Non-similar solutions for mixed convection along a wedge embedded in a porous medium saturated by a non-Newtonian nanofluid : Natural convection dominated regime

Abstract

Purpose

The purpose of this paper is to present a boundary layer analysis for the mixed convection past a vertical wedge in a porous medium saturated with a power law type non-Newtonian nanofluid. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt, Lewis number Le and the power law exponent n. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.

Design/methodology/approach

This general non-linear problem cannot be solved in closed form and, therefore, a numerical solution is necessary to describe the physics of the problem. An implicit, tri-diagonal finite-difference method has proven to be adequate and sufficiently accurate for the solution of this kind of problems. Therefore, it is adopted in the present study. Variable step sizes were used. The convergence criterion employed in this study is based on the difference between the current and the previous iterations. When this difference reached 10−5 for all the points in the η directions, the solution was assumed to be converged, and the iteration process was terminated.

Findings

The results indicate that as the buoyancy ratio parameter (Nr) and thermophoresis parameter (Nt) increase, the friction factor increases whereas the heat transfer rate (Nusselt number) and mass transfer rate (Sherwood number) decrease. As the Brownian motion parameter (Nb) increases, the friction factor and surface mass transfer rates increase whereas the surface heat transfer rate decreases. As Le increases, mass transfer rates increase. As the power law exponent n increases, the heat and mass transfer rates increase.

Research limitations/implications

The analysis is valid for natural convection dominated regime. The combined forced and natural convection dominated regimes will be reported in a future work.

Practical implications

The approach used is useful in optimizing the porous media heat transfer problems in geothermal energy recovery, crude oil extraction, ground water pollution, thermal energy storage and flow through filtering media.

Originality/value

The results of the study may be of some interest to the researchers of the field of porous media heat transfer. Porous foam and microchannel heat sinks used for electronic cooling are optimized utilizing the porous medium. The utilization of nanofluids for cooling of microchannel heat sinks requires understanding of fundamentals of nanofluid convection in porous media.

Citation

J. Chamkha, A., Rashad, M. and Subba Reddy Gorla, R. (2014), "Non-similar solutions for mixed convection along a wedge embedded in a porous medium saturated by a non-Newtonian nanofluid : Natural convection dominated regime", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 24 No. 7, pp. 1471-1486. https://doi.org/10.1108/HFF-07-2012-0169