper we point out that the correct way to solve the Blasius problem by numerical means is to reformulate it as free boundary value problem. In the new formulation the truncated boundary (instead of infinity) is the unknown free boundary and it has to be determined as part of the numerical solution. Taking into account the “partial” inavariance of the mathematical model at hand with respect to a stretching group we define a non-iterative transformation method. Further, we compare the improved numerical results, obtained by the method in point, with analytical and numerical ones. Moreover, the numerical results confirm that the question of accuracy depends on the value of the free boundary. Therefore, this indicates that boundary value problems with a boundary condition at infinity should be numerically reformulated as free boundary value problems.

The Blasius problem formulated as a free boundary value problem

Effects of transverse magnetic field on a rotating micropolar fluid between parallel plates with heat transfer

Chebyshev finite difference method for the solution of boundary-layer equations

An expansion procedure using the Chebyshev polynomials is proposed by using El-Gendi method [1], which yields more accurate results than those computed by P. M. Beckett [2] and A. R. Wadia and F. R. Payne [6] as indicated from solving the Falkner-Skan equation, which uses a boundary value technique. This method is accomplished by starting with Chebyshev approximation for the highest-order derivative and generating approximations to the lower-order derivatives through integration of the highest-order derivative.

Chebyshev solution of laminar boundary layer flow

An expansion procedure using the Chebyshev polynomials is proposed by using El-Gendi method [1], which yields more accurate results than those computed by D.Hatziavrmidis [2] as indicated from solving the Orr-Sommerfeld equation for both the plane poiseuille flow and the Blasius velocity profile. The present results are also more accurate results than those computed by A.R.Wadia & F.R.Fayne C31 as indicated from solving the Falkner-Skan equation, which uses a boundary value technique. This method is accomplished by starting with Chebyshev approximation for the highest-order derivative and generating approximations to the lower-order derivatives through integration of the highest-order derivative.

https://asat.journals.ekb.eg/article_25864_6efbb3852382046f2040a0f316881042.pdf

A chebyshev method for the solution of boundary value problems

The aim of this paper is to study the thermal radiation effects on the flow and heat transfer of an unsteady magnetohydrodynamic (MHD) micropolar fluid over a vertical heated nonisothermal stretching surface in the presence of a strong nonuniform magnetic field. The symmetries of the governing partial differential equations are de- termined by the two-parameter group method. One of the resulting systems of reduced nonlinear ordinary differential equations are solved numerically by the Chebyshev spec- tral method. The effects of various parameters on the velocity, the angular velocity, and the temperature profiles as well as the skin-friction coefficient, the wall couple stress co- efficient, and the Nusselt number are studied.

Thermal radiation effect on flow and heat transfer of unsteady MHD micropolar fluid over vertical heated nonisothermal stretching surface using group analysis

H. M. El-Hawary

Papers

Chebyshev solution of laminar boundary layer flow

A chebyshev method for the solution of boundary value problems

Thermal radiation effect on flow and heat transfer of unsteady MHD micropolar fluid over vertical heated nonisothermal stretching surface using group analysis