This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

Numerical study of laminar convective cooling of ribs in a parallel plate channel is investigated. Single rib mounted on one channel wall in forced, mixed and free convection is analyzed. Furthermore, the series ribs array with in-line and staggered mounted on channel walls are considered. Through the use of a stream function vorticity transformation, solution of the transformed governing equations for the system is obtained using the control volume method with non-uniform grid. The effects of the Reynolds number, thermal conductivity ratio of rib to fluid and rib¡¦s profile area on heat transfer rate of single rib and rib array are presented. In addition, the effects of the length from inlet to the first rib and the space between ribs for rib array are carried out. A correlation for single and rib array in forced convection is presented to estimate the optimum aspect ratio of rib with various Reynolds number, thermal conductivity ratio of rib to fluid, rib¡¦s profile area. Furthermore, the results of different Gr/Re2 and various channel inclination angle in mixed convection are also examined numerically. The results indicate that both in forced and mixed convection, the optimum aspect ratio of a rib corresponding to the rib with maximum heat transfer rate increases with increasing Re but decreases with K for a fixed rib profile area. In forced convection the optimum aspect ratio of rib array increases with rib¡¦s space but decreases with the length from inlet to the first rib of channel. Then, numerical correlations to predict the optimum aspect ratio of single rib and rib array are developed for fixed rib¡¦s area with various Re, K and rib number. In mixed convection, the optimum aspect ratios of single rib and staggered rib array increase with not only the inclination angle but also Gr/Re2.

Current high power LEDs are used popularly, energy saving can be achieved if the heat transfer performance of a high power LED is increased. Numerical analysis is carried out herein to study the parameters effect on the cooling performance for the heat sinks of the LED projector. The parameters include fin spacing, fin depth, fin thickness, base thickness and flow speed. The numerical results reveal that the parameters of the heat sinks significantly affects the average Nusselt Number. The results of this study can provide design references for LED projector.

Heat transfer and fluid flow are studied numerically for a repeating microchannel array with water as the circulating fluid. Generalized transport equations are discretized and solved in three dimensions for velocities, pressure, and temperature. The SIMPLE algorithm is used to link pressure and velocity fields, and a thermally repeated boundary condition is applied along the repeating direction to model the repeating nature of the geometry. The computational domain includes solid silicon and fluid regions. The fluid region consists of a microchannel with a hydraulic diameter of 85.58μm. Independent parameters that were varied in this study are channel aspect ratio and Reynolds number. The aspect ratios range from 0.10 to 1.0 and Reynolds number ranges from 50 to 400. A constant heat flux of 90 W/cm2 is applied to the northern face of the computational domain, which simulates thermal energy generation from an integrated circuit. A simplified model is validated against analytical fully developed flow results and a grid independence study is performed for the complete model. The numerical results for apparent friction coefficient and convective thermal resistance at the channel inlet and exit for the 0.317 aspect ratio are compared with the experimental data. The numerical results closely match the experimental data. This close matching lends credibility to this method for predicting flows and temperatures of water and the silicon substrate in microchannels. Apparent friction coefficients linearly increase with Reynolds number, which is explained by increased entry length for higher Reynolds number flows. The mean temperature of water in the microchannels also linearly increases with channel length after a short thermal entry region. Inlet and outlet thermal resistance values monotonically decrease with increasing Reynolds number and increase with increasing aspect ratio. Thermal and friction coefficient results for large aspect ratios (1 and 0.75) do not differ significantly, but results for small aspect ratios (0.1 and 0.25) notably differ from results of other aspect ratios.

This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1959. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 228-232).

abstract: As miniature and high-heat-dissipation equipment became major manufacture and operation trends, heat-rejecting and heat-transport solutions faced increasing challenges. In the 1970s, researchers showed that particle suspensions can enhance the heat transfer efficiency of their base fluids. However, their work was hindered by the sedimentation and erosion issues caused by the relatively large particle sizes in their suspensions. More recently, nanofluids--suspensions of nanoparticles in liquids-were proposed to be applied as heat transfer fluids, because of the enhanced thermal conductivity that has generally been observed. However, in practical applications, a heat conduction mechanism may not be sufficient for cooling high-heat-dissipation devices such as microelectronics or powerful optical equipment. Thus, the thermal performance under convective, i.e., flowing heat transfer conditions becomes of primary interest. In addition, with the presence of nanoparticles, the viscosity of a nanofluid is greater than its base fluid and deviates from Einstein's classical prediction. Through the use of a test rig designed and assembled as part of this dissertation, the viscosity and heat transfer coefficient of nanofluids can be simultaneously determined by pressure drop and temperature difference measurements under laminar flow conditions. An extensive characterization of the nanofluid samples, including pH, electrical conductivity, particle sizing and zeta potential, is also documented. Results indicate that with constant wall heat flux, the relative viscosities of nanofluid decrease with increasing volume flow rate. The results also show, based on Brenner's model, that the nanofluid viscosity can be explained in part by the aspect ratio of the aggregates. The measured heat transfer coefficient values for nanofluids are generally higher than those for base fluids. In the developing region, this can be at least partially explained by Prandtl number effects. The Nusselt number ( Nu ) results for nanofluid show that Nu increases with increasing nanofluid volume fraction and volume flow rate. However, only DI-H2O (deionized water) and 5/95 PG/H2O (PG = propylene glycol) based nanofluids with 1 vol% nanoparticle loading have Nu greater than the theoretical prediction, 4.364. It is suggested that the nanofluid has potential to be applied within the thermally developing region when utilizing the nanofluid as a heat transfer liquid in a circular tube. The suggested Reynold's number is greater than 100. / Dissertation/Thesis / Ph.D. Mechanical Engineering 2010

[pt] Abreu (1967) estudou o problema do escoamento bi-dimensional viscoso, incomprenssível, com vorticidadade constante, aplicado ao escoamento simético em torno de uma cunha infinita. Este trabalho adorda o problema de Abreu para acaso em que o fluido em escoamento acha-se a uma temperatura constante e a superfície da cunha é não-isotérmica, ocorrendo o surgimento de uma camada limite térmica. Foi aplicado o método das expressões assintóticas acopladas. Existem quatro problemas a serem resolvidos: dois externos e dois internos. A solução desses problemas conduz a solução assintótica do problema para altos valores do número de Reynolds. Foi resolvido o sistema composto pelas equações de Navier-Stokes, continuide e energia. É apresentada a solução geral para semi-ângulos de cunha entre 0 grau e 90 graus, e a solução numérica para casos particulares de semi-ângulos de 0 grau, 18 graus, 72 graus e para valores de Prandtl iguais a 0.7, 1 e 10. / [en] Abreu (1967) studied the two-dimensional ,inconpressible, constant vorticity flow past an infinite wedge. In the present work the problem solved by Abreu is considered for the case where a constant temperature fluid flows past an infinite wedge with non-isothernal surface, thus given rise to a thermal boundary layer. The matched asyntotic expansion netod,as present in Van Dyke(1962), was applied to the solution of the problem. According to Van Dyke there are four problems leads to the desired asynpotic solution for large values of the Reynolds number. The solution defines a system forned by the Navier Strokes, continuity and energy equations. The asym ptotic expansions found by Abreu (1967) for the hydrodynamic problem i.e for the continuity and Navier-Stokes equations were used in our solution. Although a general analytical solution was found for any angle of the wedge between 0 degree and 90 degrees numerical solutions are show for the particular semi-angle values of 0 degree, 18 degrees and 72 degrees and Prandt 1 numbers values of 0.7,1.0 and 10.