Eur. Phys. J. Plus (2017) 132: 376
https://doi.org/10.1140/epjp/i2017-11652-0

Regular Article

Exact similarity solutions for forced convection flow over horizontal plate in saturated porous medium with temperature-dependent viscosity

¹ LAMFA, CNRS UMR 6140, Department of Mathematics, University of Picardie Jules-Verne, Amiens, France
² LPMC, Department of Physics, University of Picardie Jules-Verne, Amiens, France
³ LES, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah University, Taza, Morocco
⁴ LESA, Department of Civil Engineering and Energetics, National School of Applied Sciences, Frist Mohammed University, Al Hoceima, Morocco

^* e-mail: driss_achemlal@yahoo.fr

Received: 8 June 2017
Accepted: 17 July 2017
Published online: 5 September 2017

Abstract

In this paper, we revisit a mathematical model representing a two-dimensional forced convection boundary-layer flow over a horizontal impermeable plate with a variable heat flux and viscosity. It is assumed that the fluid viscosity varies as an inverse linear function of temperature, the free stream velocity varies as an inverse linear of x and the wall heat flux varies with x as ; where and x measures the distance along the surface. Analytical local similarity solutions are presented which reveal that there are two competing effects: and ; where is the variable viscosity parameter. It has been shown that for dual solutions exist and boundary separation occurs, while a unique local similarity solution exists for any .