The problem of low Mach number (non-Boussin´esq) conjugate laminar natural convection combined with surface radiation in a vertical annulus with a centrally located vertical heat generating rod is studied numerically, taking into account the variable transport properties of the fluid. Such problems arise often in practical applications like spent nuclear fuel casks, cooling of electrical and electronic equipment, convection in ovens, cooling of enclosed vertical bus bars and underground transmission cables. The physical model consists of a vertical heat generating rod, a concentric outer isothermal boundary and adiabatic top and bottom surfaces. The heat generation in the rod drives the natural convection in the annulus. Surface radiation is coupled to natural convection through the solid-fluid interface condition and the adiabatic condition of the top and bottom surfaces. A mathematical formulation is written using the governing equations expressing the conservation of mass, momentum and energy for the fluid as well as the energy balance for the solid heat generating rod. The governing equations are discretized on a staggered mesh and are solved using a pressure-correction algorithm. Steady-state solutions are obtained by time-marching of the time dependent equations. The discretized equations for the dependent variables are solved using the Modified Strongly Implicit Procedure. A global iteration is introduced on the variables at each time step for better coupling. The parameters of the problem are the heat generation and gap width based Grashof number, aspect ratio, radius ratio and the solid-to-fluid thermal conductivity ratio. The coupling of radiation introduces the wall emissivity and the radiation number as the additional parameters and also necessitates the calculation of radiation configuration factors between the elemental surfaces formed by the computational mesh. The radiant heat exchange is calculated using the radiosity matrix method. A parametric study is performed by varying Grashof number from 106 to 1010 , aspect ratio from 1 to 15, radius ratio from 2 to 8, the solid-to-fluid thermal conductivity ratio from 1 to 100, with the Prandtl number 0.7 corresponding to air as the working medium. The characteristic dimension and the outer boundary temperature are fixed. For Radiative calculations, and the emissivity is varied between 0.25 and 0.75. Converged solutions with laminar model could be obtained for high Grashof numbers also as the heat generation based Grashof number is generally two orders of magnitude higher than the temperature difference based Grashof number. Results are presented for the flow and temperature distributions in the form of streamline and isotherm maps. Results are also presented for the variation of various quantities of interest such as the local Nusselt numbers on the inner and outer boundaries, the axial variation of the centerline and interface temperatures, maximum solid, average solid and average interface temperature variations with Grashof number and the average Nusselt number variation for the inner and outer boundaries with Grashof number. The results show that simplification of conjugate problems involving heat generation by the prescription of an isoflux boundary condition on the rod surface is inadequate because a truly isoflux condition cannot be realised on the one hand and because the solid temperature distribution remains unknown with such an approach. The average Nusselt numbers on the inner and outer boundaries show an increasing trend with the Grashof number. For pure natural convection, the Boussin´esq model predicts higher temperatures in the solid and lower average Nusselt numbers on the inner and outer boundaries, compared to the non-Boussin´esq model and the Boussin´esq approximation appears to be adequate roughly upto a Grashof number of 109, beyond which the non-Boussin´esq model is to be invoked. The average pressure in the annulus is found to increase with an increase in the Grashof number. Radiation is found to cause convective drop and homogenize the temperature distribution in the fluid.

Rigorous bounds on heat transfer in rapidly rotating convection have existed for several years in the case of free-slip or stress-free boundary conditions. No-slip boundary conditions result in a phenomenon known as Ekman pumping, which significantly impacts the heat transport. A recent collaborative effort in which the author was involved significantly sharpened the bound on heat transfer in the presence of Ekman pumping. The resulting publication was targeted for an audience consisting primarily of physicists and other non-mathematicians. This work stems from the same effort, but is intended for a mathematical audience. Two additional, new results are presented that provide a more solid mathematical footing. These are firstly, a rigorous justification of the infinite Prandtl limit relied on in the referenced work, and secondly, a maximum principle for the temperature field, which provides the needed justification for the application of the background method.

One approach recently proposed for reducing the frictional resistance to liquid flow in microchannels is the patterning of micro-ribs and cavities on the channel walls. When treated with a hydrophobic coating, the liquid flowing in the microchannel wets only the top surfaces of the ribs, and does not penetrate into the cavities, provided the pressure is not too high. The net result is a reduction in the surface contact area between channel walls and the flowing liquid. For micro-ribs and cavities that are aligned normal to the channel axis (principal flow direction), these micropatterns form a repeating, periodic structure. This thesis presents numerical results of a study exploring the momentum and thermal transport in a parallel plate microchannel with such microengineered walls. The liquid-vapor interface (meniscus) in the cavity regions is approximated as flat in the numerical analysis. Two conditions are explored with regard to the cavity region: 1) The liquid flow at the liquid-vapor interface is treated as shear-free (vanishing viscosity in the vapor region), and 2) the liquid flow in the microchannel core and the vapor flow within the cavity are coupled through the velocity and shear stress matching at the interface. Predictions reveal that significant reductions in the frictional pressure drop (as large as 80%) can be achieved relative to the classical smooth channel Stokes flow. In general, reductions in the friction factor-Reynolds number product (fRe) are greater as the cavity-to-rib length ratio is increased (increasing shear-free fraction), as the relative module length (length of a rib-cavity module over the channel hydraulic diameter) is increased, as the Reynolds number decreases, and as the vapor cavity depth increases. The thermal transport results predict lower average Nusselt (Nu) numbers as the cavity-to-rib length ratio is increased (increasing shear-free fraction), as the relative module length (is increased, and as the Reynolds number decreases with little dependence on cavity depth. The ratio of Nu to fRe was evaluated to characterize the relative change in heat transfer with respect to the reduction in driving pressure. Results show that the benefits of reduction in driving pressure outweigh the cost of reduction in heat transfer at higher Reynolds numbers and narrower relative channel widths.

No description available.

No description available.

Gas-solid flow is fundamental to many industrial processes. Extensive experimental and numerical studies have been devoted to understand the interphase momentum and heat transfer in these systems. Most of the studies have focused on spherical particle shapes, however, in most natural and industrial processes, the particle shape is seldom spherical. In fact, particle shape is one of the important parameters that can have a significant impact on momentum, heat and mass transfer, which are fundamental to all processes. In this study particle-resolved simulations are performed to study momentum and heat transfer in flow through a fixed random assembly of ellipsoidal particles with sphericity of 0.887. The incompressible Navier-Stokes equations are solved using the Immersed Boundary Method (IBM). A Framework for generating particle assembly is developed using physics engine PhysX. High-order boundary conditions are developed for immersed boundary method to resolve the heat transfer in the vicinity of fluid/particle boundary with better accuracy. A complete framework using particle-resolved simulation study assembly of particles with any shape is developed. The drag force of spherical particles and ellipsoid particles are investigated. Available correlations are evaluated based on simulation results and recommendations are made regarding the best combinations. The heat transfer in assembly of ellipsoidal particle is investigated, and a correlation is proposed for the particle shape studied. The lift force, lateral force and torque of ellipsoid particles in assembly and their variations are quantitatively presented and it is shown that under certain conditions these forces and torques cannot be neglected as is done in the larger literature. / Ph. D.

We examine the Rayleigh–Bénard convection as modelled by the Boussinesq equation. Our aim is at deriving bounds for the heat enhancement factor in the vertical direction, the Nusselt number, which reproduce physical scalings. In the first part of the dissertation, we examine the the simpler model when the acceleration of the fluid is neglected (Pr=∞) and prove the non-optimality of the temperature background field method by showing a lower bound for the Nusselt number associated to it. In the second part we consider the full model (Pr<∞) and we prove a new upper bound which improve the existing ones (for large Pr numbers) and catches a transition at Pr~Ra^(1/3).

Resumo: O objetivo deste trabalho é a análise numérica e experimental de escoamento viscoso, incompressível, permanente, com transferência de calor, em um canal estreito contendo um arranjo de obstáculos retangulares. A análise experimental envolveu determinação de coeficiente de transferência de calor médio bem como o número de Nusselt médio e medidas de temperatura em esteira térmica para comparação com os resultados obtidos por simulação numérica. Para a análise numérica usamos o programa comercial de mecânica dos fluidos e transferência de calor computacional ICEPAK®. Verificamos que quanto mais adentro o obstáculo estiver no arranjo maior é a transferência de calor por convecção forçada. Determinamos coeficientes de transferência de calor médio e número de Nusselt médio (com incerteza entre 6 e 15%) e verificamos que o efeito da posição diminui à medida que a velocidade aumenta. Concluímos também que ambos os modelos de turbulência utilizados, k-ε padrão e k-ε RNG, foram incapazes de predizer o efeito da posição apropriadamente. Entretanto, o modelo k-ε RNG apresentou melhor comportamento, pois o seu uso resultou em soluções com valores de temperatura intermediários aos experimentais / Abstract: The purpose of this work is the study of the numerical and experimental viscous incompressible steady flow with heat transfer into a narrow channel containing a rectangular array of obstacles. The experimental approach involves determining the coefficient of heat transfer and temperature measurements in thermal wake for comparison with the results obtained in numerical simulations. For the numerical analysis we use the commercial program of fluid mechanics and heat transfer computational ICEPAK™. We confirmed that in the last lines of the array the biggest is the heat transfer by forced convection. We determined the average heat transfer coefficients (with uncertainty between 6 and 15%) and found that the effect of the position decreases as flow speed increases. We use in the simulations the k-ε turbulence model and the k-ε RNG turbulence model. We conclude that both turbulence models used were unable to predict the effect of the position properly. However, the k-ε RNG model showed better behavior. The numerical temperatures with this model were consistent to the experimental temperature / Orientador: João Batista Campos Silva / Coorientador: Amarildo Tabone Paschoalini / Coorientador: Marcio Antonio Bazani / Banca: Ricardo Alan Verdú Ramos / Banca: Marcio Higa / Mestre

Solid propellant gas generators that have high gas capacity are used for fast pressurization of inflatable devices or elastic shells. However, many applications such as control surface actuation, air bottle pressurization in rocket engines and safety systems of automobiles (airbags) require exit gases at near ambient temperature. A scheme suitable for short duration applications is passive cooling of gas generator gases by using a packed bed as compact heat exchanger. A study indicated that the mass flow rates of solid propellant gas generators for applications such as air bottle pressurization and control system actuators were of the order of 1 kg/s. Since pressure and enthalpy drop correlations for packed beds with mass flow rates (~1 kg/s) and packing sphere based Reynolds number (Red) ~ 9X104 were unavailable in open literature, an experimental investigation was deemed necessary. The objectives of the present study were (a) characterization of packed beds for pressure and enthalpy drop, (b) develop Euler and Nusselt number correlations at Red~105 and (c) evolve an engineering procedure for estimation of packed bed pressure and enthalpy drop. An experimental test facility with a hydrogen-air combustor was designed and fabricated for this purpose to characterize a variety of packed beds for pressure drop and heat transfer. Flow through separate packed beds consisting of 9.5mm and 5mm steel spheres and lengths ~200mm and ~300mm were studied in the sphere based Reynolds numbers (Red) range of 0.4X104 to 8.5X104. The average porosity (є) of the randomly packed beds was ~0.4. The ratios of packed bed diameter to packing diameter for 9.5mm and 5mm sphere packing were ~ 9.5 and 18 respectively. The inlet flow temperature was unsteady and a suitable arrangement using mesh of spheres was used at either ends to eliminate flow entrance and exit effects. Stagnation pressures were measured at entry and exit of the packed beds. The pressure drop factor fpd, (ratio of Euler number (Eu) to packed bed dimensions) for packed bed with 9.5mm spheres exhibited an asymptotically decreasing trend with increasing Reynolds number, and a correlation for the pressure drop factor is proposed as, fpd=Eu/ [6(1-є) (L/dp)] =125.3 Red-0.4; 0.8X104 < Red < 8.5X104 (9.5mm sphere packing). However, for packed beds with 5mm spheres the pressure drop factor fpd, was observed to increase in the investigated Reynolds number range. The correlation based for pressure drop factor is proposed as, fpd= Eu/ [6(1-є) (L/dp)] =0.0479 Red0.37; 0.4X104 < Red < 3.9X104 (5mm sphere packing). The pressure drop factor was observed to be independent of the inlet flow temperature. Gas temperatures were measured at the entry, exit and at three axial locations along centerline in the packed beds. The solid packing temperature was measured at three axial locations in the packed bed. At Red~104, the influence of gas phase and solid phase thermal conductivity on heat transfer coefficient was found to be negligible based on order of magnitude analysis and solid packing temperature data obtained from the experiments. Evaluation of sphere based Nusselt number (Nud) at axial locations in the packed bed indicated a length effect on the heat transfer coefficient, which was a function of Reynolds number and size of spheres used in packing. The arithmetic average of Nusselt numbers at different axial locations in the packed bed were correlated as Nud=3.85 Red0.5; 0.5X104 < Red < 8.5X104. The Nusselt numbers obtained in the experiments were consistent with corresponding literature data available at lower Reynolds numbers. In this experimental study Euler number correlations for pressure drop and Nusselt number correlations for heat transfer were obtained for packed beds at Red~105. An engineering model for estimation of packed bed pressure and enthalpy drop was evolved, which is useful for sizing of packed bed heat exchanger in solid propellant gas generation systems.

All heat pump cycles have one common feature that connects them to one another; this feature is the presence of a heat exchanger. There are even some heat–driven cycles that are completely composed of heat exchangers, every heat exchanger fulfilling a different, though critical role. The need therefore exists to optimize heat exchangers, more specifically Compact Heat Exchangers (CHE). This study deals with the optimization of such a CHE by determining an optimal hydraulic diameter of the micro–channels in a CHE, for minimal hydraulic losses. Two Computational Fluid Dynamics (CFD) models were developed for a single micro–channel that is present in a CHE. The first model had a semi–circular cross–section, the second a triangular cross–section. The results were verified by comparing it with existing experimental data. Following the verification of the results, the micro–channel was optimized by implementing an optimum diameter for the lowest pressure drop over the micro–channel. This was done for both the semi–circular and triangular micro–channel cross–sections. / Thesis (M.Ing. (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2011.