This work considers the conjugate convective heat transfer between a sphere containing heat sources and a concentric envelope maintained at a specified constant temperature. The space between the two is filled with an essentially incompressible fluid. Steady, laminar and rotationally symmetrical free convection is assumed to take place over the gap width and conduction is the sole transport mechanism considered inside the core. Two limiting cases, of an inner sphere of infinitely large relative heat conductivity, leading to an isothermal core to fluid interface; and of the converse case of small conductivity leading to a constant flux interface are considered separately. The analysis of heat transport leads to the solution of the governing equations through regular perturbation expansions with the Grashof number as main parameter. The ratio of conductivities, radius ratio and Prandtl number appear as secondary parameters. Streamlines, isovorticity curves and isotherms are obtained for various combinations of the parameters. The velocity distribution is determined and both local and overall values of the Nusselt number are obtained. A flow visualization test was undertaken and the core surface temperature distribution was determined experimentally. Reasonable qualitative agreement with the analysis is found. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

This thesis presents experimental results of combined free aid forced convection laminar heat transfer for water flowing through a circular horizontal tube with uniform wall heat flux. The Reynolds number ranged from 100 to 2000, and changes in heat transfer rate allowed a variation, of Grashof number from 300 to 30,000. The Prandtl number ranged from 4 to 9. The effect of secondary flow created by free convection occurring at higher Grashof number indicates an increase in Nusselt number up to 200 per cent. For the fully-developed region two tentative correlations are given. The expression Nu = 48/11 + 0.047 Pr¹′³(Re Ra)¹′⁵correlates 53 per cent of the data to within ± 10 per cent. Another slightly more accurate expression which correlates 68 per cent of the data to within ± 10 per cent, but does not satisfy the pure forced convection, is Nu = 2.41 + 0.082 Pr¹′³ (Re Ra)¹′⁵. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

A theoretical analysis and experimental results are presented for .free convection and combined free and forced convection from a heated horizontal surface. The principal objective was to investigate a laminar boundary layer flow which had been shown, theoretically only, to form above a heated surface. This boundary layer flow is fundamentally different from flows above inclined or vertical surfaces since the driving force or buoyancy force acts perpendicular to the primary boundary layer motion. The flows analyzed are those for which the system of partial differential equations describing the flow can be reduced to simultaneous total differential equations. The method involves the introduction of similarity parameters and then the numerical integration of the resulting simplified system of total differential equations. These solutions are restricted, for 2-dimensional flow, to a semi-infinite surface, and for axially-symmetrical flow, to an infinite disc. In conjunction with the former only free convection is considered while for the latter combined convection is considered as well. The flow was examined experimentally with a semi-focusing colour schlieren system. From the photographs it may be concluded that the semi-infinite surface analysis would correctly portray a physical flow. The flow, though, remains laminar for a short distance only and then breaks down into an unstable cellular pattern. The axially-symmetrical analysis, although it yielded analytically a valid boundary layer solution, appears to have no physical parallel above a disc of finite radius. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The problem of laminar combined free and forced convection through vertical noncircular ducts and passages in the fully developed region has been treated. The fluid properties are considered to be constant, except the variation of the density in the buoyancy term of the momentum equation. Pressure work and viscous dissipation terms of the energy equation have been neglected. Heat flux has been considered to be constant in the flow direction. A general solution to the problem has been obtained in "the form of infinite series containing modified Bessel functions. Two possible thermal boundary conditions on the circumference of the heated wall have been analyzed, Case 1 - uniform circumferential wall temperature, and Case 2 - uniform circumferential wall heat flux. Information of engineering interest like Nusselt number, heat flux, ratio, shear stress ratio, temperature distribution on the' wall, velocity and temperature distributions in the flow field have been obtained for two sets of geometries, namely, (i) flow through regular polygonal ducts, and (ii) flow between cylinders arranged in regular arrays. For flow through regular polygonal ducts, the case of uniform circumferential wall temperature results in higher values of Nusselt numbers as compared to the case of uniform circumferential wall heat flux. This difference in Nusselt number values decreases as the number of sides of the regular polygon is increased, until for a circle it completely disappears. For both the cases, at higher values of Rayleigh number, the Nusselt number is less sensitive to the number of sides of the polygon. Also, at higher values of Rayleigh number, both the cases tend to produce the same results. For low sided polygons, an increase in Rayleigh number tends to shift the maximum value of shear stress from the centre of the duct wall towards the apex of the duct. For flow between cylinders arranged in regular arrays, Case 1 results in higher values of Nusselt number compared to Case 2, for low spacing ratios. However, as the spacing ratio is increased, the two cases tend to produce the same results. Cylinders arranged in equilateral triangular arrays produce higher values of Nusselt number compared to those in square arrays. This difference in Nusselt number values decreases when the spacing ratio is high. For higher values of Rayleigh number, however, the results are less sensitive to the type of arrays. Also, at higher values of Rayleigh number, both the cases tend to produce the same results. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Analysis of combined free and forced convection through vertical non-circular ducts has been carried out using variational technique. Fully developed flow with uniform axial heat input is assumed. All fluid properties are considered invariant with temperature except the variation of density in the buoyancy term of the equation of motion. A general study of the problem has been made in three stages: (i) Forced convection without circumferential wall conduction. For this case, a known velocity expression is used and a particularly simple variational expression has been presented. Nusselt numbers are calculated for rectangular, rhombic, isosceles triangular, and right-angled triangular ducts. Results compared with the available solutions have shown excellent agreement. (ii) Combined free and forced convection without circumferential wall conduction. Nusselt numbers have been computed for rectangular and rhombic ducts. A finite-difference procedure has also been carried out and the results are presented for rhombic duct only. In both of the above cases (i) and (ii), the condition of uniform peripheral heat flux has been directly utilized in deriving the variational expression, thus releasing the thermal boundary condition from satisfying exactly the condition at the wall. The condition of uniform circumferential heat flux results in lower values of Nusselt numbers as compared to that of uniform circumferential wall temperature. This difference in Nusselt number values decreases with the increase in Rayleigh number. At higher values of Rayleigh number, both the conditions tend to produce about the same results. (iii) Conjugate problem of combined free and forced convection when peripheral wall conduction is included. The equations coupling heat conduction in the walls with the convection inside the fluid are solved to establish the influence of peripheral wall conduction. The problem has been solved in a generalized way and the results have been presented for rectangular ducts. It is found that large values of the free convection effects and/or of the conduction parameter tend to minimize the asymmetries in circumferential wall temperature. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

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本論文由兩部分組成。第一部分介紹了關於瑞利－伯纳德對流的兩項工作。第一項工作在五個側向寬高比不同的矩形對流槽中研究了空間約束效應對流體動力學和傳熱效率的影響。實驗發現，整體流場隨著約束強度的增加而明顯減弱，而且大尺度環流的流向反轉變得更為頻繁。令人驚訝的是，儘管流動變慢，總體傳熱效率卻顯著地提高。仔細分析表明，空間約束改變了邊界層中羽流的形態和動力學特性，表現為形成的羽流結構更為有序和充滿活力，從而導致邊界層變得更薄更均勻，傳熱效率由此得以提高。第二項工作研究了不同溫度邊界條件對湍流熱對流的影響。實驗在兩個對流槽中進行：其中一個在上邊界固定溫度而在下邊界固定熱通量（HC 對流槽），另一個則在兩個邊界都保持恆定溫度（CC對流槽）。研究發現，在恆定溫度的邊界條件下，溫度邊界層的厚度對瑞利數的依賴關係滿足于1/3的標度律，區別于在恆定熱通量下的行為（標度律近似為2/7）。此外，CC 對流槽中的流場強度平均比HC對流槽中的要強∼9% ，其流向反轉頻率也要快1.5倍。我們把這些現象歸咎於不同溫度邊界條件下羽流的發射強度不同。 / 論文的第二部分對另外一種重要的熱對流系統，水平對流，進行了實驗研究。在加熱和冷卻位于系統上邊界同一高度的條件下，我們觀測到了一個貫穿整個對流槽的大尺度環流。通過染料示蹤表明，流場中的迴流并不一定需要損耗能量來跨越溫度邊界層，因此可以更有效地維持其流動強度。對於熱傳輸效率以及溫度邊界層厚度隨瑞利數的變化關係，實驗觀測到了一個0.3的標度律，不同于經常被報道的理論值（0.2），這可能是因為在高瑞利數下流動狀態發生了轉變。本研究的结果表明，表面温度梯度不仅可以驱动大尺度环流，而且其強度也比人们普遍认为的要强。 / This thesis consists of two self-contained parts, both related to the topic of thermal convection. / In the first part, two sets of studies on turbulent Rayleigh-Bénard convection are presented. / The first study addresses the confinement effects on the heat transport and flow dynamics in quasi-2D geometry. The experiments were conducted in five rectangular cells with the same height and length, while the width being varied to produce a lateral aspect ratio Γ ranging from 0.6 to 0.1. As expected, with decreasing Γ, i.e. increasing the level of confinement, the overall flow slows down and more plumes travel through the bulk region, thus resulting in a large-scale circulation with more frequent reversals. Surprisingly, despite a slower flow, the global heat transport efficiency enhances significantly. Detailed examinations from experiment and simulation show that this enhancement is brought about by the changes in the dynamics and morphology of the thermal plumes in the boundary layers: the confined geometry produces more coherent and energetic plume clusters that in turn result in more uniform and thinner thermal boundary layers. This study demonstrates how changes in turbulent bulk flow can influence the boundary layer dynamics and shows that the quasi-2D geometry is very different from the true 2D and also the 3D systems. / The second study investigates the influence of thermal boundary conditions. Two experimentally achievable configurations are examined; one is fixed-flux at the bottom boundary and fixed-temperature at the top (HC cell), while the other is fixed-temperature at both boundaries (CC cell). It is found that, rather surprisingly, the Rayleigh number dependence of the thermal boundary layer thickness follows a 1/3 power law approximately under the condition of constant temperature, in contrast to the behavior in the case of constant flux (close to a 2/7 scaling). It is further found that the flow strength is on average ∼ 9% larger in the CC cell, and its flow reversal frequency is ∼ 1.5 faster than that for the HC case, which may be understood as changes in the plume emission dynamics. / The second part deals with horizontal convection. The experiment was conducted with a long apparatus (∼ 2.4 m) with the heating and cooling imposed over the top boundary. Flow visualization studies revealed a full penetrating circulation and suggest that the returning flow does not necessarily overcome the stratification to penetrate the entire thermal BL, in such a way that it can “save its kinematic energy thus supports the motion more efficiently. Both the heat transport efficiency and thermal BL thicknesses are found to follow a 0.3 power law, in contrast to the often-reported value of 0.2. This is likely caused by a flow-regime transition in the high Ra number range. This study demonstrates experimentally that a surface temperature gradient is capable of driving a large-scale circulation and its strength is much stronger than what is generally believed by the oceanography community. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Huang, Shidi = 瑞利-伯納德對流及水平對流的實驗研究 / 黃仕迪. / Thesis (Ph.D.) Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 97-110). / Abstracts also in Chinese. / Huang, Shidi = Ruili-Bonade dui liu ji shui ping dui liu de shi yan yan jiu / Huang Shidi.

Cheng, Wai Chi = 利用殼模型對熱對流湍流的研究 / 鄭偉智. / "September 2007." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 72-74). / Text in English; abstracts in English and Chinese. / Cheng, Wai Chi = Li yong qiao mo xing dui re dui liu tuan liu de yan jiu / Zheng Weizhi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- What is turbulence? --- p.1 / Chapter 1.1.1 --- The governing equation --- p.1 / Chapter 1.1.2 --- Richardson cascade and the K41 theory --- p.2 / Chapter 1.2 --- Thermal turbulence --- p.4 / Chapter 1.2.1 --- Entropy cascade and the Bolgiano-0bukhov scaling --- p.5 / Chapter 1.2.2 --- Interesting issues in turbulent convection --- p.7 / Chapter 1.2.3 --- Shell model of turbulence --- p.8 / Chapter 1.3 --- Motivations and structure of thesis --- p.11 / Chapter 2 --- Different scaling behavior in different shell models of turbulent convection --- p.13 / Chapter 2.1 --- Introduction --- p.13 / Chapter 2.1.1 --- Model dependence of scaling behavior --- p.15 / Chapter 2.1.2 --- Bolgiano scale and the dynamical significance of buoyancy --- p.26 / Chapter 2.2 --- Summary --- p.34 / Chapter 3 --- Scaling behavior in Brandenburg's model --- p.35 / Chapter 3.1 --- Introduction --- p.35 / Chapter 3.2 --- Scaling behavior in Brandenburg's model with different forcing mechanisms and parameters --- p.36 / Chapter 3.3 --- Summary --- p.43 / Chapter 4 --- Understanding the scaling behavior in Brandenburg's model --- p.45 / Chapter 4.1 --- Introduction --- p.45 / Chapter 4.2 --- Theory --- p.46 / Chapter 4.3 --- Summary --- p.48 / Chapter 5 --- Testing our theory against numerical results --- p.49 / Chapter 5.1 --- Introduction --- p.49 / Chapter 5.2 --- Testing of the hierarchical structure --- p.49 / Chapter 5.3 --- "Testing ζp, and тp with our prediction" --- p.52 / Chapter 5.4 --- Scaling behavior with fixed entropy transfer rate --- p.55 / Chapter 5.5 --- Summary --- p.57 / Chapter 6 --- Distinguishing feature for active and passive scalars --- p.59 / Chapter 6.1 --- Introduction --- p.59 / Chapter 6.2 --- Distinguishing feature of active and passive scalar --- p.60 / Chapter 6.3 --- Scaling behavior of the auxiliary scalar --- p.66 / Chapter 6.4 --- Summary --- p.69 / Chapter 7 --- Conclusion --- p.70 / Bibliography --- p.72 / A Constraint equations on the parameters in the extended GOY model --- p.75

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