901 publications from this institution
This paper reports an analytical and numerical study of natural convection heat and mass transfer through a vertical porous layer subjected to uniform fluxes of heat and mass from the side. The flow is driven by the combined buoyancy effect due to temperature and concentration variations through the porous medium. The first part of the study contains an analytical Oseen-linearized solution for the boundary-layer regime and Le = l,and a similarity solution for heat-transfer-driven flows(n = 0)and Le > 1. The second part of the study contains an extensive series of numerical experiments that validate the analytical results and provide heat and mass transfer data in the domain not covered by analysis. The numerical results cover the Rayleigh number range 20 ⩽ Ra ⩽ 105, the buoyancy ratio range −11 ⩽ n ⩽ 9, the geometric aspect ratio range 1 ⩽ H/L ⩽ 4 and the Lewis number range 0.03 ⩽ Le ⩽ 40.
The heat transfer by free convection in a horizontal cavity with adiabatic horizontal walls and differentially heated end walls is studied analytically. The paper develops three models for explaining and predicting the heat transfer mechanism in a cavity with the height/length aspect ratio considerably smaller than one. The three models are: 1) the regime of vanishing Rayleigh numbers, 2) the intermediate regime, and 3) the boundary layer regime. The transition from one model to the next occurs as the Rayleigh number increases. The Nusselt number prediction based on the three-regime theory agrees very well with available numerical and experimental heat transfer data.
No abstract is provided for this article.
Since we have dealt with natural convection and forced convection in some detail, our treatment of mixed convection can be brief. It is guided by the review paper by Lai et al. (1991a). We start with a treatment of boundary layer flow on heated plane walls inclined...
In this paper, we show analytically how to optimize the spacing between heat generating boards in a stack cooled by single-phase laminar forced convection. The thickness of each board is not negligible. The theoretical results for optimal spacing and maximum overall thermal conductance between stack and coolant are validated by means of numerical simulations of the complete flow and temperature fields. Results are reported for three different situations, which are dictated by the way in which the stack is attached to the rest of the cooling network of the electronics package : (1) fixed pressure drop, (2) fixed mass flowrate, and (3) fixed pumping power.
This paper extends to economics the constructal theory of generation of shape and structure in natural flow systems that connect one point to a finite size area or volume. It is shown that by invoking the principle of cost minimization in the transport of goods between a point and an area, it is possible to anticipate the dendritic pattern of transport routes that cover the area, and the shapes and numbers of the interstitial areas of the dendrite. It is also shown that by maximizing the revenue in transactions between a point and an area, it is possible to derive not only the dendritic pattern of routes and their interstices, but also the optimal size of the smallest (elemental) interstitial area. Every geometric detail of the dendritic structures is the result of a single (deterministic) generating principle. The refining of the performance of a rough design (e.g., rectangles-in-rectangle) pushes the design toward a structure that resembles a theoretically fractal structure (triangle-in-triangle). The concluding section shows that the law of optimal refraction of transport routes is a manifestation of the same principle and can be used to optimize further the dendritic patterns. The chief conclusion is that the constructal law of physics has a powerful and established analog in economics: the law of parsimony. The constructal theory extended in this paper unites the naturally organized flow structures that occur spontaneously over a vast territory, from geophysics to biology and economics.
This paper extends to the field of convective heat transfer the constructal theory of optimizing the access of a current that flows between one point and a finite-size volume, when the volume size is constrained. The volume is bathed by a uniform stream. A small amount of high-conductivity fin material is distributed optimally through the volume, and makes the connection between the volume and one point (fin root) on its boundary. The optimization proceeds in a series of volume subsystems of increasing sizes (elemental volume, first construct, second construct). The shape of the volume and the relative thicknesses of the fins are optimized at each level of assembly. The optimized structure emerges as a tree of fins in which every geometric detail is a result of minimizing the thermal resistance between the finite-size volume and the root point (source, sink). Convection occurs in the interstitial spaces of the tree. The paper shows that several of the geometric details of the optimized structure are robust, i.e., relatively insensitive to changes in other design parameters. The paper concludes with a discussion of constructal theory and the relevance of the optimized tree structures to predicting natural self-organization and self-optimization.
Refrigeration costs constitute an important aspect of the economics of force-cooled cable superconductors. The refrigerator power required to operate a forced cooled superconducting magnet is analyzed. The paper develops a simple method for estimating the total refrigerator power associated with a given length of cabled conductor of specified geometry. The estimate relies on the thermodynamics of supercritical helium in the superconducting cable. Finally, the technique is used to point out what features of the forced cooled superconductor design are desirable from a refrigeration cost standpoint.
This paper outlines a newly emerging body of work that relies on exergy analysis and thermodynamic optimization in the design of energy systems for modern aircraft. Exergy analysis establishes the theoretical performance limit. The minimization of exergy destruction brings the design as closely as permissible to the theoretical limit The system architecture springs out of this constrained optimization principle. A key problem is the extraction of maximum exergy from a hot gaseous stream that is gradually cooled and eventually discharged into the ambient. The optimal configuration consists of a heat transfer surface with a temperature that decays exponentially in the flow direction. This configuration can be achieved in a counterflow heat exchanger with an optimal imbalance of flow capacity rates. The same optimal configuration emerges when the surface is minimized subject to specified exergy extraction rate. Similar opportunities for optimally matching components and streams exist in considerably more complex systems for power and refrigeration. They deserve to be pursued, and can be approached first at the conceptual level, based on exergy analysis and thermodynamic optimization. The application of such principles in aircraft energy system design also sheds light on the design principle that generated all the systems that use powered flight, engineered and natural.
The ‘constructal theory’ of formation of structure in nature is extended to fluid-flow systems. The fluid flow path between one point and a finite-size volume (an infinite number of points) is optimized by minimizing the overall flow resistance when the flow rate and the duct volume are fixed. The solution is constructed as a sequence of optimization and organization steps. The sequence has a definite time direction: it begins with the smallest building block (elemental system, with flow by volumetric diffusion), and proceeds toward larger building blocks (assemblies, with flow collected in ducts). Optimized at each level are the shape of the assembly, the number of constituents (ie, smaller assemblies), and the distribution of the duct volume. It is shown that the ducts of the optimized assemblies form a tree-like structure, in which every architectural detail is deterministic. It is also shown that the structure cannot be determined when the time direction is reversed, from large elements toward smaller elements. The general importance of the constructal law (access-optimization principle) in physics, biology and economics is discussed.
Here, we show that vascular design emerges naturally when a volume is bathed by a single stream in turbulent flow. The stream enters the volume, spreads itself to bathe the volume, and then reconstitutes itself as a single stream before it exits the volume. We show that in the pursuit of a smaller global flow resistance and larger volumes, the flow architecture changes stepwise from a stack of identical elements bathed in parallel flow (like a deck of cards) to progressively more complex structures configured as trees matched canopy to canopy. The transition from one architecture to the next occurs at a precise volume size, which is identified. Each transition marks a decrease in the rate at which the global flow resistance increases with the volume size. This decrease accelerates as the volume size increases. The emergence of such vasculatures for turbulent flow is compared with the corresponding phenomenon when the flow is laminar. To predict this design generation phenomenon is essential to being able to scale up the designs of complex flow structures, from small scale models to life size models. The constructal law is a bridge between the principles of physics and biology.
A mathematical model for skin burn injury induced by radiation heating, where the skin was considered to be a 3-D triple-layered structure with embedded three-level dendritic countercurrent vascular network, has been developed. Since there are up to seven levels of arteries and veins, the motivation of this study is to extend the model to a more complex case that considers a seven-level dendritic countercurrent vascular network, where the dimensions and blood flow of the blood vessels are determined based on the constructal theory of multi-scale tree-shaped heat exchangers. The method is illustrated by an example.
The second law of thermodynamics is used to analyze the potential for exergy conservation in solar collector systems. It is shown that the amount of useful energy (exergy) delivered by solar collector systems is affected by heat transfer irreversibilities occurring between the sun and the collector, between the collector and the ambient air, and inside the collector. Using as working examples an isothermal collector, a nonisothermal collector, and the design of the collector-user heat exchanger, the optimum operating conditions for minimum heat transfer irreversibility (maximum exergy delivery) are derived.
Predicting Design Evolution, will focus on one of his major contributions: evolutionary design illustrated in the case of multiscale vasculature, a methodology that can be used generally to predict the evolution toward flow access, miniaturization, high density of heat transfer, and the scaling up (or down) of an existing design.
Enclosures heated from the side are most representative of porous systems that function while oriented vertically, as in the insulations for buildings, industrial cold-storage installations, and cryogenics. As in the earlier chapters, we begin with the most...
Abstract : This project developed the fundamental features and strategy for the design of vascular solid structures with embedded volumetric functionalities: vascular flow access throughout the solid volume, superior overall mechanical strength, and volumetric self cooling. The research was based on constructal design, which is the philosophy that the flow and solid structures are free to morph hand in glove to provide greater access to all the currents including the flow of stresses. The project was constructed in several stages: the natural emergence of vascular design in the pursuit of greater flow access, the design of vascular structures for volumetric cooling and mechanical strength, the merits of hybrid designs consisting of grid & tree channels, vascularized plates subjected to randomly moving heat sources, and the overall design merits of allowing the flow architecture to morph more and more freely. The main feature of all this work is that it is fundamental. The design principles developed in this project have applicability across the spectrum of mechanical structures with embedded heating, cooling, and fluid flow.
This paper shows that the mass inventory for steam turbines can be distributed between high-pressure (HP) and low-pressure (LP) turbines such that the global performance of the power plant is maximal. This is demonstrated for two design classes. For an HP turbine in series with an LP turbine, the optimal intermediate pressure (IP) is a geometric average of HP and LP. The total mass is distributed in a balanced way based on the total mass of turbines. For a train consisting of many turbines expanding the steam at nearly constant temperature, the pressure ratio between consecutive IP should be constant, and more mass should be distributed at HPs. This approach to discovering the configuration of the power plant should be used in conjunction with classical approaches that account for vibration, centrifugal force and blade length. Copyright © 2009 John Wiley & Sons, Ltd.
This article reports an open discussion that took place during the Keenan Symposium "Meeting the Entropy Challenge" (held in Cambridge, Massachusetts, on October 5, 2007) following the short presentations—each reported as a separate article in the present volume—by Thomas Widmer, Ernest Geskin, James Keck, Noam Lior, Debjyoti Banerjee, Richard Peterson, Erik Ydstie, Ron Zevenhoven, Zhuomin Zhang, and Ahmed Ghoniem.All panelists and the audience were asked to address the following questions• Current state‐of‐the‐art efficiency of combined‐cycle energy conversion technology is about 60%. Based on the trend of historical data, some forecast that second‐law efficiency of energy conversion will reach 80% by the end of the century. What technologies are at sight that might hold this promise?• Nanotechnologies and microtechnologies point towards the development of microscopic heat engines? How do second law limitations map down to these scales?• Combustion is the principal way of converting the chemical energy of fossil fuels to thermal energy, but it is highly irreversible. Are there promising ways to reduce combustion irreversibility? Are fuel cells the only alternative to combustion?
In this paper we describe a new concept for vascularizing the flow architectures of compact devices. Vascularization is achieved by using tree-shaped (dendritic) flow passages on both sides of the heat transfer surface. For each side, we propose to use an architecture that consists of trees that alternate with upside down trees. By evaluating the fluid flow performance we show that dendritic vascularization is superior to the use of parallel microchannels when the tree structures have four or more levels of bifurcation. The local pressure losses that occur at the multiple junctions of each tree structure become negligible when the svelteness of the architecture (Sv) exceeds the order of 10. The svelteness is a global geometric property defined as the external length scale of the architecture divided by the internal length scale (the total flow volume raised to the power 1/3). The combination of fluid architectures and solid constitute a “smart” composite material: the fluids that bathe the volume can be used to provide multiple functions, such as serf-healing, serf-cooling, and variable transport properties. For example, when placed in counterflow, the vascularized hot and cold sides of the surface are a compact heat exchanger. The article shows under what conditions the tree vascularization offers greater flow access than parallel single-scale channels oriented perpendicularly to the parallel lines.
