Darcy-Forchheimer flow with variable thermal conductivity and Cattaneo-Christov heat flux

Abstract

Purpose

The objectives of present communication are threefolds. First is to model and analyze the two-dimensional Darcy-Forchheimer flow of Maxwell fluid induced by a stretching surface. Temperature-dependent thermal conductivity is taken into account. Second is to examine the heat transfer process through non-classical flux by Cattaneo-Christov theory. Third is to derive convergent homotopic solutions for velocity and temperature distributions. The paper aims to discuss these issues.

Design/methodology/approach

The resulting non-linear system is solved through the homotopy analysis method.

Findings

An increment in Deborah number β causes a reduction in velocity field f′(η) while opposite behavior is observed for temperature field θ(η). Velocity field f′(η) and thickness of momentum boundary layer are decreased when the authors enhance the values of porosity parameter λ while opposite behavior is noticed for temperature profile θ(η). Temperature field θ(η) is inversely proportional to the thermal relaxation parameter γ. The numerical values of temperature gradient at the sheet − θ′(0) are higher for larger values of thermal relaxation parameter γ.

Originality/value

To the best of author’s knowledge, no such consideration has been given in the literature yet.

Citation

Hayat, T., Muhammad, T., Al-Mezal, S. and Liao, S.J. (2016), "Darcy-Forchheimer flow with variable thermal conductivity and Cattaneo-Christov heat flux", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 8, pp. 2355-2369. https://doi.org/10.1108/HFF-08-2015-0333