scholarly journals Fem Simulation of Triple Diffusive Natural Convection Along Inclined Plate in Porous Medium: Prescribed Surface Heat, Solute and Nanoparticles Flux

2017 ◽  
Vol 22 (4) ◽  
pp. 883-900 ◽  
Author(s):  
M. Goyal ◽  
R. Goyal ◽  
R. Bhargava
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Fem Simulation ◽  
Lewis Number ◽  
Vertical Surface ◽  
Inclined Plate ◽  
Cross Diffusion ◽  
Boundary Layer Equations ◽  
Wide Range

Abstract In this paper, triple diffusive natural convection under Darcy flow over an inclined plate embedded in a porous medium saturated with a binary base fluid containing nanoparticles and two salts is studied. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. The vertical surface has the heat, mass and nanoparticle fluxes each prescribed as a power law function of the distance along the wall. The boundary layer equations are transformed into a set of ordinary differential equations with the help of group theory transformations. A wide range of parameter values are chosen to bring out the effect of buoyancy ratio, regular Lewis number and modified Dufour parameters of both salts and nanofluid parameters with varying angle of inclinations. The effects of parameters on the velocity, temperature, solutal and nanoparticles volume fraction profiles, as well as on the important parameters of heat and mass transfer, i.e., the reduced Nusselt, regular and nanofluid Sherwood numbers, are discussed. Such problems find application in extrusion of metals, polymers and ceramics, production of plastic films, insulation of wires and liquid packaging.

An Integral Treatment for Dissipative Boundary Layer Flow along a Radiating Vertical Surface by Natural Convection in a Porous Medium

2017 ◽  
Vol 11 ◽  
pp. 191-207 ◽  
Author(s):  
Shoeb R. Sayyed ◽  
B.B. Singh ◽  
Nasreen Bano
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Radiation Effects ◽  
Lewis Number ◽  
Vertical Surface ◽  
Integral Treatment ◽  
Layer Flow ◽  
Dissipative Boundary ◽  
Local Sherwood Number

In the present study, an integral method of Von Karman type has been used to analyse the phenomenon of natural convection heat and mass transfer near a vertical surface embedded in a fluidsaturated porous medium considering the viscous dissipation and radiation effects. The buoyancy effect is due to the variation of temperature and concentration across the boundary layer. The effects of the governing parameters e.g. buoyancy ratio (N), Lewis number (Le), Eckert number (Ec) and radiation parameter (R) on local Nusselt number, local Sherwood number, velocity profile, temperature profile and concentration profile have been investigated. The results obtained in the present analysis have been compared with the published results available in the literature and they have been found in precise agreement.

A Study of Double Diffusive Free Convection From a Corrugated Vertical Surface in a Darcy Porous Medium Under Soret and Dufour effects

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
S.V.S.S.N.V.G. Krishna Murthy ◽  
B.V. Rathish Kumar ◽  
Peeyush Chandra ◽  
Vivek Sangwan ◽  
Mohit Nigam
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Free Convection ◽  
Nonlinear Partial Differential Equations ◽  
Lewis Number ◽  
Boussinesq Approximation ◽  
Vertical Surface ◽  
Soret And Dufour Effects ◽  
Boundary Layer Equations ◽  
Double Diffusive

This study examines the influence of Soret and Dufour effects on double diffusive free convection due to wavy vertical surface immersed in a fluid saturated semi-infinite porous medium under Darcian assumptions. A wavy to flat surface transformation is applied, and the resulting coupled nonlinear partial differential equations under Boussinesq approximation are reduced to boundary layer equations. A finite difference scheme based on the Keller-Box approach has been used in conjunction with block-tridiagonal solver for obtaining the solution for boundary layer equations. Results from the current study are compared with those available in literature. The effect of various parameters such as wave amplitude (a), Lewis number (Le), buoyancy ratio (B), and Soret (Sr) and Dufour (Df) numbers are analyzed through local and average Nusselt number, and local and average Sherwood number plots.

scholarly journals Soret and Dufour Effects on Natural Convection Flow Past a Vertical Surface in a Porous Medium with Variable Viscosity

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
M. B. K. Moorthy ◽  
K. Senthilvadivu
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Variable Viscosity ◽  
Saturated Porous Medium ◽  
Soret Effect ◽  
Lewis Number ◽  
Vertical Surface ◽  
Convection Flow ◽  
Soret And Dufour Effects ◽  
Similarity Transformations

The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium subject to variable viscosity are numerically analyzed, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects. The governing equations of continuity, momentum, energy, and concentrations are transformed into nonlinear ordinary differential equations, using similarity transformations, and then solved by using Runge-Kutta-Gill method along with shooting technique. The parameters of the problem are variable viscosity, buoyancy ratio, Lewis number, Prandtl number, Dufour effect, Soret effect, and Schmidt number. The velocity, temperature, and concentration distributions are presented graphically. The Nusselt number and Sherwood number are also derived and discussed numerically.

Natural Convection Heat Transfer From an Isothermal Vertical Surface to a Stable Thermally Stratified Fluid

1992 ◽  
Vol 114 (4) ◽  
pp. 917-923 ◽  
Author(s):  
D. Angirasa ◽  
J. Srinivasan
Keyword(s):  
Natural Convection ◽  
Thermal Stratification ◽  
Average Nusselt Number ◽  
Convection Heat Transfer ◽  
Stratified Fluid ◽  
Vertical Surface ◽  
Natural Convection Heat Transfer ◽  
Plate Temperature ◽  
Transient Nature ◽  
Wide Range

Natural convection from an isothermal vertical surface to a thermally stratified fluid is studied numerically. A wide range of stratification levels is considered. It is shown that at high levels of ambient thermal stratification, a portion at the top of the plate absorbs heat, while a horizontal plume forms around a location where the plate temperature equals the ambient temperature. The plume is shown to be inherently unsteady, and its transient nature is investigated in detail. The effect of the temperature defect in striating the plume is discussed. Average Nusselt number data are presented for Pr=6.0 and 0.7.

Natural Convection Inside a Bidisperse Porous Medium Enclosure

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Arunn Narasimhan ◽  
B. V. K. Reddy
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Solid Phase ◽  
Darcy Number ◽  
The Core ◽  
Side Walls ◽  
Porous Blocks ◽  
Rayleigh Numbers

Bidisperse porous medium (BDPM) consists of a macroporous medium whose solid phase is replaced with a microporous medium. This study investigates using numerical simulations, steady natural convection inside a square BDPM enclosure made from uniformly spaced, disconnected square porous blocks that form the microporous medium. The side walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The bidispersion effect is generated by varying the number of blocks (N2), macropore volume fraction (ϕE), and internal Darcy number (DaI) for several enclosure Rayleigh numbers (Ra). Their effect on the BDPM heat transfer (Nu) is investigated. When Ra is fixed, the Nu increases with an increase in both DaI and DaE. At low Ra values, Nu is strongly affected by both DaI and ϕE. When N2 is fixed, at high Ra values, the porous blocks in the core region have negligible effect on the Nu. A correlation is proposed to evaluate the heat transfer from the BDPM enclosure, Nu, as a function of Raϕ, DaE, DaI, and N2. It predicts the numerical results of Nu within ±15% and ±9% in two successive ranges of modified Rayleigh number, RaϕDaE.

scholarly journals Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shreenivas R. Kirsur ◽  
Achala L. Nargund ◽  
N. M. Bujurke
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Similarity Solutions ◽  
Positive Pressure ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Wide Range

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness.

Non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium

2019 ◽  
Vol 29 (8) ◽  
pp. 2524-2544 ◽  
Author(s):  
Mikhail A. Sheremet ◽  
Ioan Pop ◽  
A. Cihat Baytas
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Good Control ◽  
Solid Matrix ◽  
Content Type ◽  
Practical Applications ◽  
Nanofluid Viscosity ◽  
Non Equilibrium

Purpose This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non-equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used. Design/methodology/approach Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed. Findings It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium. Originality/value The results of this paper are new and original with many practical applications of nanofluids in the modern industry.

Numerical Study of Natural Convection in Vertical Cylindrical Annular Enclosure Filled with Cu-Water Nanofluid under Magnetic Fields

2019 ◽  
Vol 392 ◽  
pp. 123-137 ◽  
Author(s):  
Mohamed A. Medebber ◽  
Abderrahmane Aissa ◽  
Mohamed El Amine Slimani ◽  
Noureddine Retiel
Keyword(s):  
Natural Convection ◽  
Magnetic Fields ◽  
Volume Fraction ◽  
Numerical Study ◽  
Physical Parameters ◽  
Cold Temperatures ◽  
Simpler Algorithm ◽  
Wide Range ◽  
Nanoparticles Volume Fraction ◽  
Volume Method

The two dimensional study of natural convection in vertical cylindrical annular enclosure filled with Cu-water nanofluid under magnetic fields is numerically analyzed. The vertical walls are maintained at different uniform hot and cold temperatures, THand TC, respectively. The top and bottom walls of the enclosure are thermally insulated. The governing equations are solved numerically by using a finite volume method. The coupling between the continuity and momentum equations is effected using the SIMPLER algorithm. Numerical analysis has been carried out for a wide range of Rayleigh number (103≤Ra≤106), Hartmann number (1 ≤Ha≤100) and nanoparticles volume fraction (0 ≤φ≤0.08). The influence of theses physical parameters on the streamlines, isotherms and average Nusselt has been numerically investigated.

Non-Darcy natural convection flow for non-Newtonian nanofluid over cone saturated in porous medium with uniform heat and volume fraction fluxes

2015 ◽  
Vol 25 (2) ◽  
pp. 422-437 ◽  
Author(s):  
A Chamkha ◽  
S Abbasbandy ◽  
A.M. Rashad
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Mass Flux ◽  
Volume Fraction ◽  
Viscosity Index ◽  
Convection Flow ◽  
Content Type ◽  
Surface Mass ◽  
Uniform Heat ◽  
Nanoparticles Volume Fraction

Purpose – The purpose of this paper is to investigate the effect of uniform lateral mass flux on non-Darcy natural convection of non-Newtonian fluid along a vertical cone embedded in a porous medium filled with a nanofluid. Design/methodology/approach – The resulting governing equations are non-dimensionalized and transformed into a non-similar form and then solved numerically by Keller box finite-difference method. Findings – A comparison with previously published works is performed and excellent agreement is obtained. Research limitations/implications – The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. It is assumed that the cone surface is preamble for possible nanofluid wall suction/injection, under the condition of uniform heat and nanoparticles volume fraction fluxes. Originality/value – The effects of nanofluid parameters, Ergun number, surface mass flux and viscosity index are investigated on the velocity, temperature, and volume fraction profiles as well as the local Nusselt and Sherwood numbers.

Radiation Effect on Heat and Mass Transfer by Natural Convection from a Horizontal Surface Embedded in a Porous Medium

2018 ◽  
Vol 16 ◽  
pp. 140-157 ◽  
Author(s):  
Nasreen Bano ◽  
Oluwole Daniel Makinde ◽  
B.B. Singh ◽  
Shoeb R. Sayyed
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Heat And Mass Transfer ◽  
Saturated Porous Medium ◽  
Lewis Number ◽  
Similarity Solutions ◽  
Horizontal Surface ◽  
Integral Approach ◽  
Power Law Exponent

This paper deals with the study of the heat and mass transfer characteristics of natural convection from a horizontalsurface embedded in a radiating fluid saturated porous medium. Similarity solutions for buoyancy induced heat and masstransfer from a horizontal surface, where the wall temperature and concentration are a power function of distance fromthe origin, are obtained by using an integral approach of Von Karman type. The effects of the governing parameters suchas buoyancy ratio, Lewis number, radiation parameter and the power-law exponent on local Nusselt and local Sherwoodnumbers have been investigated both numerically and graphically.

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