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Forced-cooled superconductors are viewed as a promising alternative in the development of high field superconducting magnets for future fusion devices. The high current density cable superconductor is protected against thermal instabilities by forcing (single phase) supercritical helium through the cable. The cryogenic cooling system for a forced-cooled superconducting magnet works as a refrigerator and a reciculator at the same time. The paper discusses the conceptual design of the cooling systems for forced-cooled superconducting magnets with the overall objective of reducing the refrigeration costs. The general conclusion of this article is that economic cooling systems must employ efficient cold pump recirculators in which the large flow demanded by the forced-cooled superconducting magnet is confined to the cold end of the refrigerating column. If the liquid helium pump efficiency is less than 40%, systems employing elevated temperature compressors are more economic.

The Constructal Law is the law of physics that accounts for the universal phenomenon of evolution of flow configuration in nature. Evolution and the Constructal Law unite all the “live” systems, bio and nonbio, which are characterized by flow and freedom...

In this chapter we turn our attention to processes of combined (simultaneous) heat and mass transfer that are driven by buoyancy. The density gradients that provide the driving buoyancy force are induced by the combined effects of temperature and species...

Spreading and collecting flows are united by the flow design known as the S-curve: when plotted versus time, the size of the domain that is filled or emptied has a history that is shaped as an S. Here, we show that the fastest spreading or collecting (i.e., the steepest S curve) is discovered by allowing the tree architecture to morph freely, toward greater access over time, in accord with the constructal law of design in nature. The angles between the lines of the invading flow architecture can be selected such that the overall flow proceeds the fastest, covering the greatest territory at any moment. The design is a sequence of two distinct phenomena: “invasion” by channels and branches that grow fast, and “consolidation” by slow diffusion perpendicular to the channels. Invasion and consolidation collaborate hand-in-glove to facilitate the spreading or collecting over the available finite area or volume.

This is a fundamental study of the periodic in & out flow through a single orifice into an enclosure. The purpose of the ‘breathing’ flow is to refresh the enclosure air. The injected air differs from the original enclosure air with respect to concentration of undesirable components or temperature. Two scenarios are considered. (i) Single puff of fresh air injected during an interval t1, followed by a pause t0, and extraction of mixed enclosure air during a second time interval t1. It is shown that the time-averaged rate of enclosure air replacement is maximum when the rhythm is such that t0 ~ t1. (ii) Fresh air injected as a turbulent jet of duration t1, and withdrawal of mixed air during another interval, t2. It is found that the spent power averaged during the cycle is minimum when t1/t2 ~ 1. The concentration of fresh air in the enclosure increases in S-curve fashion, slow-fast-slow. The time scale of the fast (viral) portion of the S curve increases with the length scale of the enclosure and decreases with the Reynolds number based on port diameter and flow velocity. Numerical simulations of the flow confirm several features of the regimes documented theoretically.

The phenomenon of buoyancy-induced convection in an infinite porous medium with a concentrated heat source is studied analytically. The transient and steady-state temperature distribution and flow pattern around the source are determined using a perturbation analysis in the Rayleigh number based on the heat generation rate at the source. The first-order transient solution derived in the paper is valid for Rayleigh numbers less than 10. The transient flow pattern consists of an expanding vortex ring situated in the horizontal plane containing the source. The steady-state solution, valid for Rayleigh numbers of the order of 20 or less, reveals an upward flow pattern which becomes very intense near the source. The upward flow extends throughout the medium. Both solutions show that as the Rayleigh number increases the region situated above the source is effectively heated by natural convection in addition to direct heat conduction from the source.

No abstract is provided for this article.

Technical Briefs The Prandtl Number Effect on the Transition in Natural Convection Along a Vertical Surface 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 J. L. Lage J. L. Lage 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 A. Bejan Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 J. L. Lage Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27706 J. Heat Transfer. Aug 1990, 112(3): 787-790 (4 pages) https://doi.org/10.1115/1.2910457 Published Online: August 1, 1990 Article history Received: September 25, 1989 Revised: January 4, 1990 Online: May 23, 2008

The objective of this chapter is to review a modern transformation in the teaching, research and practice of energy engineering: the increasingly important roles played by thermodynamics (especially the second law) in problem formulation, modeling and design...

This is a numerical and theoretical investigation of natural convection in a two-dimensional square enclosure with one side cold and isothermal, and the other side heated with pulsating heat flux. It is shown numerically that the buoyancy induced circulation resonates to a certain (single) frequency of the pulsating heat input. The resonance is characterized by maximum fluctuations in the total heat transfer rate through the vertical midplane of the cavity. The numerical experiments cover the Prandtl number range 0.01–7, the heat flux Rayleigh number range 103–109, and the nondimensional frequency range 0– 0.3. It is shown that the critical frequencies determined numerically can be anticipated based on theoretical grounds, by matching the period of the pulsating heat input to the period of the rotation (circulation) of the enclosed fluid. In the last section, the same theoretical argument is used to predict the critical period for natural convection resonance in an enclosed porous medium saturated with fluid.

In this paper we consider the complete thermofluid design and performance of a thermoelectric module. We increase the temperature difference that must be maintained across the module, and at the same time we reduce the pumping power required by the streams that bathe the hot and cold plates of the module. We find that for greater power output the two streams must be configured in parallel, not in counterflow, and not between two well mixed plenums. We also find that the loss of thermoelectric power due to the temperature nonuniformity of the two plates competes with the power lost during the pumping of the two streams, and that from this competition results the optimal mass flow rates of the two streams. At the optimum, the maximized power output of the module is proportional to a group of geometric parameters (Eq. (39)), which can be maximized further by designing vascular flow architectures for the two plates. The vascular designs reveal an optimal ratio of channel diameters, optimal plate aspect ratio, and a channel flow volume fraction that is of the same order as the ratio of the fluid thermal conductivity divided by the solid thermal conductivity. The flow architectures are further illustrated with numerical examples of vascular and serpentine configuration and performance.

Here we explore the idea that the highest heat transfer rate between two fluids in a given volume is achieved when plate channel lengths are given by the thermal entrance length, i.e., when the thermal boundary layers meet at the exit of each channel. The overall design can be thought of an elemental construct of a dendritic heat exchanger, which consists of two tree-shaped streams arranged in cross flow. Every channel is as long as the thermal entrance length of the developing flow that resides in that channel. The results indicate that the overall design will change with the total volume and total number of channels. We found that the lengths of the surfaces swept in cross flow would have to decrease sizably as number of channels increases, while exhibiting mild decreases as total volume increases. The aspect ratio of each surface swept by fluid in cross flow should be approximately square, independent of total number of channels and volume. We also found that the minimum pumping power decreases sensibly as the total number of channels and the volume increase. The maximized heat transfer rate per unit volume increases sharply as the total volume decreases, in agreement with the natural evolution toward miniaturization in technology.

end of Chapter 11 (geophysical aspects). Once again we decided that, except for a brief mention, convection in unsaturated media had to be beyond the scope of this book. D.A.N.againenjoyedthehospitalityoftheDepartmentofMechanicalEngine- ing and Materials Science at Duke University while on Research and Study Leave from the University of Auckland, and both of those institutions again provided ?nancial support. We are grateful for comments from Graham Weir and Roger Young on a draft of Section 11.9, a topic on which we had much to learn. We also are grateful to a large number of people who provided us with preprints of their papers prior to publication. Other colleagues have improved our understanding of the subject of this book in ways too numerous to mention here. Once again we relied on the expertise and hard work of Linda Hayes for the preparation of the electronic version of our manuscript, and again the staff at the Engineering Library of Duke University made our search of the literature an enjoyable experience.

This article addresses the fundamental question of whether a flow system that has freedom to morph also exhibits the natural tendency to configure itself to provide greater access to its currents. The reason for questioning this evolutionary tendency in nature is that there are several flow architectures that seem to contradict the tendency. First, the flow of rain water on an inclined street covered with gravel does not carve a smooth channel with uniform depth and width. Instead, it carves a straight path with cataracts, which are periodic “dams” interspaced with pools and waterfalls. The pools are most evident after the rain. Second, sheet flow that is smooth and rectilinear terminates itself into a “wall” posed by a thicker layer of fluid that flows more slowly. This is known as a “hydraulic jump.” Are these abrupt morphological changes hindering or liberating the flow? By questioning the directionality of these changes we have an excellent opportunity to check and validate the constructal law of evolutionary design toward greater access.

This paper is a proposal to design flow structures with maximal heat transfer rate per unit volume, by shaping each duct so that it fits optimally on the body of the convective flow. Optimally shaped ducts can be assembled into larger constructs. Two examples are given. In the first, a heat-generating strip is cooled inside a duct of rectangular cross-section. The duct geometry has two degrees of freedom, which can be selected so that the fixed duct volume packs a maximum of heat transfer rate. In the second example, the duct is a tube with isothermal internal surface, and the flow is sufficiently slow so that boundary layers do not form inside the duct. Once again, the duct aspect ratio can be optimized for maximal heat transfer rate density. Further improvements can be sought by endowing the duct geometry with more degrees of freedom.

The effect of nonuniform permeability and thermal diffusivity on natural convection through a porous system heated from the side is investigated numerically. The first part of the study, in Section 2, focuses on systems composed of vertical sublayers. It is shown that the heat transfer rate is influenced substantially by the thickness and permeability of the peripheral sublayers adjacent to the heated vertical walls. The heat transfer results are correlated by using the ratio of peripheral sublayer thickness divided by the boundary layer thickness based on peripheral sublayer properties. The second part of the study, in Section 3, deals with porous systems composed of horizontal sublayers with different permeabilities. It is shown that due to the lack of homogeneity the vertical walls of the system are lined by boundary layers whose thicknesses vary from one sublayer to the next. A general heat transfer scaling law for horizontally layered systems is reported.

The thermal design of counterflow heat exchangers for gas-to-gas applications is based on the thermodynamic irreversibility rate or useful power no longer available as a result of heat exchanger frictional pressure drops and stream-to-stream temperature differences. The irreversibility (entropy production) concept establishes a direct relationship between the heat exchanger design parameters and the useful power wasted due to heat exchanger nonideality. The paper presents a heat exchanger design method for fixed or for minimum irreversibility (number of entropy generation units NS). In contrast with traditional design procedures, the amount of heat transferred between streams and the pumping power for each side become outputs of the NS design approach. To illustrate the use of this method, the paper develops the design of regenerative heat exchangers with minimum heat transfer surface and with fixed irreversibility NS.