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Crystallization is done in the sugar industry using natural circulation vacuum evaporative crystallizers known as vacuum pans. the fluid which is known as massecuite consists of a suspension of crystals in concentrated molasses. It is highly viscous and slightly non-Newtonian, and laminar conditions prevail in the apparatus. Research on forced convection boiling heat transfer, pressure drop and vapour holdup has been done mostly in turbulent flow under pressures higher than atmospheric, but no studies have been made when boiling viscous fluids under vacuum. This thesis describes a series of experiments which were undertaken with the following objectives: (a) to determine the influence of the pertinent variables on heat transfer, friction losses and vapour holdup while boiling under laminar conditions (b) to produce a method for the calculation of the evaporation and circulation rates in vacuum pans, as this would make possible the optimization of this type of equipment. The apparatus used consisted of a single tube steam heated forced circulation evaporator. The void fraction, pressure and centerline temperature were measured along the tube. The fluids used were syrup, molasses and massecuite covering a thousandfold change in viscosity. The tests were conducted under different conditions of vacuum and steam pressures with varying tube inlet velocities. The experimental results show that the boiling heat transfer coefficient can be correlated as a function of the two phase Reynolds number and dimensionless density ratio and that it is inversely proportional to the tube length to the power of one third. The pressure drop can be estimated using the equation of Oliver and Wright (1964) for bubbly flow. Equations are proposed for calculating the void fraction in the highly subcooled region and point of bubble departure. These equations form the basis of a computer program which by a stepwise and iterative method simulates the boiling process along the tube. Measurements taken on a natural circulation pan with tubes of different length show that this method predicts the effect of the tube length with reasonable accuracy. The limitations of this study are that the experiments were done with a single diameter tube so that the effect of diameter has not been established with certainty. Only sugar products were used in the experiments, and caution is necessary if this method is applied to other fluids. / Thesis (Ph.D.)-University of Natal, Durban, 1985.

By using the finite element method to solve the appropriate momentum and energy equations the friction factors and Nusselt numbers for fully developed laminar flow were determined for one- and two-dimensional flow systems. The Nusselt numbers were determined for domain boundaries subjected to a constant heat flux (H1) or a constant surface temperature (T) around the computational boundaries and in the axial directions. C++ programs, that were rewritten and extended from previous programs, were used to solve the laminar flow and to determine the values. The required wall shear stresses and heat fluxes were directly obtained for a duct as part of the primary finite-element solution; these values were then used to determine the Nusselt number and friction factor for the specific duct. The computations were performed for circular-, annular-, trapezoidal-, rectangular- and triangular ducts. Special emphasis was placed on trapezoidal ducts since only a limited number of studies have been performed on trapezoidal duct shapes and none of these studies employed the finite element method. Excellent agreement was found when the determined values were compared with the values reported in the literature. In general, the agreement of the values improved as the number of elements was increased. It was, therefore, concluded that the methods used in this study yielded friction factors and Nusselt numbers that are very accurate and usable. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2009.

By using the finite element method to solve the appropriate momentum and energy equations the friction factors and Nusselt numbers for fully developed laminar flow were determined for one- and two-dimensional flow systems. The Nusselt numbers were determined for domain boundaries subjected to a constant heat flux (H1) or a constant surface temperature (T) around the computational boundaries and in the axial directions. C++ programs, that were rewritten and extended from previous programs, were used to solve the laminar flow and to determine the values. The required wall shear stresses and heat fluxes were directly obtained for a duct as part of the primary finite-element solution; these values were then used to determine the Nusselt number and friction factor for the specific duct. The computations were performed for circular-, annular-, trapezoidal-, rectangular- and triangular ducts. Special emphasis was placed on trapezoidal ducts since only a limited number of studies have been performed on trapezoidal duct shapes and none of these studies employed the finite element method. Excellent agreement was found when the determined values were compared with the values reported in the literature. In general, the agreement of the values improved as the number of elements was increased. It was, therefore, concluded that the methods used in this study yielded friction factors and Nusselt numbers that are very accurate and usable. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2009.

The problem of condensation of steam on a vertical tier of horizontal tubes is investigated by both analytical and experimental methods in this study. A computer program is written to perform the analysis of laminar film condensation on the horizontal tubes. The program is capable to calculate condensate film thickness and velocity distribution, as well as the heat transfer coefficient within the condensate. An experimental setup was also manufactured to observe the condensation phenomenon. Effects of tube diameter and temperature difference between steam and the tube wall on condensation heat transfer have been analytically investigated with the computer program. Experiments were carried out at different inclinations of the tier of horizontal tubes. Effects of the steam velocity and the distance between the horizontal tubes are also experimentally investigated. Results of the experiments are compared to those of the studies of Abdullah et al., Kumar et al. and Nusselt as well as to the analytical results of the present study.

Thesis (M.S.)--Ohio University, November, 2008. / Title from PDF t.p. Includes bibliographical references.

Thesis (M.Sc.) -- Memorial University of Newfoundland, 1987. / Typescript. Bibliography: leaves 102-104. Also available online.

Thesis (Ph. D.)--Technische Hogeschool Delft, 1986. / Errata slip inserted. Summary in English and Dutch; acknowledgements in Dutch. Vita. Includes bibliographical references (p. 105-111).

Resumo: O presente trabalho trata da solução de uma classe de problemas difusivo-convectivos, tanto de natureza elíptica como parabólica, em domínios de geometrias não-convencionais, através da aplicação da Transformada Integral. Para facilitar o tratamento analítico e a aplicação das condições de contorno, antes da aplicação da Técnica da Transformada Integral Generalizada - TTIG sobre a equação governante do problema estudado, emprega-se uma Transformação Conforme - TC visando efetuar uma mudança de coordenadas adequada. Analisa-se inicialmente o problema hidrodinâmico do escoamento laminar completamente desenvolvido de fluidos Newtonianos no interior de dutos. Para a obtenção do campo de velocidades do escoamento aplica-se a TTIG sobre a equação da quantidade de movimento. Os parâmetros hidrodinâmicos de interesse, tais como: velocidades média e máxima, fator de atrito de Fanning, fator de Hagenbach, número de Poiseuille, comprimento de entrada hidrodinâmico e queda de pressão são calculados para as diversas geometrias. Feito isso, efetua-se o estudo dos problemas difusivo-convectivos relacionados à transferência de calor do escoamento laminar hidrodinamicamente desenvolvido e termicamente em desenvolvimento de fluidos Newtonianos com perfil de temperatura de entrada uniforme em dutos submetidos a condições de contorno de Dirichlet. Para a obtenção do campo de temperatura aplica-se a TTIG sobre a equação da energia e então, calculam-se os parâmetros térmicos de interesse: temperatura média de mistura, números de Nusselt local e médio e comprimento de entrada térmica. Realiza-se, quando possível, a comparação dos resultados obtidos para os parâmetros termos-hidráulicos com os disponíveis na literatura. / Abstract: The present work describes the solution of a class of elliptical-parabolic diffusiveconvective problems, on unconventional geometries, employing the Generalized Integral Transform Technique (GITT). In order to facilitate the analytical treatment and the application of the boundary conditions, a Conformal Transform (CT) is used to change the domain into a more suitable coordinate system, just before GITT is to be applied. First of all, using this procedure, the hydrodynamic problem of fully developed Newtonian laminar flow inside ducts is analyzed. In order to obtain the velocity field, GITT is applied on the momentum equation. Interesting hydrodynamic parameters, such as: maximum and minimum velocity values, Fanning friction and Hagenbach factors, Poiseuille number, hydrodynamic entry length, as well as pressure loss, are evaluated for several geometries. Following that, diffusive-convective problems are studied in relationship to the heat transfer in hydrodynamically fully developed and thermally non-developed Newtonian laminar flow inside ducts under Dirichlet boundary conditions, considering uniform temperature entrance profile. In order to obtain the temperature field, GITT is applied on the energy equation, evaluating the relevant parameters: bulk mean temperature, average and local Nusselt numbers and thermal entry length. The results are compared, as much as possible, with the parameter values available in the literature. / Orientador: Cassio Roberto Macedo Maia / Coorientador: Ricardo Alan Verdú Ramos / Banca: João Batista Campos Silva / Banca: Marcelo Moreira Ganzarolli / Mestre

A high level of free-stream turbulence and surface roughness are known to cause breakdown of an otherwise stable laminar flow. In transition induced by free-stream turbulence, streaks are formed due to the lift-up effect and low-speed streaks with high shear breakdown to turbulence. Streaks are also present in transition caused by a roughness element and they may breakdown via sinuous or varicose instability. In general, streamwise streaks, their lift-up and streak instability are integral to the bypass transition process. If the lift-up of a high-shear layer or its breakdown is manipulated by some external means, then the downstream flow is expected to change. An experimental study was carried out to understand the effect of flow modification caused by a mesh placed normal to the flow and at different wall-normal locations in the late stage of bypass transitions induced separately by an isolated cylindrical roughness element and a high level of free-stream turbulence. The measurements were made on a flat plate boundary layer in a low-speed wind tunnel using the particle image velocimetry technique. The mesh causes an approximately 30% reduction in the free-stream velocity, and mild acceleration in the boundary layer, irrespective of its wall-normal location. Interestingly, when located near the wall, the mesh suppresses several transitional events leading to transition delay over a large downstream distance. The transition delay is found to be mainly caused by suppression of the lift-up of the high-shear layer and its distortion, along with modification of the spanwise streaky structure to an orderly one. However, with the mesh well away from the wall, the lifted-up shear layer remains largely unaffected, and the downstream boundary layer velocity profile develops an overshoot which is found to follow a plane mixing layer type profile up to the free stream. Reynolds stresses, and the size and strength of vortices increase in this mixing layer region. The high-intensity disturbance in this region can possibly enhance the transition of accelerated flow far downstream, although a reduction in streamwise turbulence intensity occurs over a short distance downstream of the mesh. However, the shape of large-scale streamwise structure in the wall-normal plane is found to be more or less the same as that without the mesh.