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

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.

Natural convection heat transfer in an oscillating vertical cylinder

“…Aaiza et al [ 4 ], further pointed out that in mixed convection energy transfer, the buoyancy force is responsible for free convection and at least one of the two, non-homogeneous boundary conditions on velocity or external pressure gradient results forced convection. Amongst the important studies on mixed convection energy transfer, we include here the attempts those made by Kumari et al [ 5 ], Tiwari and Das [ 6 ], Chamkha et al [ 7 ], Sheikhzadeh et al [ 8 ], Prasad et al [ 9 ], Hasnain et al [ 10 ] and Ganapathirao et al [ 11 ]. However, most of these studies on energy transfer were focused in simple geometrical configurations.…”

Nanofluid Transport in Porous Media: A Review

“…A non-similarity transformation was used to reduce the mass, momentum, thermal energy, and the nanoparticle concentration equations into a set of nonlinear partial differential equations. Chamkha et al (2014a) numerically analyzed the natural convection in differentially heated and partially porous cavity filled with a nanofluid based on the double-domain formulation. The main feature of this study was to determine if the conventional studied parameters in partially porous cavity like the permeability and the thickness of porous layer, Rayleigh number, and the cavity aspect ratio were determined by the volume fraction of the nanoparticles or not.…”

“…The thermal radiation effect on mixed convection heat transfer in porous media is very important in high-temperature processes and space technology and has many important applications such as space technology, and processes involving high temperatures such as geothermal engineering, the sensible heat storage bed, the nuclear reactor cooling system, and underground nuclear wastes disposal . Chamkha et al (2014a) presented 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. The approach used was useful in optimizing the porous media heat transfer problems in geothermal energy recovery, crude oil extraction, groundwater pollution, thermal energy storage, and flow through filtering media.…”

Time-dependent three-dimensional Oldroyd-B nanofluid flow due to bidirectional movement of surface with zero mass flux

“…[13][14][15][16][17][18] Soret effect on mixed convection nanofluid flow with convective boundary conditions was explored by RamReddy et al 19 Rashad et al 20 considered mixed convection of non-Newtonian nanofluid flow in vertical porous surface. The non-similar solution of mixed convection along a wedge of a non-Newtonian nanofluid flow in a porous medium was studied by Chamkha et al 21 Ghalambaz et al 22 executed the analysis of nanofluid flow under different impacts of nanoparticles shapes and sizes. Some recent studies can be found in the literature.…”