Cattaneo-Christov heat flux model for Darcy-Forchheimer flow of an Oldroyd-B fluid with variable conductivity and non-linear convection

Here an analysis is presented to explore the salient characteristics of Darcy-Forchheimer flow of an Oldroyd-B liquid. The expression of energy is formulated via Cattaneo-Christov heat flux theory. The thermal conductivity of liquid is variable. The governing mathematical expressions of momentum and energy are highly nonlinear and coupled due to consideration of nonlinear convection. The homotopic procedure is carried out to compute the solutions of velocity and temperature. The convergence of presented series solutions is verified through plots and numerical data. The computed solutions are sketched to examine the influences of Deborah numbers, porosity and Forchheimer parameters, mixed convection, nonlinear convection and variable conductivity parameters. A comparison is presented to validate the homotopic solutions with previous published numerical data under some limitations. (C) 2016 Elsevier B.V. All rights reserved.