Natural Convection in Horizontal Porous Layers: Effects of Darcy and Prandtl Numbers

1989 ◽  
Vol 111 (4) ◽  
pp. 926-935 ◽  
Author(s):  
N. Kladias ◽  
V. Prasad
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Darcy Number ◽  
Solid Particles ◽  
Convection Regime ◽  
Porous Layers

Natural convection in horizontal porous layers heated from below is studied by employing a formulation based on the Brinkman–Forchheimer–extended Darcy equation of motion. The numerical solutions show that the convective flow is initiated at lower fluid Rayleigh number Raf than that predicted by the linear stability analysis for the Darcy flow model. The effect is considerable, particularly at a Darcy number Da greater than 10−4. On the other hand, an increase in the thermal conductivity of solid particles has a stabilizing effect. Also, the Rayleigh number Raf required for the onset of convection increases as the fluid Prandtl number is decreased. In the stable convection regime, the heat transfer rate increases with the Rayleigh number, the Prandtl number, the Darcy number, and the ratio of the solid and fluid thermal conductivities. However, there exists an asymptotic convection regime where the porous media solutions are independent of the permeability of the porous matrix or Darcy number. In this regime, the temperature and flow fields are very similar to those obtained for a fluid layer heated from below. Indeed, the Nusselt numbers for a porous medium with kf = ks match with the fluid results. The effect of Prandtl number is observed to be significant for Prf < 10, and is strengthened with an increase in Raf, Da, and ks/kf. An interesting effect, that a porous medium can transport more energy than the saturating fluid alone, is also revealed.

A Novel Methodology for Thermal Analysis of a Composite System Consisting of a Porous Medium and an Adjacent Fluid Layer

2005 ◽  
Vol 127 (6) ◽  
pp. 648-656 ◽  
Author(s):  
Jung Yim Min ◽  
Sung Jin Kim
Keyword(s):  
Porous Medium ◽  
Analytical Solutions ◽  
Composite System ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Darcy Number ◽  
Jump Conditions ◽  
Interfacial Conditions ◽  
Innovative Methodology ◽  
Flux Jump

An innovative methodology is presented for the purpose of analyzing fluid flow and heat transfer in a porous–fluid composite system, where the porous medium is assumed to have a periodic structure, i.e., solid and fluid phases repeat themselves in a regular pattern. With the present method, analytical solutions for the velocity and temperature distributions are obtained when the distributions in the adjacent fluid layer are allowed to vary in the directions both parallel and perpendicular to the interface between the porous medium and the adjacent fluid layer. The analytical solutions are validated by comparing them with the corresponding numerical solutions for the case of the ideal composite channel, and with existing experimental data. The present analytical solutions have a distinctive advantage in that they do not involve any unknown coefficients resulting from the previous interfacial conditions. Moreover, by comparing interfacial conditions derived from the present study with the stress- and flux-jump conditions developed by previous investigators, the unknown coefficients included in the stress- and flux-jump conditions are analytically determined and are shown to depend on the porosity, the Darcy number and the pore diameter.

scholarly journals Natural Convection over Two Superellipse Shapes with a Porous Cavity Populated by Nanofluid

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6952
Author(s):  
Noura Alsedais
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Governing Equations ◽  
Porous Layers ◽  
Porous Cavity ◽  
The Mean ◽  
Volume Method

The influences of superellipse shapes on natural convection in a horizontally subdivided non-Darcy porous cavity populated by Cu-water nanofluid are inspected in this paper. The impacts of the inner geometries (n = 0.5,1,1.5,4) Rayleigh number (103 ≤ Ra ≤ 106), Darcy number (10−5 ≤ Da ≤ 10−2), porosity (0.2 ≤ ϵ ≤ 0.8), and solid volume fraction (0.01 ≤ ∅ ≤ 0.05) on nanofluid heat transport and streamlines were examined. The hot superellipse shapes were placed in the cavity’s bottom and top, while the adiabatic boundaries on the flat walls of the cavity were considered. The governing equations were numerically solved using the finite volume method (FVM). It was found that the movement of the nanofluid upsurged as Ra boosted. The temperature distributions in the cavity’s core had an inverse relationship with increasing Rayleigh number. An extra porous resistance at lower Darcy numbers limited the nanofluid’s movement within the porous layers. The mean Nusselt number decreased as the porous resistance increased (Da ≤ 10−4). The flow and temperature were strongly affected as the shape of the inner superellipse grew larger.

Natural Convection in a Stably Heated Corner Filled With Porous Medium

1985 ◽  
Vol 107 (2) ◽  
pp. 293-298 ◽  
Author(s):  
S. Kimura ◽  
A. Bejan
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Single Cell ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Number Range ◽  
Corner Flow ◽  
Horizontal Wall

This is a study of the single-cell natural convection pattern that occurs in a “stably heated” corner in a fluid-saturated porous medium, i.e., in the corner formed between a cold horizontal wall and a hot vertical wall situated above the horizontal wall, or in the corner between a hot horizontal wall and a cold vertical wall situated below the horizontal wall. Numerical simulations show that this type of corner flow is present in porous media heated from the side when a stabilizing vertical temperature gradient is imposed in order to suppress the side-driven convection. Based on numerical solutions and on scale analysis, it is shown that the single cell corner flow becomes increasingly more localized as the Rayleigh number increases. At the same time, the mass flow rate engaged in natural circulation and the conduction-referenced Nusselt number increase. Numerical results for the flow and temperature fields and for the net heat transfer rate are reported in the Darcy-Rayleigh number range 10–6000.

Natural Convection From a Buried Pipe With a Superimposed Fluid Layer

2007 ◽  
Author(s):  
C. C. Ngo ◽  
F. C. Lai
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Rayleigh Number ◽  
Layer Thickness ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Velocity Shear ◽  
Buried Pipe

Heat transfer induced by buoyancy from a pipe buried in a semi-infinite porous medium with a superimposed fluid layer has been numerically examined in this study. Due to the complexity involved, finite difference method along with body-fitted coordinate systems has been employed. The Brinkman-extended Darcy equations are used to model flow in the porous medium while Navier-Stokes equations are used for the fluid layer. The conditions applied at the interface between the fluid and porous layers are the continuity of temperature, heat flux, normal and tangential velocity, shear stress and pressure. A parametric study has been performed to investigate the effects of Rayleigh number, Prandtl number, Darcy number, and fluid layer thickness on the flow patterns and heat transfer rates. The results show that heat transfer increases with the Rayleigh number, but the convective strength decreases with the Darcy number. The heat transfer rate is smaller when the superimposed fluid is air instead of water. For a porous layer with Da ≤ 0.0005 and an overlaying fluid layer thickness of L/ri ≥ 1, convection is initiated in the fluid layer and it may develop into multiple recirculating cells at a moderate Rayleigh number (i.e., Ra ≤ 104), and may further develop into a single cell at a higher Rayleigh number of 105.

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jinhu Zhao ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fawang Liu ◽  
Xuehui Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Prandtl Number ◽  
Fractional Derivative ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Elastic Effect

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

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.

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.

Numerical simulations of MHD forced convection flow of micropolar fluid inside a right-angled triangular cavity saturated with porous medium: Effects of vertical moving wall

2019 ◽  
Vol 97 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Mubbashar Nazeer ◽  
N. Ali ◽  
Tariq Javed
Keyword(s):  
Porous Medium ◽  
Prandtl Number ◽  
Forced Convection ◽  
Micropolar Fluid ◽  
Richardson Number ◽  
Hartmann Number ◽  
Darcy Number ◽  
Convection Flow ◽  
Penalty Parameter ◽  
Forced Convection Flow

The present article explores the effects of moving lid on the forced convection flow of micropolar fluid inside a right-angle triangular cavity saturated with porous medium. The base and hypotenuse or inclined sides of the cavity are maintained at constant temperatures, while the vertical side of the enclosure is adiabatic and moving with constant velocity in upward or downward direction. The flow equations are simulated by using the robust finite element numerical technique. The pressure term from the momentum equations is eliminated by using the penalty parameter. For a consistent solution, the value of the penalty parameter is selected as 107. The simulations are performed for the cases based on the direction of moving lid. The numerical outcomes are shown in terms of streamlines, temperature contours, and local and average Nusselt numbers for sundry parameters, such as micropolar parameter, Reynolds number, Richardson number, Darcy number, Hartmann number, and Prandtl number. It is observed that the shape of the inner circulating cell is elliptic when the lid is moving in the upward direction and fluid is clear (Newtonian fluid). It is also found that average Nusselt number in both cases increases with increasing Prandtl number, Richardson number, micropolar parameter, and Darcy number, whereas it decreases with increasing Hartmann number. Further, it achieves a maximum when the lid is moving in the downward direction, regardless of the choice of involved parameters. The numerical code is also validated with previous published results. The investigation of the current study is beneficial in porous heat exchangers, construction of triangular-shaped solar collectors, rigid crystal, polymeric fluid transport, etc.

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