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.

Flows in Rotating Cylinders With a Porous Lining

2007 ◽  
Author(s):  
M. Subotic ◽  
F. C. Lai
Keyword(s):  
Porous Layer ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Outer Cylinder ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Temperature Fields ◽  
Rotating Cylinders ◽  
Press Fit ◽  
Porous Sleeve

Flow and temperature fields in an annulus between two rotating cylinders have been examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press-fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The Brinkman-extended Darcy equations are used to model the flow in the porous layer while Navier-Stokes equations are used for the fluid layer. The conditions applied at the interface between the porous and fluid layers are the continuity of temperature, heat flux, tangential velocity and shear stress. Analytical solutions have been attempted. Through these solutions, the effects of Darcy number, Brinkman number, and porous sleeve thickness on the velocity profile and temperature distribution are studied.

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.

Flows Between Rotating Cylinders With a Porous Lining

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
M. Subotic ◽  
F. C. Lai
Keyword(s):  
Porous Layer ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Outer Cylinder ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Temperature Fields ◽  
Rotating Cylinders ◽  
Press Fit ◽  
Porous Sleeve

Flow and temperature fields in an annulus between two rotating cylinders have been examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The Brinkman-extended Darcy equations are used to model the flow in the porous layer while the Navier–Stokes equations are used for the fluid layer. The conditions applied at the interface between the porous and fluid layers are the continuity of temperature, heat flux, tangential velocity, and shear stress. Analytical solutions have been attempted. Through these solutions, the effects of Darcy number, Brinkman number, and porous sleeve thickness on the velocity profile and temperature distribution are studied.

scholarly journals Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition

1992 ◽  
Vol 15 (4) ◽  
pp. 789-794 ◽  
Author(s):  
G. Ramanaiah ◽  
V. Kumaran
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Free Convection ◽  
Transformation Group ◽  
Darcy Number ◽  
Thermal Boundary Condition ◽  
High Porosity

The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. The surfaces are subjected to a mixed thermal boundary condition characterized by a parameterm;m=0,1,∞correspond to the cases of prescribed temperature, prescribed heat flux and prescribed heat transfer coefficient respectively. It is shown that the solutions for differentmare dependent and a transformation group has been found, through which one can get solution for anymprovided solution for a particular value ofmis known. The effects of Darcy number on skin friction and rate of heat transfer are analyzed.

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.

Natural convective heat transfer in a hemispherical cavity filled with ZnO–H2O nanofluid saturated porous medium

2018 ◽  
Vol 29 (10) ◽  
pp. 1850097 ◽  
Author(s):  
Abderrahmane Baïri ◽  
Najib Laraqi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Physical Parameters ◽  
Numerical Work

This three-dimensional (3D) numerical work based on the volume control method quantifies the convective heat transfer occurring in a hemispherical cavity filled with a ZnO–H2O nanofluid saturated porous medium. Its main objective is to improve the cooling of an electronic component contained in this enclosure. The volume fraction of the considered monophasic nanofluid varies between 0% (pure water) and 10%, while the cupola is maintained isothermal at cold temperature. During operation, the active device generates a heat flux leading to high Rayleigh number reaching [Formula: see text] and may be inclined with respect to the horizontal plane at an angle ranging from 0[Formula: see text] to 180[Formula: see text] (horizontal position with cupola facing upwards and downwards, respectively) by steps of 15[Formula: see text]. The natural convective heat transfer represented by the average Nusselt number has been quantified for many configurations obtained by combining the tilt angle, the Rayleigh number, the nanofluid volume fraction and the ratio between the thermal conductivity of the porous medium’s solid matrix and that of the base fluid. This ratio has a significant influence on the free convective heat transfer and ranges from 0 (without porous media) to 70 in this work. The influence of the four physical parameters is analyzed and commented. An empirical correlation between the Nusselt number and these parameters is proposed, allowing determination of the average natural convective heat transfer occurring in the hemispherical cavity.

Optimum fluid layer thickness for heat transfer effectiveness using water-based nanofluids-A numerical estimation

2019 ◽  
Vol 48 (8) ◽  
pp. 3945-3967 ◽  
Author(s):  
S. Ramesh Krishnan ◽  
V.N. Narayanan Namboothiri ◽  
Abin Mathew
Keyword(s):  
Heat Transfer ◽  
Layer Thickness ◽  
Fluid Layer ◽  
Numerical Estimation ◽  
Water Based

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.

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