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.

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.

Finite element analysis of heat transfer and mineralization in layered hydrothermal systems with upward throughflow

We use the finite element method to solve the coupled problem between convective pore-fluid flow, heat transfer and mineralization in layered hydrothermal systems with upward throughflow. In particular, we present the improved rock alteration index (IRAI) concept for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in the systems. To validate the numerical method used in the computation, analytical solutions to a benchmark problem have been derived. After the numerical method is validated, it is used to investigate the pattern of pore-fluid Aom, the distribution of temperature and the mineralization pattern of gold minerals in a layered hydrothermal system with upward throughflow. The related numerical results have demonstrated that the present concept of IRAI is useful and applicable for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in hydrothermal systems. (C) 2000 Elsevier Science S.A. All rights reserved.

Finite element modelling of heat transfer through permeable cracks in hydrothermal systems with upward throughflow

We use the finite element method to model the heat transfer phenomenon through permeable cracks in hydrothermal systems with upward throughflow. Since the finite element method is an approximate numerical method, the method must be validated before it is used to soh,e any new, kind of problem. However, the analytical solution, which can be used to validate the finite element method and other numerical methods, is rather limited in the literature, especially, for the problem considered here. Keeping this in mind, we have derived analytical solutions for the temperature distribution along the vertical axis of a crack in a fluid-saturated porous layer. After the finite element method is validated by comparing the numerical solution with the analytical solution for the same benchmark problem, it is used to investigate the pore-fluid flow and heat transfer in layered hydrothermal systems with vertical permeable cracks. The related analytical and numerical results have demonstrated that vertical cracks are effective and efficient members to transfer heat energy from the bottom section to the top section in hydrothermal systems with upward throughflow.

Numerical simulation of combined heat transfer phenomena (conduction, convection, and radiation). Application to he optimisation of thermal systems

Thermal systems interchanging heat and mass by conduction, convection, radiation (solar and thermal ) occur in many engineering applications like energy storage by solar collectors, window glazing in buildings, refrigeration of plastic moulds, air handling units etc. Often these thermal systems are composed of various elements for example a building with wall, windows, rooms, etc. It would be of particular interest to have a modular thermal system which is formed by connecting different modules for the elements, flexibility to use and change models for individual elements, add or remove elements without changing the entire code. A numerical approach to handle the heat transfer and fluid flow in such systems helps in saving the full scale experiment time, cost and also aids optimisation of parameters of the system. In subsequent sections are presented a short summary of the work done until now on the orientation of the thesis in the field of numerical methods for heat transfer and fluid flow applications, the work in process and the future work.

Simulation of Boundary Layers and Heat Transfer in the Entrance Region of Pipes

The study of fluid flow in pipes is one of the main topic of interest for engineers in industries. In this thesis, an effort is made to study the boundary layers formed near the wall of the pipe and how it behaves as a resistance to heat transfer. Before few decades, the scientists used to derive the analytical and empirical results by hand as there were limited means available to solve the complex fluid flow phenomena. Due to the increase in technology, now it has been practically possible to understand and analyze the actual fluid flow in any type of geometry. Several methodologies have been used in the past to analyze the boundary layer equations and to derive the expression for heat transfer. An integral relation approach is used for the analytical solution of the boundary layer equations and is compared with the FLUENT simulations for the laminar case. Law of the wall approach is used to derive the empirical correlation between dimensionless numbers and is then compared with the results from FLUENT for the turbulent case. In this thesis, different approaches like analytical, empirical and numerical are compared for the same set of fluid flow equations.

CFD simulation of complex phenomena containing suspensions and flow throughporous media

There is an increasing reliance on computers to solve complex engineering problems. This is because computers, in addition to supporting the development and implementation of adequate and clear models, can especially minimize the financial support required. The ability of computers to perform complex calculations at high speed has enabled the creation of highly complex systems to model real-world phenomena. The complexity of the fluid dynamics problem makes it difficult or impossible to solve equations of an object in a flow exactly. Approximate solutions can be obtained by construction and measurement of prototypes placed in a flow, or by use of a numerical simulation. Since usage of prototypes can be prohibitively time-consuming and expensive, many have turned to simulations to provide insight during the engineering process. In this case the simulation setup and parameters can be altered much more easily than one could with a real-world experiment. The objective of this research work is to develop numerical models for different suspensions (fiber suspensions, blood flow through microvessels and branching geometries, and magnetic fluids), and also fluid flow through porous media. The models will have merit as a scientific tool and will also have practical application in industries. Most of the numerical simulations were done by the commercial software, Fluent, and user defined functions were added to apply a multiscale method and magnetic field. The results from simulation of fiber suspension can elucidate the physics behind the break up of a fiber floc, opening the possibility for developing a meaningful numerical model of the fiber flow. The simulation of blood movement from an arteriole through a venule via a capillary showed that the model based on VOF can successfully predict the deformation and flow of RBCs in an arteriole. Furthermore, the result corresponds to the experimental observation illustrates that the RBC is deformed during the movement. The concluding remarks presented, provide a correct methodology and a mathematical and numerical framework for the simulation of blood flows in branching. Analysis of ferrofluids simulations indicate that the magnetic Soret effect can be even higher than the conventional one and its strength depends on the strength of magnetic field, confirmed experimentally by Völker and Odenbach. It was also shown that when a magnetic field is perpendicular to the temperature gradient, there will be additional increase in the heat transfer compared to the cases where the magnetic field is parallel to the temperature gradient. In addition, the statistical evaluation (Taguchi technique) on magnetic fluids showed that the temperature and initial concentration of the magnetic phase exert the maximum and minimum contribution to the thermodiffusion, respectively. In the simulation of flow through porous media, dimensionless pressure drop was studied at different Reynolds numbers, based on pore permeability and interstitial fluid velocity. The obtained results agreed well with the correlation of Macdonald et al. (1979) for the range of actual flow Reynolds studied. Furthermore, calculated results for the dispersion coefficients in the cylinder geometry were found to be in agreement with those of Seymour and Callaghan.

Inverse convection problem of simultaneous estimation of two boundary heat fluxes in parallel plate channels

This paper deals with the use of the conjugate gradient method of function estimation for the simultaneous identification of two unknown boundary heat fluxes in parallel plate channels. The fluid flow is assumed to be laminar and hydrodynamically developed. Temperature measurements taken inside the channel are used in the inverse analysis. The accuracy of the present solution approach is examined by using simulated measurements containing random errors, for strict cases involving functional forms with discontinuities and sharp-corners for the unknown functions. Three different types of inverse problems are addressed in the paper, involving the estimation of: (i) Spatially dependent heat fluxes; (ii) Time-dependent heat fluxes; and (iii) Time and spatially dependent heat fluxes.

Experimental analysis of heat recoveries with heat pipes operating in low inclination angle

Heat recovery devices are important in the optimization of thermal systems, since they can be used to reduce thermal losses to the environment. The use of heat pipes in these types of equipment can provide heat recoveries of higher efficiency, since both fluid flows are external and there are less contamination risks between the hot and cold fluids. The objective of this work is to study a heat recovery unit constructed with heat pipes and mainly, to analyze the influence of the inclination of the heat pipes on the performance of the equipment. For this analysis, a heat recovery unit was constructed which possesses 48 finned heat pipes in triangular geometry, the evaporator and condenser being of the same length. This unit was tested in an air-air system simulating a heat recovery process in which heat was supplied to the hot fluid by electrical resistances. The results have shown that there exists an inclination at which the system has a better performance, but for higher inclinations there is no significant increase of the efficiency of the system. This paper also presents the influence of inclination of heat pipes on effectiveness and NTU parameters which are important in heat exchanger design.

Integral transform method for laminar heat transfer convection of herschel-bulkley fluids within concentric annular ducts

ABSTRACT: Related momentum and energy equations describing the heat and fluid flow of Herschel-Bulkley fluids within concentric annular ducts are analytically solved using the classical integral transform technique, which permits accurate determination of parameters of practical interest in engineering such as friction factors and Nusselt numbers for the duct length. In analyzing the problem, thermally developing flow is assumed and the duct walls are subjected to boundary conditions of first kind. Results are computed for the velocity and temperature fields as well as for the parameters cited above with different power-law indices, yield numbers and aspect ratios. Comparisons are also made with previous work available in the literature, providing direct validation of the results and showing that they are consistent.

Development of heat sink device by using topology optimization

Small scale fluid flow systems have been studied for various applications, such as chemical reagent dosages and cooling devices of compact electronic components. This work proposes to present the complete cycle development of an optimized heat sink designed by using Topology Optimization Method (TOM) for best performance, including minimization of pressure drop in fluid flow and maximization of heat dissipation effects, aiming small scale applications. The TOM is applied to a domain, to obtain an optimized channel topology, according to a given multi-objective function that combines pressure drop minimization and heat transfer maximization. Stokes flow hypothesis is adopted. Moreover, both conduction and forced convection effects are included in the steady-state heat transfer model. The topology optimization procedure combines the Finite Element Method (to carry out the physical analysis) with Sequential Linear Programming (as the optimization algorithm). Two-dimensional topology optimization results of channel layouts obtained for a heat sink design are presented as example to illustrate the design methodology. 3D computational simulations and prototype manufacturing have been carried out to validate the proposed design methodology.

EXPERIMENTAL INVESTIGATION OF CERTAIN INTERNAL CONDENSING AND BOILING FLOWS: THEIR SENSITIVITY TO PRESSURE FLUCTUATIONS AND HEAT TRANSFER ENHANCEMENTS

Space-based (satellite, scientific probe, space station, etc.) and millimeter – to – microscale (such as are used in high power electronics cooling, weapons cooling in aircraft, etc.) condensers and boilers are shear/pressure driven. They are of increasing interest to system engineers for thermal management because flow boilers and flow condensers offer both high fluid flow-rate-specific heat transfer capacity and very low thermal resistance between the fluid and the heat exchange surface, so large amounts of heat may be removed using reasonably-sized devices without the need for excessive temperature differences. However, flow stability issues and degradation of performance of shear/pressure driven condensers and boilers due to non-desirable flow morphology over large portions of their lengths have mostly prevented their use in these applications. This research is part of an ongoing investigation seeking to close the gap between science and engineering by analyzing two key innovations which could help address these problems. First, it is recommended that the condenser and boiler be operated in an innovative flow configuration which provides a non-participating core vapor stream to stabilize the annular flow regime throughout the device length, accomplished in an energy-efficient manner by means of ducted vapor re-circulation. This is demonstrated experimentally. Second, suitable pulsations applied to the vapor entering the condenser or boiler (from the re-circulating vapor stream) greatly reduce the thermal resistance of the already effective annular flow regime. For experiments reported here, application of pulsations increased time-averaged heat-flux up to 900 % at a location within the flow condenser and up to 200 % at a location within the flow boiler, measured at the heat-exchange surface. Traditional fully condensing flows, reported here for comparison purposes, show similar heat-flux enhancements due to imposed pulsations over a range of frequencies. Shear/pressure driven condensing and boiling flow experiments are carried out in horizontal mm-scale channels with heat exchange through the bottom surface. The sides and top of the flow channel are insulated. The fluid is FC-72 from 3M Corporation.

Reactive mass transport modelling of a three-dimensional vertical fault zone with a finger-like convective flow regime

For a three-dimensional vertically-oriented fault zone, we consider the coupled effects of fluid flow, heat transfer and reactive mass transport, to investigate the patterns of fluid flow, temperature distribution, mineral alteration and chemically induced porosity changes. We show, analytically and numerically, that finger-like convection patterns can arise in a vertically-oriented fault zone. The onset and patterns of convective fluid flow are controlled by the Rayleigh number which is a function of the thermal properties of the fluid and the rock, the vertical temperature gradient, and the height and the permeability of the fault zone. Vigorous fluid flow causes low temperature gradients over a large region of the fault zone. In such a case, flow across lithological interfaces becomes the most important mechanism for the formation of sharp chemical reaction fronts. The degree of rock buffering, the extent and intensity of alteration, the alteration mineralogy and in some cases the formation of ore deposits are controlled by the magnitude of the flow velocity across these compositional interfaces in the rock. This indicates that alteration patterns along compositional boundaries in the rock may provide some insights into the convection pattern. The advective mass and heat exchanges between the fault zone and the wallrock depend on the permeability contrast between the fault zone and the wallrock. A high permeability contrast promotes focussed convective flow within the fault zone and diffusive exchange of heat and chemical reactants between the fault zone and the wallrock. However, a more gradual permeability change may lead to a regional-scale convective flow system where the flow pattern in the fault affects large-scale fluid flow, mass transport and chemical alteration in the wallrocks

Transport and mixing enhancement in fluid-thermal microsystems

En esta tesis se investiga de forma experimental el transporte pasivo de magnitudes físicas en micro-sistemas con carácter de inmediata aplicación industrial, usando métodos innovadores para mejorar la eficiencia de los mismos optimizando parámetros críticos del diseño o encontrar nuevos destinos de posible aplicación. Parte de los resultados obtenidos en estos experimentos han sido publicados en revistas con un índice de impacto tal que pertenecen al primer cuarto del JCR. Primero de todo se ha analizado el efecto que produce en un intercambiador de calor basado en micro-canales el hecho de dejar un espacio entre canales y tapa superior para la interconexión de los mismos. Esto genera efectos tridimensionales que mejoran la exracción de calor del intercambiador y reducen la caída de presión que aparece por el transcurso del fluido a través de los micro-canales, lo que tiene un gran impacto en la potencia que ha de suministrar la bomba de refrigerante. Se ha analizado también la mejora producida en términos de calor disipado de un micro-procesador refrigerado con un ampliamente usado plato de aletas al implementar en éste una cámara de vapor que almacena un fluido bifásico. Se ha desarrollado de forma paralela un modelo numérico para optimizar las nuevas dimensiones del plato de aletas modificado compatibles con una serie de requerimientos de diseño en el que tanto las dimensiones como el peso juegan un papel esencial. Por otro lado, se han estudiado los fenomenos fluido-dinámicos que aparecen aguas abajo de un cuerpo romo en el seno de un fluido fluyendo por un canal con una alta relación de bloqueo. Los resultados de este estudio confirman, de forma experimental, la existencia de un régimen intermedio, caracterizado por el desarrollo de una burbuja de recirculación oscilante entre los regímenes, bien diferenciados, de burbuja de recirculación estacionaria y calle de torbellinos de Karman, como función del número de Reynolds del flujo incidente. Para la obtención, análisis y post-proceso de los datos, se ha contado con la ayuda de un sistema de Velocimetría por Imágenes de Partículas (PIV). Finalmente y como adición a este último punto, se ha estudiado las vibraciones de un cuerpo romo producidas por el desprendimiento de torbellinos en un canal de alta relación de bloqueo con la base obtenida del estudio anterior. El prisma se mueve con un movimiento armónico simple para un intervalo de números de Reynolds y este movimiento se transforma en vibración alrededor de su eje a partir de un ciero número de Reynolds. En relación al fluido, el régimen de desprendimiento de torbellinos se alcanza a menores números de Reynolds que en el caso de tener el cuerpo romo fijo. Uniendo estos dos registros de movimientos y variando la relación de masas entre prisma y fluido se obtiene un mapa con diferentes estados globales del sistema. Esto no solo tiene aplicación como método para promover el mezclado sino también como método para obtener energía a partir del movimiento del cuerpo en el seno del fluido. Abstract In this thesis, experimental research focused on passive scalar transport is performed in micro-systems with marked sense of industrial application, using innovative methods in order to obtain better performances optimizing critical design parameters or finding new utilities. Part of the results obtained in these experiments have been published into high impact factor journals belonged to the first quarter of the Journal Citation Reports (JCR). First of all the effect of tip clearance in a micro-channel based heat sink is analyzed. Leaving a gap between channels and top cover, letting the channels communicate each other causes three-dimensional effects which improve the heat transfer between fluid and heat sink and also reducing the pressure drop caused by the fluid passing through the micro-channels which has a great impact on the total cooling pumping power needed. It is also analyzed the enhancement produced in terms of dissipated heat in a micro-processor cooling system by improving the predominantly used fin plate with a vapour chamber based heat spreader which contains a two-phase fluid inside. It has also been developed at the same time a numerical model to optimize the new fin plate dimensions compatible with a series of design requirements in which both size and wight plays a very restrictive role. On the other hand, fluid-dynamics phenomena that appears downstream of a bluff body in the bosom of a fluid flow with high blockage ratio has been studied. This research experimentally confirms the existence of an intermediate regime characterized by an oscillating closed recirculation bubble intermediate regime between the steady closed recirculation bubble regime and the vortex shedding regime (Karman street like regime) as a function of the incoming flow Reynolds number. A particle image velocimetry technique (PIV) has been used in order to obtain, analyze and post-process the fluid-dynamic data. Finally and as an addition to the last point, a study on the vortexinduced vibrations (VIV) of a bluff body inside a high blockage ratio channel has been carried out taking advantage of the results obtained with the fixed square prism. The prism moves with simple harmonic motion for a Reynolds number interval and this movement becomes vibrational around its axial axis after overcoming at definite Reynolds number. Regarding the fluid, vortex shedding regime is reached at Reynolds numbers lower than the previous critical ones. Merging both movement spectra and varying the square prism to fluid mass ratio, a map with different global states is reached. This is not only applicable as a mixing enhancement technique but as an energy harvesting method.

(Table 1) Summary of basalt unit thickness, vesicularity, number of flow units, and average porosity at ODP Site 135-839

An inflatable drill-string packer was used at Site 839 to measure the bulk in-situ permeability within basalts cored in Hole 839B. The packer was inflated at two depths, 398.2 and 326.9 mbsf; all on-board information indicated that the packer mechanically closed off the borehole, although apparently the packer hydraulically sealed the borehole only at 398.2 mbsf. Two pulse tests were run at each depth, two constant-rate injection tests were run at the first set, and four were run at the second. Of these, only the constant-rate injection tests at the first set yielded a permeability, calculated as ranging from 1 to 5 * 10**-12 m**2. Pulse tests and constant-rate injection tests for the second set did not yield valid data. The measured permeability is an upper limit; if the packer leaked during the experiments, the basalt would be less permeable. In comparison, permeabilities measured at other Deep Sea Drilling Project and Ocean Drilling Program sites in pillow basalts and flows similar to those measured in Hole 839B are mainly about 10**-13 to 10**-14 m**2. Thus, if our results are valid, the basalts at Site 839 are more permeable than ocean-floor basalts investigated elsewhere. Based on other supporting evidence, we consider these results to be a valid measure of the permeability of the basalts. Temperature data and the geochemical and geotechnical properties of the drilled sediments all indicate that the site is strongly affected by fluid flow. The heat flow is very much less than expected in young oceanic basalts, probably a result of rapid fluid circulation through the crust. The geochemistry of pore fluids is similar to that of seawater, indicating seawater flow through the sediments, and sediments are uniformly underconsolidated for their burial depth, again indicating probable fluid flow. The basalts are highly vesicular. However, the vesicularity can only account for part of the average porosity measured on the neutron porosity well log; the remainder of the measured porosity is likely present as voids and fractures within and between thin-bedded basalts. Core samples, together with porosity, density, and resistivity well-log data show locations where the basalt section is thin bedded and probably has from 15% to 35% void and fracture porosity. Thus, the measured permeability seems reasonable with respect to the high measured porosity. Much of the fluid flow at Site 839 could be directed through highly porous and permeable zones within and between the basalt flows and in the sediment layer just above the basalt. Thus, the permeability measurements give an indication of where and how fluid flow may occur within the oceanic crust of the Lau Basin.