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nonlinear convection in a non-darcy porous medium

Applied Mathematics and Mechanics(English Edition) 2010年第5期31卷 565-574页

作者： M. K. PARTHA Department of Mathematics Malnad College of Engineering

In this paper, the natural convection in a non-darcy porous medium is studied using a temperature-concentration-dependent density relation. The effect of the two parameters responsible for the nonlinear convection is analyzed for different values of the inertial parameter, dispersion parameters, Rayleigh number, Lewis number, Soret number, and Dufour number. In the aiding buoyancy, the tangential velocity increases steeply with an increase in the nonlinear temperature parameter and the nonlinear concentration parameter when the inertial effect is zero. However, when the inertial effect is non-zero, the effect of the nonlinear temperature parameter and the nonlinear concentration parameter on the tangential velocity is marginal. The concentration distribution varies appreciably and spreads in different ranges for different values of the double dispersion parameters, the inertial effect parameter, and also for the parameters which control the nonlinear temperature and the nonlinear concentration. Heat and mass transfer varies extensively with an increase in the nonlinear temperature parameter and the nonlinear concentration parameter depending on Dacry and non-darcy porous media. The variation in heat and mass transfer when all the effects, i.e., the inertial effect, double dispersion ef- fects, and Soret and Dufour effects, are simultaneously zero and non-zero. The combined effects of the nonlinear temperature parameter, the nonlinear concentration parameter and buoyancy are analyzed. The effect of the nonlinear temperature parameter and the nonlinear concentration parameter and also the cross diffusion effects on heat and mass transfer are observed to be more in darcy porous media compared with those in non- darcy porous media. In the opposing buoyancy, the effect of the temperature parameter is to increase the heat and mass transfer rate, whereas that of the concentration parameter is to decrease.

关键词： non-darcy porous medium natural convection double dispersion

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Effect of thermal radiation on mixed convection of a nanofluid from an inclined wavy surface embedded in a non-darcy porous medium with wall heat flux

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Propulsion and Power Research 2018年第2期7卷 147-157页

作者： D.Srinivasacharya P.Vijay Kumar Department of Mathematics National Institute of TechnologyWarangal 506004TelanganaIndia

This article focuses on the effect of radiation on mixed convection in a nanofluid along an inclined wavy surface embedded in a non-darcy porous medium.A coordinate transformation is employed to transform the complex wavy surface to a smooth *** governing equations are transformed into a set of partial differential equations using the nonsimilarity transformation and then a local similarity and non-similarity method is applied to obtain coupled ordinary differential *** resulting equations are linearized using the successive linearization method and then solved by the Chebyshev spectral *** effects of radiation,non-darcy parameter,Brownian motion parameter,thermophoresis parameter,the amplitude of the wavy surface,angle of inclination of the wavy surface on the non-dimensional heat and nanoparticle mass transfer rates are studied and presented graphically.

关键词： Mixed convection Nanofluid Inclined wavy surface non-darcy porous medium Radiation Heat flux

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BIOCONVECTION IN A non-darcy porous medium SATURATED WITH A NANOFLUID AND OXYTACTIC MICRO-ORGANISMS

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International Journal of Biomathematics 2014年第1期7卷 91-105页

作者： S. SHAW P. K. KAMESWARAN M. NARAYANA P. SIBANDA School of Mathematics Statistics and Computer Science University of KwaZulu-Natal Private Bag X01 Scottsville Pietermaritzburg 3209 South Africa

The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-darcy porous medium and to investigate the effects of bio- convection and mixed convection on the steady boundary layer flow past a horizontal plate embedded in a porous medium filled with a water-based nanofluid. The governing partial differential equations for momentum, heat, oxygen and micro-organism conser- vation are reduced to a set of nonlinear ordinary differential equations using similarity transformations that are numerically solved using a built-in MATLAB ODE solver. The effects of the bioconvection parameters on the nanofluid fluid properties, nanoparticle concentration and the density of the micro-organism are analyzed. A comparative anal- ysis of our results with those previously reported in the literature is given. Among the significant findings in this study is that bioconvection parameters highly influence beat, mass and motile micro-organism transfer rates.

关键词： Bioconvection non-darcy porous medium oxytactic micro-organisms nanofluid.

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darcy-Forchheimer flows of copper and silver water nanofluids between two rotating stretchable disks

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Applied Mathematics and Mechanics(English Edition) 2017年第12期38卷 1663-1678页

作者： T.HAYAT H.NAZAR M.IMTIAZ A.ALSAEDI Department of Mathematics Quaid-i-Azam UniversityIslamabad 44000Pakistan nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department ofMathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics University of WahWahcantt 47040Pakistan

This investigation describes the nanofluid flow in a non-darcy porous medium between two stretching and rotating disks. A nanofluid comprises of nanoparticles of silver and copper. Water is used as a base fluid. Heat is being transferred with thermal radiation and the Joule heating. A system of ordinary differential equations is obtained by appropriate transformations. Convergent series solutions are obtained. Effects of various parameters are analyzed for the velocity and temperature. Numerical values of the skin friction coefficient and the Nusselt number are tabulated and examined. It can be seen that the radial velocity is affected in the same manner with both porous and local inertial parameters. A skin friction coefficient depicts the same impact on both disks for both nanofluids with larger stretching parameters.

关键词： magnetohydrodynamics (MHD) nanofluid stretchable rotating disk non-darcy porous medium thermal radiation

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