Call number: LD2668 .T4 1959 B86

Call number: LD2668 .T4 1963 S82 / Master of Science

Unsteady heat transfer by natural convection in a closed square cavity is investigated numerically. A new finite-volume approach is developed and applied to the two-dimensional continuity, vorticity, and energy equations. The variation of the field variables is approximated by bi-quadratic interpolation formulas over the space occupied by the finite volume and the region surrounding it. These are used in the integral conservation laws for energy, vorticity and mass. The convective transport is modelled using a new upstream-weighting approach which uses volume averages for the vorticity and the energy transported across the boundaries of the finite volume. The weighting is dependent on the skewness of the velocity field to the surfaces of the finite volume as well as its strength. It is adaptive to local flow conditions. The velocities are obtained from the application of the velocity induction law. Use is made of an image system for the free vorticity of fluid. In this way, the no-penetration condition is enforced at the cavity boundaries, but at the same time it may allow a slip condition to exist. This is not permitted in a viscous flow analysis, and the slip velocity is reduced to zero by the production of free vorticity at the boundaries. Two test cases are treated which have exact solutions. The first is not new and involves a rotating shaft. The errors are less than.06% for this case. The second case is new and involves convection past a source and sink. The maximum error is 2.3%. For both test cases, the maximum error occurs at moderate values of the cell Peclet number and diminishes at the extreme low and high values. The time-development of the profiles of the vorticity, horizontal velocity, and temperature is examined at different locations within the cavity for Rayleigh numbers equal to 10³, 10⁴, and 10⁵. For these calculations, a 21 x 21 grid was used. The flow is found to approach a steady-state condition. The steady-state results are compared with a benchmark solution. In general, the agreement is excellent. The discrepancy is found to be less than 2% for the vast majority of the results for this relatively coarse grid.

Heat transfer in moist porous media has been given extensive theoretical consideration. In attempting to define the problem mathematically, either one of two approaches has been followed. There is the mechanistic approach which is based upon the diffusion of vapor and the capillary movement of liquids, and there is the approach which applies the theory of the thermodynamics of irreversible processes. The latter is the more general but both approaches give rise to simultaneous equations for the steady-state flow of matter and energy. These equations contain coefficients which are measures of physical properties of the particular medium under study. In this dissertation two heat transfer coefficients are evaluated: "real" thermal conductivity and "real" thermal diffusivity. Real thermal conductivity is one of the coefficients referred to above and real thermal diffusivity is a coefficient that appears in the equations for the transient flow of heat in moist porous media. Both thermal constants are those that would be obtained if measurements could be made without the interference of moisture transfer. A large-diameter, cylindrical thermal probe was designed and used for evaluation of these real thermal constants. The probe is heated uniformly at a constant rate and as the heat is dissipated in the surrounding medium, the probe temperature is recorded as a function of time. Thermal constants are obtained by comparing a theoretical expression with the experimental data. The theoretical expression includes the probe diameter, the heat capacity per unit length of the probe, and the thermal contact "resistance" between the probe and the surrounding medium. The analysis requires evaluation of the thermal contact resistance from the experimental data and independent determination of the volumetric heat capacity of the surrounding medium. Thermal constants close to real values but which include effects of distillation are obtained from the initial portion of the experimental record. These are then corrected for distillation by subtracting out a small quantity which can be evaluated theoretically. Values of real thermal conductivity and diffusivity were obtained at different moisture contents for 20/30 mesh Ottawa sand and for a sandy loam soil. Real thermal conductivity of the Ottawa sand (with a dry bulk density of approximately 1,7 gms/cm³) increases rapidly from a value of 0.000870 cal/°C/cm/sec when dry to 0.00Lt4 cal/°C/cm/sec at about 15% of saturation. Thereafter it apparently increases at a rate equal to the rate of increase of the volumetric heat capacity of the sand-water system to a value of 0.00755 cal/°C/cm/sec at saturation. Real thermal diffusivity of this material increases from 0.00275 cm²/sec when dry to 0,012 cm²/sec at about 15% of saturation. It remains nearly constant with further increase in water content. In a similar manner, real thermal conductivity of the sandy loam soil (with a dry bulk density of approximately 1.5 gms/cm³) increases rapidly from a value of 0,000605 cal/°C/cm/sec when dry to 0.0036 cal/°C/cm/sec at about 30% of saturation. It then increases at a rate approximately equal to the rate of increase of the volumetric heat capacity of the soil-water system to 0.00595 cal/°C/cm/ sec at saturation. Real thermal diffusivity for this material increases from 0.00223 cm²/sec when dry to 0.0090 cm²/sec at about 30% of saturation. Thereafter it remains essentially constant with further increase in water content. Thus, a single measurement of thermal diffusivity in the saturated sand and soil is sufficient to define real thermal diffusivity over a wide range of moisture contents.

This investigation forms part of an attempt to provide an alternative to conventional power generation technologies that use fossil fuels which have impact on global warming. The field of this investigation covers the development of a latent heat thermal storage system which has a potential of conserving available solar energy. The advantages of using thermal energy storage that have been found previously include reduced energy cost, energy consumption, equipment size and pollutant emissions, also increased flexibility of operation, efficiency and effectiveness of equipment utilization. Traditionally, available heat has been stored in the form of sensible heat (typically by raising the temperature of the energy storage medium) for later use. Latent heat storage on the other hand, is a young and developing technology which has found considerable interest in recent times due to its advantages over sensible heat storage which include smaller temperature swing, smaller size and lower weight per unit of storage capacity. It has been demonstrated that, for the development of a latent heat thermal energy storage system, the choice of the phase change material (PCM) as well as the heat transfer mechanism in the PCM play important roles. In this study, a suitable phase change material and an appropriate heat transfer enhancement technique are identified for utilization in a proposed latent heat thermal energy storage system. Also included, is the design of the proposed heat storage system. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2010.

M.Ing. / Experiments are being conducted with regard to heat exchange systems. However, there are errors and uncertainties attached to each system. Journals, which publish articles concerning heat transfer experiments, require an estimate of this uncertainty. These uncertainties must be calculated in order to determine how valid a set of results is. The uncertainty describes to what level one may rely on a set of experimental results and conclusions. The uncertainty was calculated by the formulation of an uncertainty equation with the use of various statistical methods. Adjustments or modifications had to be made to the present uncertainty equations in order to calculate the uncertainty in heat transfer systems. Uncertainty based on a general uncertainty equation by Schultz and Cole (1979) enabled the derivation of the equations to calculate the necessary uncertainty factor for heat transfer systems. Implementation of the equations in various experimental set-ups was achieved. The uncertainty equations yielded results that seemed consistent with the subjective view of the experimenter. Therefore, the equations were considered valid.

M.Ing. / Since the promulgation of the Montreal Protocol many refrigerants needed to be phased out. R-22, which is a widely used refrigerant in refrigeration systems, was one of these. Many replacements have been found throughout the years but very few have the same refrigeration capacity without being penalised by an increase in pressure drop. R-407C is one of the refrigerants having the potential to replace R-22 as it has the same theoretical coefficient of performance and has a lower global warming potential. However, due to its zeotropic characteristics there is a degradation in heat transfer during evaporation and condensation attributed to mass transfer resistance. Thus, augmentation techniques are needed not only to increase the heat capacity, but also to achieve an increase without incurring an excessive pressure drop. One approach to cope with this problem is to make use of the recently developed herringbone micro-fin tubes. Unfortunately very little data exists for refrigerants undergoing condensation inside herringbone micro-fin tubes. There is also little pressure drop information available for this type of tube. An experimental set-up was designed to determine the characteristics of this type of tube due to the scarcity of information. With the aid of current literature, various techniques were used to determine the pressure drops inside the herringbone micro-fin tube. One of these techniques was the use of the Kattan-Thome-Favrat flow regime map which helped to identify the flow patterns inside the tube. Knowledge of the type of flow occurring inside the tube helped to clarify the behaviour of the pressure drop relationships. The type of refrigerant being used also affected the behaviour of the pressure drop curves. A low-pressure refrigerant had a higher pressure drop due to the high vapour velocities achieved. Another cause for excessive pressure drop is the friction created by the high velocity vapour and condensate inside the tube. Many relationships for the friction factor exist and these are used to analyse the experimental data.The experimental facility comprised of a vapour compression loop and a water loop. The vapour compression loop consisted of a hermetically sealed compressor with a cooling capacity of 9.6 kW, a manually operated expansion valve and an evaporator. Three condensers were tested, namely a smooth tube, a helical micro-fin tube, and a herringbone micro-fin tube. The condensers were of the tube-in-tube type with the refrigerant flowing in the inner tube and the water in counter flow in the annulus. The hot water loop was used as a source for the evaporator and a cold loop as a heat sink for the condenser. Three refrigerants were tested, namely R-22, R-134a, and R-407C, all operating at a nominal saturation temperature of 40°C and at mass fluxes between 300 and 800 kg/m 2s. Accurate sensors and transducers were used to measure the temperatures, pressures, and mass flows at predefined points. Video cameras were attached to sight glasses to aid in the identification of the type of flow regime. Data were captured using a computerised data acquisition programme designed specifically for use with the experimental study. The experimental results showed that transition between the annular and intermittent flow regimes occurred at around 25% vapour quality for the herringbone micro-fin tube, as opposed to 30% for the helical micro-fin tube and 50% for the smooth tube. Pressure drops for the herringbone micro-fin tube were higher than those for the smooth tube but slightly lower than those for the helical micro-fin tube when using refrigerants R-22 and R-134a. The correlation of Liebenberg was modified for the pressure drops inside the herringbone micro-fin tube and gave a mean deviation of 12%. The efficiency ratio for the herringbone tube using R-22 was 1.85 and 1.69 when compared with the helical micro-fin and smooth tube respectively. For R-134 the efficiency ratio was 2.02 and 2.13 when compared with the helical micro-fin and smooth tube respectively, while for R-407C it was 1.58 and 1.26 for the two respectively. It was also concluded that R-407C could be used as a replacement refrigerant for R-22when used with a herringbone micro-fin tube.

M.Ing. / The Montreal Protocol led to the phasing-out of ozone layer depleting refrigerants and replacing them with more environmentally friendly refrigerants, which in many cases caused heat transfer degradation in heat exchanger equipment. To make up for the heat transfer degradation, there was a need for the application of heat transfer enhancement techniques. One such technique is the use of micro-fin tubes as opposed to traditional smooth tubes. The purpose of this study is to develop a flow regime map for the condensation of R-22, R-407C and R-134a in a herringbone micro-fin tube. It was perceived that with the knowledge of flow patterns inside the tube and especially the annular-to-intermittent transition, it is possible to perform improved analyses of the heat transfer and pressure drop characteristics. Experimental and analytical work was performed to investigate the flow regimes during condensation of the refrigerants in smooth, helical micro-fin and herringbone micro-fin tubes at an average saturation temperature of 40oC, with mass fluxes ranging from 300 to 800 kg/m2s. Condensation occurred in tube-in-tube type condensers with cooling water flowing in the annulus and the refrigerant in the inner tubes. The condensers consisted of eight sub-sections to allow for the acquisition of sectional heat transfer and pressure data. Various criteria were considered in order to generate flow regime maps. The Thome flow regime transition criterion was used and complemented with visually-observed and photographic imaging, as well as the objective power spectral density distributions of the pressure signals of the condensing refrigerants. The observed flow regimes were mainly annular flow and intermittent flow. Stratified-wavy flow was observed at low mass fluxes and low vapour qualities. There were notable similarities in the flow pattern between the smooth and micro-fin tubes. However, the experimental results show that the transition from annular to intermittent flow regimes occurred at average vapour quality values of 0.26, 0.29 and 0.48 for the herringbone micro-fin, the helical micro-fin and smooth tubes respectively. The combined analyses assisted in adapting the helical micro-fin tube condensing flow pattern map, to ensure its application in accurately predicting herringbone micro-fin tube condensation. The new transition criterion effectively predicts the delay in transition from annular to intermittent flow for all three refrigerants, condensing in the herringbone micro-fin tube.

長期以來，人們知道壁面受限湍流中的聚合物添加劑將顯著降低摩擦阻力，但是對聚合物在熱對流熱傳輸的影響還沒有太多研究。作為第一步，一項最近的工作[1]研究了在穩態邊界層流中熱量傳輸是怎樣被聚合物添加劑所影響的。在這項工作中[1]，聚合物是用Oldroyd-B模型來描述，這個模型允許聚合物無限伸展而沒有限制。 / 在這篇論文中，我們用一個更加真實的聚合物模型來研究聚合物在穩態邊界層流中對熱量傳輸的影響。我們採用FENE-P（有限擴展非線性彈性Peterlin）模型，在這個模型中，聚合物僅可以被伸展到一個最大的長度。聚合物的有限伸展性由參數L來衡量，它是聚合物最大長度與平衡長度的比例。基於該模型，我們發現，相對於與聚合物溶劑在底板處粘度相同的牛頓流體，熱量傳輸可以被提高或者被降低，這取決於聚合物不同的L值。而在不同的L值下，流場中底板的阻力始終加強。在早期的工作中，可以用一個隨位置改變的有效粘度來理解聚合物的效果。我們探討了聚合物的有效粘度和流速場是怎樣被聚合物改變的，以理解這個問題。我們也對熱量傳輸與不同參數的依賴關係進行了研究，這些參數包括威森博格數，普朗特數和聚合物對零剪切下溶劑粘度作出的貢獻的比例。 / It has long been known that friction drag will be reduced signicantly due to polymer additives in turbulent wall-bounded flows, but the effect of polymers on heat transport in thermal convection has not been studied much. As a rst step, a recent work [1] has studied how heat transport in a steady-state boundary layer flow might be influenced by the addition of polymers. In this work [1], polymers are modeled by the Oldroyd-B model, in which they can be extended innitely without a limit. / In this thesis, we study the effect of polymers on the heat transport in steady-state boundary layer flow using a more realistic model of polymers. We apply the FENE-P (nite extensible nonlinear elastic-Peterlin) model, in which the polymers can only be extended up to a maximum length. The nite extensibility of the polymers is measured by the parameter L, which is the ratio of the maximum length to the equilibrium one. Based on the model, we nd that compared to a Newtonian flow with the same viscosity as that of the polymer solution at the plate, heat transport can be enhanced or reduced depending on L. The fraction drag is always enhanced by the polymers for all different L. In the earlier work, the effect of the polymers has been understood to produce an effective viscosity that is position-dependent. We have explored the effective viscosity of the polymers and how the velocity eld is modied by the polymers to understand our results. We have also studied how the results depend on the different parameters, including Weissenberg number, Prandtl number and the ratio of polymer contribution to the total zero-shear viscosity. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Yiqu = 有限伸展的聚合物對邊界層流中熱量傳輸的改變 / 王異曲. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 68-69). / Abstracts also in Chinese. / Wang, Yiqu = You xian shen zhan de ju he wu dui bian jie ceng liu zhong re liang chuan shu de gai bian / Wang Yiqu. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Prandtl-Blasius boundary layer flow --- p.7 / Chapter 3 --- Earlier work with Oldroyd-B polymers --- p.13 / Chapter 4 --- Theoretical formulation of the problem with polymers of finite extensibility --- p.20 / Chapter 4.1 --- Equations of motion --- p.20 / Chapter 4.2 --- Quantities of interest --- p.30 / Chapter 5 --- Checking validity of fixed angle approximation --- p.34 / Chapter 6 --- Results and Discussion --- p.42 / Chapter 6.1 --- Calculations --- p.42 / Chapter 6.2 --- The effect on heat transport --- p.45 / Chapter 6.3 --- The effect on drag --- p.48 / Chapter 6.4 --- The velocity field due to polymers --- p.49 / Chapter 6.5 --- Effective viscosity --- p.55 / Chapter 6.6 --- Dependence on Weissenberg number --- p.58 / Chapter 6.7 --- Dependence on Prandtl number --- p.61 / Chapter 6.8 --- Dependence on the ratio of polymer contribution to the total zero-shear viscosity --- p.64 / Chapter 7 --- Conclusion --- p.66

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