Darcy-Forchheimer flow of variable conductivity Jeffrey liquid with Cattaneo-Christov heat flux theory

doi:10.1007/s10483-017-2188-6

Abstract

Abstract:

The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier's law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model.

Key words: error analysis, Cattaneo-Christov heat flux, Jeffrey liquid, differential Riccati equation (DRE), precise integration method (PIM), exponential of matrix, Darcy-Forchheimer porous medium, variable conductivity

2010 MSC Number:

O361

M. A. MERAJ, S. A. SHEHZAD, T. HAYAT, F. M. ABBASI, A. ALSAEDI. Darcy-Forchheimer flow of variable conductivity Jeffrey liquid with Cattaneo-Christov heat flux theory. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 557-566.

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