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.

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.

Thermal Instability of a Fluid-Saturated Porous Medium Bounded by Thin Fluid Layers

1987 ◽  
Vol 109 (3) ◽  
pp. 677-682 ◽  
Author(s):  
G. Pillatsis ◽  
M. E. Taslim ◽  
U. Narusawa
Keyword(s):  
Porous Medium ◽  
Porous Layer ◽  
Thermal Instability ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Convective Motion ◽  
Wave Number ◽  
Thermal Conductivity Ratio ◽  
Fluid Layers

A linear stability analysis is performed for a horizontal Darcy porous layer of depth 2dm sandwiched between two fluid layers of depth d (each) with the top and bottom boundaries being dynamically free and kept at fixed temperatures. The Beavers–Joseph condition is employed as one of the interfacial boundary conditions between the fluid and the porous layer. The critical Rayleigh number and the horizontal wave number for the onset of convective motion depend on the following four nondimensional parameters: dˆ ( = dm/d, the depth ratio), δ ( = K/dm with K being the permeability of the porous medium), α (the proportionality constant in the Beavers–Joseph condition), and k/km (the thermal conductivity ratio). In order to analyze the effect of these parameters on the stability condition, a set of numerical solutions is obtained in terms of a convergent series for the respective layers, for the case in which the thickness of the porous layer is much greater than that of the fluid layer. A comparison of this study with the previously obtained exact solution for the case of constant heat flux boundaries is made to illustrate quantitative effects of the interfacial and the top/bottom boundaries on the thermal instability of a combined system of porous and fluid layers.

scholarly journals Convective fluid flow and heat transfer in a vertical rectangular duct containing a horizontal porous medium and fluid layer

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
J.C. Umavathi ◽  
O. Anwar Beg
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Rectangular Cross Section ◽  
Volumetric Flow Rate ◽  
Immiscible Fluids ◽  
Temperature Fields ◽  
Numerical Code ◽  
Content Type

Purpose The purpose of this paper is to investigate thermally and hydrodynamically fully developed convection in a duct of rectangular cross-section containing a porous medium and fluid layer. Design/methodology/approach The Darcy–Brinkman–Forchheimer flow model is adopted. A finite difference method of second-order accuracy with the Southwell-over-relaxation method is deployed to solve the non-dimensional momentum and energy conservation equations under physically robust boundary conditions. Findings It is found that the presence of porous structure and different immiscible fluids exert a significant impact on controlling the flow. Graphical results for the influence of the governing parameters i.e. Grashof number, Darcy number, porous media inertia parameter, Brinkman number and ratios of viscosities, thermal expansion and thermal conductivity parameters on the velocity and temperature fields are presented. The volumetric flow rate, skin friction and rate of heat transfer at the left and right walls of the duct are also provided in tabular form. The numerical solutions obtained are validated with the published study and excellent agreement is attained. Originality/value To the author’s best knowledge this study original in developing the numerical code using FORTRAN to assess the fluid properties for immiscible fluids. The study is relevant to geothermal energy systems, thermal insulation systems, resin flow modeling for liquid composite molding processes and hybrid solar collectors.

scholarly journals Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip and Temperature Jump Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
M. G. Sobamowo ◽  
A. T. Akinshilo ◽  
A. A. Yinusa
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Temperature Jump ◽  
Squeezing Flow ◽  
Nonlinear Ordinary Differential Equations ◽  
Jump Conditions ◽  
Homotopy Perturbation ◽  
Parallel Disks

The various applications of squeezing flow between two parallel surfaces such as those that are evident in manufacturing industries, polymer processing, compression, power transmission, lubricating system, food processing, and cooling amongst others call for further study on the effects of various parameters on the flow phenomena. In the present study, effects of nanoparticle geometry, slip, and temperature jump conditions on thermo-magneto-solutal squeezing flow of nanofluid between two parallel disks embedded in a porous medium are investigated, analyzed, and discussed. Similarity variables are used to transform the developed governing systems of nonlinear partial differential equations to systems of nonlinear ordinary differential equations. Homotopy perturbation method is used to solve the systems of the nonlinear ordinary differential equations. In order to verify the accuracy of the developed analytical solutions, the results of the homotopy perturbation method are compared with the results of the numerical method using the shooting method coupled with the fourth-order Runge–Kutta, and good agreements are established. Through the approximate analytical solutions, parametric studies are carried out to investigate the effects of nanoparticle size and shape, Brownian motion parameter, nanoparticle parameter, thermophoresis parameter, Hartmann number, Lewis number and pressure gradient parameters, slip, and temperature jump boundary conditions on thermo-solutal and hydromagnetic behavior of the nanofluid. This study will enhance and advance the understanding of nanofluidics such as energy conservation, friction reduction, and micromixing of biological samples.

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.

Thermal Optimization of a Circular-Sectored Finned Tube Using a Porous Medium Approach

2002 ◽  
Vol 124 (6) ◽  
pp. 1026-1033 ◽  
Author(s):  
Sung Jin Kim ◽  
Jae Wook Yoo ◽  
Seok Pil Jang
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Effective Conductivity ◽  
Saturated Porous Medium ◽  
Finned Tube ◽  
Uniform Heat Flux ◽  
Total Thermal Resistance

The present work investigates the heat transfer characteristics of a laminar fully developed forced convection in a circular-sectored finned tube with axially uniform heat flux and peripherally uniform wall temperature. The tubes with circular-sectored fins are modeled as a fluid-saturated porous medium. Using the Brinkman-extended Darcy model for fluid flow and the two-equation model for heat transfer, the analytical solutions for both velocity and temperature distributions are obtained and compared with the exact solution for fluid flow and the numerical solutions for conjugate heat transfer in order to validate the porous medium approach. The agreement between the solutions based on the porous medium approach and the conventional method is close within 5.3 percent. Based on the analytical solutions, parameters of engineering importance are identified to be the angle of the circular sector α and the effective conductivity ratio C, and their effects on fluid flow and heat transfer are studied. Also, the total thermal resistance is derived from the analytical solutions and minimized in order to optimize the thermal performance of a tube with circular-sectored fins.

scholarly journals On the Onset of Thermal Convection in a Layer of Oldroydian Visco-Elastic Fluid Saturated by Brinkman–Darcy Porous Medium

2015 ◽  
Vol 37 (4) ◽  
pp. 3-10 ◽  
Author(s):  
Ramesh Chand
Keyword(s):  
Porous Medium ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Darcy Number ◽  
Horizontal Layer ◽  
Relaxation Parameter ◽  
Free Boundaries ◽  
Oscillatory Convection ◽  
Elastic Fluid ◽  
Mode Technique

AbstractThermal instability in a horizontal layer of Oldroydian visco-elastic fluid in a porous medium is investigated. For porous medium the Brinkman–Darcy model is considered. A linear stability analysis based upon perturbation method and normal mode technique is used to find solution of the fluid layer confined between two free-free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically. The influence of the Brinkman–Darcy, Prandtl–Darcy number, stress relaxation parameter on the stationary and oscillatory convection is studied both analytically and graphically. The sufficient condition for the validity of PES has also been derived.

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.

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