Natural convection effects on thermal ignition in a porous medium. I. Semenov model

1990 ◽  
Vol 429 (1877) ◽  
pp. 533-554 ◽  
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Lewis Number ◽  
Reaction Model ◽  
Heat Of Reaction ◽  
Thermal Ignition ◽  
Lumped Model ◽  
Convection Problem ◽  
Diffusion Convection

A one-dimensional diffusion-convection-reaction model is formulated to account for natural convection effects on thermal ignition in an open system consisting of a porous medium. Various limiting cases of the model are considered. A detailed analysis of the Semenov (lumped) model is presented. Explicit relations are derived for the dependence of the critical Semenov number ( ψ c ) on the Rayleigh number ( R *). It is shown that for R * → 0, ψ c approaches the classical (conduction) limit e -1 , while for R * ≫ 1, the ignition locus is given by the convection asymptote ψ c / R * = 4 e -2 . Inclusion of reactant consumption shows that the conduction asymptote disappears at B = 4 while the convection asymptote ceases to exist for B Ls < 3 + 2√2, where Ls is a modified Lewis number and B is the heat of reaction parameter. It is shown that the Semenov model has five different types of bifurcation diagrams of temperature against Rayleigh number (particle size), (single-valued, inverse S , isola, inverse S + isola and mushroom). This behaviour is found to be qualitatively identical to that of the forced convection problem investigated by Zeldovich & Zysin.

Natural convection effects on thermal ignition in a porous medium. II. Lumped thermal model-I

1990 ◽  
Vol 429 (1877) ◽  
pp. 555-567 ◽  
Keyword(s):  
Thermal Conductivity ◽  
Rayleigh Number ◽  
Thermal Model ◽  
Lewis Number ◽  
Reaction Model ◽  
Heat Of Reaction ◽  
Bifurcation Diagrams ◽  
Diffusion Term ◽  
The Impact ◽  
Species Diffusion

In this paper, we examine the disappearance of criticality, ignition locus and bifurcation diagrams of temperature against Rayleigh number of a one-dimensional diffusion-convection-reaction model with the assumption of infinite thermal conductivity and zero species diffusivity. The predictions of this model are compared with those of the Semenov model to determine the impact of the species diffusion term. It is shown that for large values of the Rayleigh number (R* ≫ 1), the ignition locus may be expressed in a parametric form B Ls = t /ln t + t /( t - 1) (1 < t ≼ 3.4955), ψ / R * = ( B Ls ) 2 (( t - 1)/ t ) exp{ - B Ls + B Ls / t } ln t , where B is the heat of reaction parameter, ψ is the Semenov number and Ls is a (modified) Lewis number. Criticality is found to disappear at B Ls = 4.194. When these results are compared with those of the Semenov model, it is found that neglecting the species diffusion term gives conservative approximations to the ignition locus, and criticality boundary. It is found that the lumped thermal model-I has five different types of bifurcation diagrams of temperature against Rayleigh number (single­-valued, isola, inverse S , mushroom, inverse S + isola). These diagrams are qualitatively identical to the bifurcation diagrams of temperature against flow rate for the forced convection problem under the assumption of infinite thermal conductivity and zero species diffusivity.

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

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.

High Rayleigh Number Natural Convection Inside 2D Porous Enclosures Using the Lattice Boltzmann Method

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Ramanathan Vishnampet ◽  
Arunn Narasimhan ◽  
V. Babu
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Parallel Implementation ◽  
Form Drag ◽  
Energy Equations ◽  
Boltzmann Method ◽  
Rayleigh Numbers

Lattice Boltzmann method (LBM) is employed to investigate natural convection inside porous medium enclosures at high Rayleigh numbers. Volume averaged porous medium model is coupled with the lattice Boltzmann formulation of the momentum and energy equations for fluid flow. A parallel implementation of the single relaxation time LBM is used, which allows the porous medium modified Rayleigh number Ram to be as high as 108. Heat transfer results in the form of the enclosure averaged Nusselt number Nu are obtained for higher modified Rayleigh numbers 104≤Ram≤108. The Nu values are compared with values in the absence of the form drag term. The form drag due to the porous medium is found to influence Nu considerably. The effect of the form drag on Nu is studied by using a form drag modified Rayleigh number RaC (extended from Ram). Utilizing the results for Nu in the high Ram range, a correlation is proposed between Nu and RaC for Darcy numbers 10−6≤Da≤10−2, encompassing the non-Darcy flow regime.

scholarly journals Double Diffusive Convection in a Layer of Maxwell Viscoelastic Fluid in Porous Medium in the Presence of Soret and Dufour Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Viscoelastic Fluid ◽  
Fluid Layer ◽  
Lewis Number ◽  
Double Diffusive Convection ◽  
Free Boundaries ◽  
Soret And Dufour Effects ◽  
Diffusive Convection ◽  
Double Diffusive

Double diffusive convection in a horizontal layer of Maxwell viscoelastic fluid in a porous medium in the presence of temperature gradient (Soret effects) and concentration gradient (Dufour effects) is investigated. For the porous medium Darcy model is considered. A linear stability analysis based upon normal mode technique is used to study the onset of instabilities of the Maxwell viscolastic fluid layer confined between two free-free boundaries. Rayleigh number on the onset of stationary and oscillatory convection has been derived and graphs have been plotted to study the effects of the Dufour parameter, Soret parameter, Lewis number, and solutal Rayleigh number on stationary convection.

A novel characteristic variational multiscale FEM for incompressible natural convection problem with variable density

2019 ◽  
Vol 29 (2) ◽  
pp. 580-601 ◽  
Author(s):  
Weilong Wang ◽  
Jilian Wu ◽  
Xinlong Feng
Keyword(s):  
Finite Element ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Variable Density ◽  
Content Type ◽  
Variational Multiscale ◽  
Numerical Tests ◽  
Convection Problem ◽  
The Stability ◽  
Natural Convection Problem

Purpose The purpose of this paper is to propose a new method to solve the incompressible natural convection problem with variable density. The main novel ideas of this work are to overcome the stability issue due to the nonlinear inertial term and the hyperbolic term for conventional finite element methods and to deal with high Rayleigh number for the natural convection problem. Design/methodology/approach The paper introduces a novel characteristic variational multiscale (C-VMS) finite element method which combines advantages of both the characteristic and variational multiscale methods within a variational framework for solving the incompressible natural convection problem with variable density. The authors chose the conforming finite element pair (P2, P2, P1, P2) to approximate the density, velocity, pressure and temperature field. Findings The paper gives the stability analysis of the C-VMS method. Extensive two-dimensional/three-dimensional numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well. Originality/value Extensive 2D/3D numerical tests demonstrated that the C-VMS method not only can deal with the incompressible natural convection problem with variable density but also with high Rayleigh number very well.

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.

Natural Convection Experiments in a Stratified Liquid-Saturated Porous Medium

1986 ◽  
Vol 108 (3) ◽  
pp. 660-666 ◽  
Author(s):  
D. C. Reda
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Saturated Porous Medium ◽  
High Permeability ◽  
Transfer Rates ◽  
Variable Porosity ◽  
Radial Extent

Natural convection heat transfer from a constant-flux cylinder, immersed vertically through a stratified (two-layer) liquid-saturated porous medium, was investigated experimentally. Measured radial temperature profiles and heat transfer rates agreed well with numerical predictions based on the work of Hickox and Gartling. The 1:6 permeability-ratio interface existing between the two layers was found to effectively trap buoyancy-driven fluid motion within the high-permeability region, beneath the interface. Within this high-permeability region, Nusselt number versus Rayleigh number data were found to correlate with previously measured results, obtained for the same basic geometry, but with a fully permeable upper-surface hydrodynamic boundary condition. In both cases, the vertical and radial extent of the region under study were large compared to the radius of the heat source. Combined results indicate that, for a given Rayleigh number in the Darcy-flow regime, heat transfer rates from cylinders immersed vertically in uniform liquid-saturated porous media of large vertical and radial extent potentially approach limiting values. Variable-porosity effects which occur in unconsolidated porous media adjacent to solid boundaries were investigated numerically for cases where the particle-to-heater diameter ratio was small (≈ 10−2). Results showed variable-porosity effects to have a negligible influence on the thermal field adjacent to such boundaries under conditions of Darcy flow.

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