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

R. Ellahi, M. Hameed

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 6 January 2012

732

Abstract

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 scheme is used to solve the resulting system of nonlinear differential equations with nonlinear boundary conditions. Numerical solutions are obtained by solving nonlinear ordinary differential equations using Chebyshev spectral method.

Findings

Due to the nonlinear and highly complicated nature of the governing equations and boundary conditions, finding an analytical or numerical solution is not easy. The authors obtained numerical solutions of the coupled nonlinear ordinary differential equations with nonlinear boundary conditions using higher order Chebyshev spectral collocation method. Spectral methods are proven to offer a superior intrinsic accuracy for derivative calculations.

Originality/value

To the best of the authors' knowledge, no such analysis is available in the literature which can describe the heat transfer, MHD and slip effects simultaneously on the flows of the non‐Newtonian fluids.

Keywords

Citation

Ellahi, R. and Hameed, M. (2012), "Numerical analysis of steady non‐Newtonian flows with heat transfer analysis, MHD and nonlinear slip effects", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 1, pp. 24-38. https://doi.org/10.1108/09615531211188775

Publisher

:

Emerald Group Publishing Limited

Copyright © 2012, Emerald Group Publishing Limited

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