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2015
The unsteady mixed convection flow near the stagnation point region of a heated vertical plate in a porous medium saturated with a nanofluid is studied analytically and numerically using Buongiorno’s model. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. An appropriate similarity transforms are used and the resultant equations are solved using the fourth-fifth order Runge-Kutta method with shooting technique for different values of the parameters governing the problem. The effects of the governing parameters on fluid velocity, temperature, nanoparticle volume fraction, skin friction, Nusselt number and Sherwood number are discussed. Keywords— Nanofluid, Porous medium, Self-similar solution, Stagnation point, Unsteady mixed convection. I. 0BINTRODUCTION tagnation-point flow generally describes the fluid motion near the stagnation region of a solid surface, which exists in the case of fixed as well as moving body in a fluid. Stagnation ...
International Journal of Micro-Nano Scale Transport, 2011
A boundary layer analysis is presented for the mixed convection past a horizontal plate in a porous medium saturated with a nano fluid. The prescribed heat and mass flux boundary conditions are considered. The entire regime of the mixed convection is included, as the mixed convection parameter ξ varies from 0 (pure free convection) to 1 (pure forced convection). The transformed nonlinear system of equations is solved by using an implicit infinite difference method. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter N r , Brownian motion parameter N b , thermophoresis parameter N t and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.
A boundary layer analysis is presented for the natural convection past a horizontal plate in a porous medium saturated with a nano fluid. 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 and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed.
Computers & Mathematics with Applications, 2012
The steady mixed convection boundary layer flow of an incompressible nanofluid along a plate inclined at an angle α in a porous medium is studied. The resulting nonlinear governing equations with associated boundary conditions are solved using an optimized, robust, extensively validated, variational finite-element method (FEM) and a finite-difference method (FDM) with a local non-similar transformation. The Nusselt number is found to decrease with increasing Brownian motion number (Nb) or thermophoresis number (Nt), ...
Applied Nanoscience, 2014
The effect of thermal and mass stratification on mixed convection boundary layer flow over a vertical flat plate embedded in a porous medium saturated by a nanofluid has been investigated. The vertical plate is maintained at uniform and constant heat, mass and nanoparticle fluxes, and the behavior of the porous medium is described by the Darcy model. The model considered for nanofluids incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. A suitable coordinate transformation is introduced, and the obtained system of non-similar, coupled and non-linear partial differential equations is solved numerically. The influence of pertinent parameters on the non-dimensional velocity, temperature, concentration and nanoparticle volume fraction are discussed. In addition, the variation of heat, mass and nanoparticle transfer rates at the plate are exhibited graphically for different values of physical parameters.
Journal of heat transfer, 2011
The steady boundary layer free convection flow past a horizontal flat plate embedded in a porous medium filled by a water-based nanofluid containing gyrotactic microorganisms is investigated. The Oberbeck-Boussinesq approximation is assumed in the analysis. The effects of bioconvection parameters on the dimensionless velocity, temperature, nanoparticle concentration and density of motile microorganisms as well as on the local Nusselt, Sherwood and motile microorganism numbers are investigated and presented graphically. In the absence of bioconvection, the results are compared with the existing data in the open literature and found to be in good agreement. The bioconvection parameters strongly influence the heat, mass, and motile microorganism transport rates.
Mathematics
The rapid advancement in technology in recent years has shown that nanofluids are very vital to further development in science and technology. Moreover, many industrial specifications cannot be met by allowing natural convection only, hence the need to incorporate forced convection and natural convection into a single flow regime. The research aims to quantify the mixed convective two-phase flow past a vertical permeable surface in a Brinkman-Extended Darcy porous medium (BEDPM) induced by nanofluid, with heat and mass transfer. In addition, the Nield condition is also incorporated. The model of the problem was initially constructed in the vital form of leading governing equations (LGEs). These LGEs are specifically called partial differential equations (PDEs) (because of two or more independent variables) which were later converted into a set of the single independent variable of ordinary differential equations (ODEs) by implementing the similarity transformations. The set of singl...
Journal of Modern Methods in Numerical Mathematics, 2011
In the present work, an analysis has been carried out to study a problem of natural convection past a vertical porous plate, in a porous medium saturated by a nanofluid with the streamwise distance x. The employed mathematical model for the nanofluid takes into account the effects of Brownian motion and thermophoresis. The Darcy model is employed for the porous medium. Non-similar solution has been obtained. This solution depends on a Lewis number Le, a buoyancy-ratio number N r, a Brownian motion number N b and a thermophoresis number N t. The variation of the reduced Nusselt number with N r, N b and N t is expressed by correlation formulas. The dependency of the Nusselt number on these four parameters and the effect of suction and injection are investigated graphicly. It is shown that the inclusion of a nanoparticle into the base fluid of this problem is capable to change the flow pattern.
Transport in Porous Media, 2014
There is a rising interest in application of nanofluids in porous media. As such, this paper is aimed at numerically investigating convective boundary layer flow over a plate embedded in a porous medium filled with nanofluid. Influence of multifarious boundary layers' applications namely concentration boundary layer of nanoparticles and thermal ones on thermal conductivity and dynamic viscosity of the nanofluid is studied. A new enhanced boundary condition, zero mass flux of nanoparticles through the surface, is adopted to calculate the volume fraction of nanoparticles on the surface. Furthermore, the effect of different practical non-dimensional parameters such as Brownian motion, thermophoresis, Lewis number, and buoyancy ratio on the hydrodynamic, thermal, and concentration boundary layers is investigated. It is revealed that an increase in buoyancy ratio culminates in temperature rise and velocity reduction. The results also show that as the dimensionless Lewis number increases, the fraction of nanoparticles at the sheet soars; on the other hand, the variation of Lewis number does not have considerable effect on the thermal and hydrodynamic boundary layers. Moreover, introducing an enhancement ratio as a criterion to examine the variation of thermal convective coefficient reveals that this value is a decreasing function of buoyancy ratio parameter. In some cases, the value of enhancement ratio becomes less than unity as the buoyancy ratio gets stronger.
International Journal of Thermal Sciences, 2015
In this article, we investigate steady triple convective-diffusive boundary layer free convection flow past a vertical flat plate embedded in a porous medium filled by a water-based nanofluid and two salts. The plate is assumed to be convectively cooled by a surrounding fluid. It is assumed that there is no nanoparticle flux at the surface and the effect of thermophoresis is taken in to account in the boundary condition. The effects of Brownian motion and thermophoresis parameters are also introduced through a Buongiorno model in the governing equations. The self-similar solutions are obtained numerically using an implicit finite difference method. The effects of the buoyancy ratio, regular Lewis numbers and modified Dufour parameters of both salts and nanofluid parameters on the flow and heat transfer are investigated. It is found that the heat transfer rate increases as we include nanoparticles and salts. Furthermore, it is also shown that the Brownian motion has negligible effects on reduced Nusselt number.