Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford, is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case.

Heat transfer and entropy generation optimization of forced convection in a porous-saturated duct of rectangular cross-section

We investigate analytically the first and the second law characteristics of fully developed forced convection inside a porous-saturated duct of rectangular cross-section. The Darcy-Brinkman flow model is employed. Three different types of thermal boundary conditions are examined. Expressions for the Nusselt number, the Bejan number, and the dimensionless entropy generation rate are presented in terms of the system parameters. The conclusions of this analytical study will make it possible to compare, evaluate, and optimize alternative rectangular duct design options in terms of heat transfer, pressure drop, and entropy generation. (c) 2006 Elsevier Ltd. All rights reserved.

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.

Thermally developing Brinkman–Brinkman forced convection in rectangular ducts with isothermal walls

The Extended Weighted Residuals Method (EWRM) is applied to investigate the effects of viscous dissipation on the thermal development of forced convection in a porous-saturated duct of rectangular cross-section with isothermal boundary condition. The Brinkman flow model is employed for determination of the velocity field. The temperature in the flow field was computed by utilizing the Green’s function solution based on the EWRM. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate. In addition to the aspect ratio, the other parameters included in this computation are the Darcy number, viscosity ratio, and the Brinkman number.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Experimental Analysis of Froude Number Effect on Air Entrainment in the Hydraulic Jump

A hydraulic jump is characterized by strong energy dissipation and mixing, large-scale turbulence, air entrainment, waves and spray. Despite recent pertinent studies, the interaction between air bubbles diffusion and momentum transfer is not completely understood. The objective of this paper is to present experimental results from new measurements performed in rectangular horizontal flume with partially-developed inflow conditions. The vertical distributions of void fraction and air bubbles count rate were recorded for inflow Froude number Fr1 in the range from 5.2 to 14.3. Rapid detrainment process was observed near the jump toe, whereas the structure of the air diffusion layer was clearly observed over longer distances. These new data were compared with previous data generally collected at lower Froude numbers. The comparison demonstrated that, at a fixed distance from the jump toe, the maximum void fraction Cmax increases with the increasing Fr1. The vertical locations of the maximum void fraction and bubble count rate were consistent with previous studies. Finally, an empirical correlation between the upper boundary of the air diffusion layer and the distance from the impingement point was provided.

Dynamic Similarity and Scale Effects Affecting Air Bubble Entrainment in Hydraulic Jumps

In an open channel, the transition from super- to sub-critical flow is a flow singularity (the hydraulic jump) characterised by a sharp rise in free-surface elevation, strong turbulence and air entrainment in the roller. A key feature of the hydraulic jump flow is the strong free-surface aeration and air-water flow turbulence. In the present study, similar experiments were conducted with identical inflow Froude numbers Fr1 using a geometric scaling ratio of 2:1. The results of the Froude-similar experiments showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding some lesser aeration of the jump roller. The dimensionless bubble count rates were significantly lower in the smaller channel, especially in the mixing layer. The bubble chord time distributions were quantitatively close in both channels, and they were not scaled according to a Froude similitude. Simply the hydraulic jump remains a fascinating two-phase flow motion that is still poorly understood.

Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.

Babesia bovis: Genome size, number of chromosomes and telomeric probe hybridisation

Pulsed field gel electrophoresis of intact chromosomes of Babesia bovis revealed four chromosomes in the haploid genome. A telomere probe, derived from Plasmodium berghei, hybridised to eight SfiI restriction fragments of genomic B. bovis DNA digests indicating the presence of four chromosomes. A small subunit (18S) ribosomal RNA gene probe hybridised to the third chromosome only. The genome size of B. bovis is estimated to be 9.4 million base pairs. The sizes of chromosomes 1, 2, 3 and 4 are estimated to be 1.4, 2.0, 2.8 and 3.2 million base pairs, respectively. (C) 1997 Australian Society for Parasitology. Published by Elsevier Science 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.

On the mechanism of microbial cell disruption in high-pressure homogenisation

The tensions produced in the wall of a rigid, thin-walled, liquid-filled sphere as it moves with an axisymmetric straining flow are examined. This problem has not been previously addressed. A generalised correlation for the maximum wall tension, expressed in dimensionless form as a Weber number (We), is developed in terms of the acceleration number (Ac) and Reynolds number (Re) of the straining flow. At low Reynolds number We is dominated by viscous forces, while inertial forces due to internal pressure gradients caused by sphere acceleration dominate at higher Re. The generalised correlation has been used to examine the case of a typical yeast cell (a thin-walled, liquid-filled sphere) passing through a typical high-pressure homogeniser (a straining-flow device). At 56 MPa homogenising pressure, a 6 mu m yeast cell experiences tensions in the inertially dominated regime (Re = 100). The correlation gives We = 0.206, corresponding to a maximum wall tension of 8 Nm(-1). This is equivalent to an applied compressive force of 150 mu N and compares favourably with the force required to break yeast cells under compressive micromanipulation (40-90 mu N). Inertial forces may therefore be an important and previously unrecognised. mechanism of microbial cell disruption during high-pressure homogenisation. Further work is required to examine the likelihood of cell deformation in the high-strain-rate short-residence-time environment of the homogeniser, and the effect that such deformation may have on the contribution of inertial forces to disruption. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

The fornax spectroscopic survey: the number of unresolved compact galaxies

We describe a sample of 13 bright (18.5 < B-J < 20.1), compact galaxies at low redshift (0.05 < z < 0.21) behind the Fornax Cluster. These galaxies are unresolved on UK Schmidt sky survey plates, and so they would be missing from most galaxy catalogs compiled from this material. The objects were found during initial observations of The Fornax Spectroscopic Survey. This project is using the Two-degree Field spectrograph on the Anglo-Australian Telescope to obtain spectra for a complete sample of all 14,000 objects, stellar and nonstellar, with 16.5 < B-J < 19.7, in a 12 deg(2) area centered on the Fornax Cluster of galaxies. The surface density of compact galaxies with magnitudes 16.5 < B-J < 19.7 is 7 +/- 3 deg(-2), representing 2.8% +/- 1.6% of all local (z < 0.2) galaxies to this limit. There are 12 +/- 3 deg(-2) with 16.5 < B-J < 20.2. They are luminous (-21.5 < M-B < -18.0, for H-o = 50 km s(-1) Mpc(-1)), and most have strong emission lines (H alpha equivalent widths of 40-200 Angstrom) and small sizes typical of luminous H II galaxies and compact narrow emission line galaxies. Four out of 13 have red colors and early-type spectra, and so they are unlikely to have been detected in any previous surveys.

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.

Approach to designing rotating drum bioreactors for solid-state fermentation on the basis of dimensionless design factors

The development of large-scale solid-stale fermentation (SSF) processes is hampered by the lack of simple tools for the design of SSF bioreactors. The use of semifundamental mathematical models to design and operate SSF bioreactors can be complex. In this work, dimensionless design factors are used to predict the effects of scale and of operational variables on the performance of rotating drum bioreactors. The dimensionless design factor (DDF) is a ratio of the rate of heat generation to the rate of heat removal at the time of peak heat production. It can be used to predict maximum temperatures reached within the substrate bed for given operational variables. Alternatively, given the maximum temperature that can be tolerated during the fermentation, it can be used to explore the combinations of operating variables that prevent that temperature from being exceeded. Comparison of the predictions of the DDF approach with literature data for operation of rotating drums suggests that the DDF is a useful tool. The DDF approach was used to explore the consequences of three scale-up strategies on the required air flow rates and maximum temperatures achieved in the substrate bed as the bioreactor size was increased on the basis of geometric similarity. The first of these strategies was to maintain the superficial flow rate of the process air through the drum constant. The second was to maintain the ratio of volumes of air per volume of bioreactor constant. The third strategy was to adjust the air flow rate with increase in scale in such a manner as to maintain constant the maximum temperature attained in the substrate bed during the fermentation. (C) 2000 John Wiley & Sons, Inc.

Extraordinary and extensive karyotypic variation: A 48-fold range in chromosome number in the gall-inducing scale insect Apiomorpha (Hemiptera : Coccoidea : Eriococcidae)

Chromosome number reflects strong constraints on karyotype evolution, unescaped by the majority of animal taxa. Although there is commonly chromosomal polymorphism among closely related taxa, very large differences in chromosome number are rare. This study reports one of the most extensive chromosomal ranges yet reported for an animal genus. Apiomorpha Rubsaamen (Hemiptera: Coccoidea: Eriococcidae), an endemic Australian gall-inducing scale insect genus, exhibits an extraordinary 48-fold variation in chromosome number with diploid numbers ranging from 4 to about 192. Diploid complements of all other eriococcids examined to date range only from 6 to 28. Closely related species of Apiomorpha usually have very different karyotypes, to the extent that the variation within some species- groups is as great as that across the entire genus. There is extensive chromosomal variation among populations within 17 of the morphologically defined species of Apiomorpha indicating the existence of cryptic species-complexes. The extent and pattern of karyotypic variation suggests rapid chromosomal evolution via fissions and (or) fusions. It is hypothesized that chromosomal rearrangements in Apiomorpha species may be associated with these insects' tracking the radiation of their speciose host genus, Eucalyptus.