Technical Briefs Mass Transfer to Natural Convection Boundary Layer Flow Driven by Heat Transfer K. R. Khair, K. R. Khair Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 Search for other works by this author on: This Site PubMed Google Scholar A. Bejan A. Bejan Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information K. R. Khair Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 A. Bejan Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 J. Heat Transfer. Nov 1985, 107(4): 979-981 (3 pages) https://doi.org/10.1115/1.3247535 Published Online: November 1, 1985 Article history Received: October 31, 1984 Online: October 20, 2009
In this paper we consider the fundamental problem of how to design a flow path with minimum overall resistance between one point (O) and many points situated equidistantly on a circle centered at O. The flow may proceed in either direction, from the center to the perimeter, or from the perimeter to the center. This problem is an integral component of the electronics cooling problem of how to bathe and cool with a single stream of coolant a disc-shaped area or volume that generates heat at every point. The smallest length scale of the flow structure is fixed (d), and represents the distance between two flow ports on the circular perimeter. The paper documents a large number of optimized dendritic flow structures that occupy a disc-shaped area of radius R. The flow is laminar and fully developed in every tube. The complexity of each structure is indicated by the number of ducts (n 0) that reach the central point, the number of levels of confluence or branching between the center and the perimeter, and the number of branches or tributaries (e.g., doubling vs. tripling) at each level. The results show that as R/d increases and the overall size of the structure grows, the best performance is provided by increasingly more complex structures. The transition from one level of complexity to the next, higher one is abrupt. Generally, the use of fewer channels is better, e.g., using two branches at one point is better than using three branches. As the best designs become more complex, the difference between optimized competitors becomes small. These results emphasize the robustness of optimized tree-shaped networks for fluid flow.
This note addresses the current debate on the correctness of power plant models and analyses of the type published by Curzon and Ahlborn (1975) among others. Such models are based on the highly questionable assumption that the heat input is freely available, i.e., a degree-of-freedom for steady-state operation. This modeling assumption is wrong when the heat input (e.g., fuel) is in limited supply. On the other hand, it is shown that a model with freely varying heat input is possible if the roles of heat source and heat sink are played by two streams pumped from fluid reservoirs of different temperatures, as in geothermal and ocean thermal energy conversion systems, for example. The simplified model has both heat transfer and fluid flow irreversibilities, however, it neglects other possible sources. Several new results are developed. There exist optimal flow rates of hot fluid and cold fluid such that the net power output is maximized. As an alternative to power maximization, the model can be optimized for maximum efficiencies (net, first law, or second law). The note illustrates the importance of separating the questioned modeling assumption (e.g., Curzon and Ahlborn, 1975) from the generally applicable method of modeling and optimization (entropy generation minimization, EGM).
This paper addresses the fundamental problem of optimizing the internal structure of a vertical wall that must meet two requirements, thermal insulation and mechanical strength. The wall is a composite of solid material (e.g., brick) and parallel air caverns with varying thickness and number. It is shown that the internal structure of the wall (the number of air caverns) can be optimized so that the overall thermal resistance of the wall is maximal, while the mechanical stiffness of the wall is fixed. The maximized thermal resistance increases when the effect of natural convection in the air gaps is weaker, and when the specified wall stiffness decreases. The optimal number of air gaps is larger when the effect of natural convection is stronger, and when the specified wall stiffness is smaller. The optimal structure is such that the volume fraction occupied by air spaces decreases when the natural convection effect (the overall Rayleigh number) increases, and when the prescribed wall stiffness increases. The paper draws attention to a new class of thermal design problems, in which the system architecture is derived from a combination of heat transfer and mechanical strength considerations. This class represents an extension of the constructal design method, which until now has been used for maximizing thermofluid performance subject to size constraints.
This article addresses the main research areas identified in the call for contributions to this special issue. With examples from published articles and books, the present article shows that all the identified areas are already covered by the universal principle underlying all evolution: the constructal law (1996), i.e. the physics law of design evolution in nature (free morphing, flowing, moving systems). The universal principle of evolution belongs in thermodynamics because thermodynamics is a universal science and evolution is a universal phenomenon. The principle unites the natural sciences with the social sciences, and the living with the non-living. It unifies the world of science and its languages (energy, economy, evolution, sustainability, etc.), and brings together the natural and artificial flow architectures, the human made and the not human made. The principle establishes firmly in physics the reality that humans are part of nature. With the principle, physics extends its coverage over phenomena that were previously considered out of reach: social organization, economics and human perceptions. Such phenomena are physical, i.e. facts. The entire world depends on the science of useful things, and benefits greatly from a physics discipline with freedom, life, wealth, time, beauty and future. This article is part of the theme issue 'Thermodynamics 2.0: bridging the natural and social sciences (Part 1)'.
The constructal theory of the origin of geometrical form in natural flow (open) systems began with the discovery that, contrary to the established view, the tree network can be deduced from a single principle: the geometric minimization of resistance in volume-to-point flow. This article reviews a series of developments that extend the constructal law over naturally shaped flow phenomena other than the tree. Examples include the proportionality between width and depth in rivers of all sizes, the nearly round cross-sections of all blood vessels and bronchial passages, the dendritic shape of the snowflake, the pattern formed by cracks in a solid that shrinks upon cooling or drying (e.g., mud cracks), the onset and multiplication of rolls in Be´nard convection, the transition (first eddy) and stepwise growth of all turbulent mixing regions, and the very existence of economics spatial structure (minimal cost routes between an area and one point).
This paper outlines a series of recent developments that provide a theoretical basis for the formation of shape and structure in nonequilibrium (flow) systems subjected to overall constraints. It is shown that geometrical form can be deduced from a single principle: the geometric minimization of resistance to flow. This is illustrated in two ways: by minimizing the flow resistance between a finite volume and one point, and by minimizing the time of travel between a finite area and one point. The discovery is that any volume element can have its shape optimized such that its flow resistance is minimal. This principle applies at any volume scale. The given volume is covered in successive steps of optimization and construction. Optimally shaped elements are grouped into a “construct,” and then the shape of the construct is optimized. The more visible portion of the optimized volume-to-point flow path that emerges is a tree network that is completely deterministic. This solution has a definite time direction: from small to large, hence the name “constructal.” Small size and slow and shapeless flow (diffusion) come first, and larger sizes and organized flows (streams) come later.
No abstract is provided for this article.
No abstract is provided for this article.
The objective of this review is to draw attention to recent advances in a relatively new subfield of fluid mechanics research, namely, the study of the buckling or meandering tendency exhibited by some flows at sufficiently high Reynolds numbers. Buckling flows appear to be governed by a number of common features, the most important being the proportionality between the buckling wavelength and the transversal length scale of the stream. The experimental evidence on buckling flows is reviewed in the first part of the article. The photographic record suggests that the wavelength ~ thickness scaling law governs also the large scale meandering structure of high Reynolds number jets, wakes and plumes, in other words, that the large scale structure of turbulent streams can be regarded as the fingerprint of buckling. The theoretical attempts that have been made in order to explain the buckling phenomenon are reviewed as an invitation to continued research. The relationship between buckling flows and older fields is discussed along with potential engineering applications of known buckling scales. Overall, this review defines an entirely new research area that demands original and first-time contributions from the computational fluid mechanics community.
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This paper describes an experimental and theoretical study of the periodic on and off heating of water on a horizontal surface. The heat transfer is effected by natural convection and isolated bubbles. The experiments cover the heat flux range 33–154 kW/m2 and the wall excess temperature range 7–13°C. It is shown experimentally that the cycle-averaged thermal conductance between the surface and the pool can be maximized by properly selecting the time intervals of the on and off heating cycle. The maximum relative augmentation of the thermal conductance is approximately 15 percent. In the second part of the study, an order of magnitude analysis shows that the cycle-averaged thermal conductance can be maximized analytically by considering only the single-phase natural convection effect, and that the optimal time interval when heating is “on” agrees with the experimental results.
The constructal law is used for the minimization of the photovoltaic cells (PVC) electrical series resistance. In this paper we report a theoretical, step by step construction of optimal PVC, from the smallest, elemental cell to the largest assembly that relies on the minimisation of the maximum voltage drop subject to volume (material) constraints. This completely deterministic approach produces optimal geometric shape for each assembly level, the optimal number and orientation of constituents within each new, higher order assembly and the optimal size of each new collector (metallic) path. Keywords: Photovoltaic cellsConstructal theoryNumerical modelFinite element
