Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium

A theoretical analysis is presented to investigate fully developed (both thermally and hydrodynamically) forced convection in a duct of rectangular cross-section filled with a hyper-porous medium. The Darcy-Brinkman model for flow through porous media was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [1], is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium

Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered: isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered.

Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium

Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered: isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

Effects of geological inhomogeneity on high Rayleigh number steady state heat and mass transfer in fluid-saturated porous media heated from below

A parametric study is carried out to investigate how geological inhomogeneity affects the pore-fluid convective flow field, the temperature distribution, and the mass concentration distribution in a fluid-saturated porous medium. The related numerical results have demonstrated that (1) the effects of both medium permeability inhomogeneity and medium thermal conductivity inhomogeneity are significant on the pore-fluid convective flow and the species concentration distribution in the porous medium; (2) the effect of medium thermal conductivity inhomogeneity is dramatic on the temperature distribution in the porous medium, but the effect of medium permeability inhomogeneity on the temperature distribution may be considerable, depending on the Rayleigh number involved in the analysis; (3) if the coupling effect between pore-fluid flow and mass transport is weak, the effect of the Lewis number is negligible on the pore-fluid convective flow and temperature distribution, hut it is significant on the species concentration distribution in the medium.

Electrical impedance particle size method (Coulter Counter) detects the large fat globules in poorly homogenised UHT processed milk

The large fat globules that can be present in UHT milk due to inadequate homogenisation cause a cream layer to form that limits the shelf life of UHT milk. Four different particle size measurement techniques were used to measure the size of fat globules in poorly homogenised UHT milk processed in a UHT pilot plant. The thickness of the cream layer that formed during storage was negatively correlated with homogenisation pressure. It was positively correlated with the mass mean diameter and the percentage volume of particles between 1.5 and 2 mu m diameter, as determined by laser light scattering using the Malvern Mastersizer. Also, the thickness of the cream layer was positively correlated with the volume mode diameter and the percentage volume of particles between 1.5 and 2 mu m diameter, as determined by electrical impedance using the Coulter Counter. The cream layer thickness did not correlate significantly with the Coulter Counter measurements of volume mean diameter, or volume percentages of particles between 2 and 5 mu m or 5 and 10 mu m diameter. Spectroturbidimetry (Emulsion Quality Analyser) and light microscopy analyses were found to be unsuitable for assessing the size of the fat particles. This study suggests that the fat globule size distribution as determined by the electrical impedance method (Coulter Counter) is the most useful for determining the efficiency of homogenisation and therefore for predicting the stability of the fat emulsion in UHT milk during storage.

Growth hormone binding protein correlates strongly with leptin and percentage body fat in GH-deficient adults, is increased by GH replacement but does not predict IGF-I response

GH-binding protein (GHBP) corresponds to the extracellular domain of the GH receptor (GHR) and has been shown to be closely related to body fat. This study aimed to examine the inter-relationship between GHBP, leptin and body fat, and to test the hypothesis that GHBP is modified by GH replacement in GH-deficient adults and predicts IGF-I response. Twenty adults, mean age 47 years (range 20-69) with proven GH deficiency were randomly allocated to either GH (up to 0.25 U/kg/week in daily doses) or placebo for 3 months before cross-over to the opposite treatment. Plasma GHBP and leptin were measured at baseline and 2, 4, 8 and 12 weeks after each treatment. Whole body composition was measured at baseline by dual-energy X-ray absorptiometry (DEXA). There was a strong correlation between baseline leptin and GHBP (r = 0.88, P < 0.0001) and between baseline GHBP and percentage body fat, (r = 0.83, P < 0.0001). Mean GHBP levels were higher on GH compared with placebo, 1.53 +/- 0.28 vs 1.41 +/- 0.25 nM, P = 0.049. There was no correlation between baseline IGF-I and GHBP (r = -0.049, P = 0.84), and GHBP did not predict IGF-I response to GH replacement. The close inter-relationship between GHBP, leptin and body fat suggests a possible role for GHBP in the regulation of body composition. GHBP is increased by GH replacement in GH-deficient adults, but does not predict biochemical response to GH replacement. (C) 1999 Churchill Livingstone.

Effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in deformable fluid-saturated porous media heated from below

In this paper, a solution method is presented to deal with fully coupled problems between medium deformation, pore-fluid flow and heat transfer in fluid-saturated porous media having supercritical Rayleigh numbers. To validate the present solution method, analytical solutions to a benchmark problem are derived for some special cases. After the solution method is validated, a numerical study is carried out to investigate the effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in fluid-saturated media when they are heated from below. The related numerical results have demonstrated that: (1) medium thermoelasticity has a little influence on the overall pattern of convective pore-fluid flow, but it has a considerable effect on the localization of medium deformation, pore-fluid flow, heat transfer and mineralization in a porous medium, especially when the porous medium is comprised of soft rock masses; (2) convective pore-fluid flow plays a very important role in the localization of medium deformation, heat transfer and mineralization in a porous medium. (C) 1999 Elsevier Science S.A. All rights reserved.

A numerical study of pore-fluid, thermal and mass flow iu fluid-saturated porous rock basins

We present a numerical methodology for the study of convective pore-fluid, thermal and mass flow in fluid-saturated porous rock basins. lit particular, we investigate the occurrence and distribution pattern of temperature gradient driven convective pore-fluid flow and hydrocarbon transport in the Australian North West Shelf basin. The related numerical results have demonstrated that: (1) The finite element method combined with the progressive asymptotic approach procedure is a useful tool for dealing with temperature gradient driven pore-fluid flow and mass transport in fluid-saturated hydrothermal basins; (2) Convective pore-fluid flow generally becomes focused in more permeable layers, especially when the layers are thick enough to accommodate the appropriate convective cells; (3) Large dislocation of strata has a significant influence off the distribution patterns of convective pore;fluid flow, thermal flow and hydrocarbon transport in the North West Shelf basin; (4) As a direct consequence of the formation of convective pore-fluid cells, the hydrocarbon concentration is highly localized in the range bounded by two major faults in the basin.

Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.

Finite element modelling of dissipative structures for nonequilibrium chemical reactions in fluid-saturated porous media

We use the finite element method to model and predict the dissipative structures of chemical species for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. In particular, we explore the conditions under which dissipative structures of the species may exist in the Brusselator type of nonequilibrium chemical reaction. Since this is the first time the finite element method and related strategies have been used to study the chemical instability problems in a fluid-saturated porous medium, it is essential to validate the method and strategies before they are put into application. For this purpose, we have rigorously derived the analytical solutions for dissipative structures of chemical species in a benchmark problem, which geometrically is a square. Comparison of the numerical solutions with the analytical ones demonstrates that the proposed numerical method and strategy are robust enough to solve chemical instability problems in a fluid-saturated porous medium. Finally, the related numerical results from two application examples indicate that both the regime and the magnitude of pore-fluid flow have significant effects on the nature of the dissipative structures that developed for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. The motivation for this study is that self-organization under conditions of pore-fluid flow in a porous medium is a potential mechanism of the orebody formation and mineralization in the upper crust of the Earth. (C) 2000 Elsevier Science S.A. All rights reserved.

Numerical modelling of double diffusion driven reactive flow transport in deformable fluid-saturated porous media with particular consideration of temperature-dependent chemical reaction rates

Numerical methods ave used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. in particular, thp temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAG and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed The coupled problem is divided into two subproblems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, if is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.

Kinetics of propranolol uptake in muscle, skin, and fat of the isolated perfused rat hindlimb

The tissue distribution kinetics of a highly bound solute, propranolol, was investigated in a heterogeneous organ, the isolated perfused limb, using the impulse-response technique and destructive sampling. The propranolol concentration in muscle, skin, and fat as well as in outflow perfusate was measured up to 30 min after injection. The resulting data were analysed assuming (1) vascular, muscle, skin and fat compartments as well mixed (compartmental model) and (2) using a distributed-in-space model which accounts for the noninstantaneous intravascular mixing and tissue distribution processes but consists only of a vascular and extravascular phase (two-phase model). The compartmental model adequately described propranolol concentration-time data in the three tissue compartments and the outflow concentration-time curve (except of the early mixing phase). In contrast, the two-phase model better described the outflow concentration-time curve but is limited in accounting only for the distribution kinetics in the dominant tissue, the muscle. The two-phase model well described the time course of propranolol concentration in muscle tissue, with parameter estimates similar to those obtained with the compartmental model. The results suggest, first that the uptake kinetics of propranolol into skin and fat cannot be analysed on the basis of outflow data alone and, second that the assumption of well-mixed compartments is a valid approximation from a practical point of view las, e.g., in physiological based pharmacokinetic modelling). The steady-state distribution volumes of skin and fat were only 16 and 4%, respectively, of that of muscle tissue (16.7 ml), with higher partition coefficient in fat (6.36) than in skin (2.64) and muscle (2.79. (C) 2000 Elsevier Science B.V. All rights reserved.