The current supply cables of large superconducting magnet systems are cooled with an axial stream of cold helium vapor. If the flow of coolant is suddenly interrupted the current cables may overheat and burn up causing extensive damage to the entire system. The transient temperature distribution in the cable after the loss-of-coolant accident is derived analytically. The paper presents the maximum cable temperature versus time for a cryogenic current cable which stretches from room temperature (300 K) to a liquid helium-cooled superconducting system (4.2 K).
A porous medium consists of a solid structure with void spaces that are in general complicated and distributed throughout the structure. The void spaces can be interconnected or not. The pores are identifiable regions that serve as elements for the void space. The...
In this chapter we focus on the equation that expresses the first law of thermodynamics in a porous medium. We start with a simple situation in which the medium is isotropic, and where radiative effects, viscous dissipation, and the work done by pressure changes are...
To clarify the place of time direction of change in nature (time arrow), the present article shows why Evolution and Irreversibility are two distinct phenomena. Their distinct laws of nature are the Constructal Law and the Second Law, respectively. The demonstration is based on the simplest setting imaginable: a solid body moving in a pool of water. The view is holistic: the system selected for analysis is the body and the pool, not the body alone, and the phenomenon is the evolution of the image (configuration) of the whole. New is also the answer to the question of what flows in this evolving flow configuration. Along the way, important terms are defined: phenomenon, law, irreversibility, nature, design, freedom, theory versus empiricism, information, knowledge, selection, purpose, engine, refrigeration, and wheel. More complex natural settings for the demonstration are in the second part of the article: engines, refrigeration, heating and cooling, the wheel, and a pushed boat sliding on water.
The subject of this chapter is the relatively recent work on melting and lubrication at the interface between two solid parts, one of which is at its melting point. It is an area of research that began in heat transfer, with studies of contact melting inside capsules and around embedded objects. Melt lubrication is now a distinct topic in tribology. The classical application of melt lubrication is in the area of sliding friction on ice and snow. Among the more modern applications is the coating of a metallic part with another metal whose melting point is considerably lower. The function of the latter is to melt and serve as lubricant in a manufacturing process to which the former may be subjected. The research reviewed in this chapter covers the contract melting of crystalline substances, anomalous crystalline substances such as ice, and the contact softening of glass-like substances. These occur in diverse contact-region geometries. The shapes of the mating solid surfaces may be concave, convex, or plane, while the perimeter of plane contact regions may be either rectangular or circular. The types of relative motion reviewed are sliding contact, rolling contact, the movement of a hot body through a melting solid medium, and the movement of a solid melting inside a heated capsule. The effect, the roughness, or contact melting over the tops of asperities is also analyzed.
This updated edition of a widely admired text provides a user-friendly introduction to the field that requires only routine mathematics. The book starts with the elements of fluid mechanics and heat transfer, and covers a wide range of applications from fibrous insulation and catalytic reactors to geological strata, nuclear waste disposal, geothermal reservoirs, and the storage of heat-generating materials. As the standard reference in the field, this book will be essential to researchers and practicing engineers, while remaining an accessible introduction for graduate students and others entering the field. The new edition features 2700 new references covering a number of rapidly expanding fields, including the heat transfer properties of nanofluids and applications involving local thermal non-equilibrium and microfluidic effects.
In this paper I use the example set by Prof. Jan Szargut as point of reference for a brief look at the current state of thermodynamics—the doctrine, its reach and importance. I start with my first encounter with Prof. Jan Szargut in 1979, and I show how his work influenced mine. Next, I review the structure that underpins thermodynamics as a discipline: the laws and the self-standing phenomena that they underpin, and graphic methods that convey these principles. Along the way, I draw attention to a recent trend that is caused by the inflation in scientific publishing due to the internet: the most common mistakes and misconceptions in thermodynamics, and how they are being spread. In sum, this paper is a call to action, to value, improve and defend the science of thermodynamics.
This study shows that the main features of a steam generator can be determined based on the method of constructal design. The generator is endowed with freedom to morph, and then is optimized by putting the right components in the right places. The number of steam tubes is sufficiently large, so that the steam generator may be modeled as continuous. The total volume of the assembly and the volume of the steam tubes are fixed. The geometry is free to vary in the search for maximum heat transfer density. The steam flow in the tubes is modeled in two ways: single-phase and two-phase fully developed turbulent flow. Results of the analysis are: the location of the flow reversal (i.e. the demarcation between the tubes of the downcomer and those of the riser), the optimal spacing between adjacent tubes, and the number of tubes for the downcomer and the riser. Copyright © 2010 John Wiley & Sons, Ltd.
This paper describes the fundamentals of the heat transfer melting process occurring in the narrow rolling contact region between a body of phase-change material and a solid body that acts as a heater. The theory is based on the following assumptions : (i) the phase-change material is at the melting point temperature, (ii) the surface of the solid is isothermal, (iii) the effect of frictional heating in the liquid gap is negligible, (iv) the peripheral length of the liquid region is much smaller than the radius of the roller, (v) the liquid gap region is slender, and (vi) the effect of surface tension is negligible. The general solution constructed in this manner relates the mechanical loading of the roller (normal force, tangential force, applied torque) to the angular speed of the roller, the temperature difference between the heater and the phase-change material and the thermophysical properties of the liquid phase. Simpler calculation procedures are developed for two special applications : (a) the melting of a cylinder mounted freely on its axle, and (b) the melting of a turning cylinder the axle of which is stationary relative to the heater surface.
This is an experimental numerical and theoretical study of the heat transfer on a pin-finned plate exposed to an impinging air stream. The pin fins are aligned with the air approach velocity. The base plate and the fin cross section are square. It is demonstrated experimentally that the thermal conductance between the plate and the air stream can be maximized by selecting the fin-to-fin spacing S. Next, a simplified numerical model is used to generate a large number of optimal spacing and maximum heat transfer data for various configurations, which differ with respect to fin length (H), fin thickness (D), base plate size (L), fluid type (Pr), and air velocity (ReL). Finally, the behavior of the optimal spacing data is explained and correlated theoretically based on the intersection of asymptotes method. The recommended correlations for optimal spacing, Sopt/L ≅ 0.81 Pr−0.25 ReL−0.32, and maximum thermal conductance, (q/ΔT)max/kaH ≅ 1.57 Pr0.45 ReL0.69 (L/D)0.31, cover the range D/L = 0.06 − 0.14, H/L = 0.28−0.56, Pr = 0.72−7, ReD = 10−700, and ReL = 90−6000.
In this paper we focus on the application of the constructal theory in predicting the dendritic solid structure. First we analyse the marginal stability criterion from the perspective of the constructal principle. Having as a guiding principle the constructal law we have shown that among the whole range of possible dendrite tip radiuses predicted by the stability analysis the dendrite tip will choose the smallest one, that is a radius equal with the smallest perturbation wavelength leading to instabilities. We identify as well the existence of a competition between the diffusion controlled growth and the dendritic growth. Second, we develop a model for the secondary arm spacing. We identify a competition between the lateral diffusion controlled growth of a needle and the dendritic growth of lateral secondary arms. By analysing this competition we are able to characterize the sidebranching mechanism and to finally compute the secondary arm spacing. The result is in good agreement with the experimental results. Finally, the primary arm spacing is analysed from the perspective of the constructal law. The constructal law predicts that the only way the columnar tips can optimize the solidification process is to minimize the spacing between two adjacent tips, namely λ1. By quantifying the two mechanisms responsible for the selection of λ1, the dendrite division and the dendrite overgrown mechanisms, we were finally able to obtain a model for the primary arm spacing. This model is also validated against various experimental data.
The temperature difference applied across the two ends of a horizontal duct generates a natural counterflow in which colder fluid flows along the bottom of the duct towards the warm end while a warmer stream flows in the opposite direction along the top. The paper presents an asymptotic solution for the velocity and temperature distributions in the middle portion of a long horizontal pipe with conducting wall. The influence of circumferential heat conduction through the pipe wall on the temperature distribution in the fluid has been investigated. An analytical expression has been established for the net axial heat-transfer rate by counterflow natural convection. The present results for the temperature distribution in the pipe wall are compared with numerical results reported recently.
Constructal tree designs are hierarchical high-conductivity paths that minimize the global resistance between an entire volume and one point. In past work, the structure was optimized as a sequence of building blocks (volume sizes), which started with the smallest size (elemental volume) and continued toward larger and more complex assemblies (first construct, second construct, etc.). The resulting structure had a `uniform' distribution of interstitial spaces, because the size of the elemental volume was fixed. In this paper we relax the elemental size constraint, and show that the added design freedom leads to significant improvements in global performance, i.e., to decreases in the global resistance to volume–point flow. Each tree structure, or the distribution of high-conductivity material through low-conductivity background, is optimized by simulating numerically and comparing large numbers of designs where the geometry changes smoothly from one design to the next. The results show that each optimized structure has not one but several elemental volume sizes, and that the volume elements situated far from the root of the tree are notably smaller. The resulting tree is nonuniform, i.e., denser near the periphery of its canopy. In sum, better global performance is achieved when the complexity and number of degrees of freedom of the structure are increased. In the same direction, the optimized nonuniform tree structure looks more and more natural.
This is a brief introduction to an engineering theory on the origin and generation of geometric form in all flow systems: the animate, the in animate and the engineered. The theory is named constructal, and is based on the thought that it is natural for cur rents to construct for them selves in time paths of greater flow access. It is shown that this process of flow path optimization can be reasoned on the basis of principle: the maximization of global performance subject to finite-size constraints. One example is the generation of tree-shaped flow pat terns, as paths of least resistance between one point (source, sink) and an infinity of points (area, volume), as in the circulatory, respiratory and nervous systems. Another is the generation of regular spacing's in heat generating volumes, such as swarms of honey - bees. The optimized tree-flow geometries ac count for allometric laws, e. g., the relation ship between the total tube contact area and the body size, the proportionality between metabolic rate and body size raised to the power 3/4, the proportionality between breathing and heart beating times and body size raised to the power 1/4, and the proportionality between the cruising speed of flying bodies (in sects, birds, air planes) and body mass raised to the power 1/6. The optimized flow structures constitute robust designs, and robustness improves as the complexity of the system increases. Flow architectures that are more efficient look more natural.
This is a review of recent theoretical, numerical and experimental studies of natural and forced convection heat transfer from surfaces with intermittent (on & off) heat flux. Scale analyses predict that in each configuration there is an optimal heat pulse interval (or frequency) that optimizes the overall thermal conductance between the heater and the external fluid. This feature was verified and determined more accurately by complete numerical simulations and experiments with water in natural convection, and air in forced convection. In natural convection, the heater configurations optimized experimentally were the vertical cyclinder, which approximates the vertical plane wall, and the horizontal cylinder. In forced convection, the tested configuration was the single cylinder in crossflow.
The heat transfer, friction and mechanical (elastic) interaction between an external laminar flow and a solid surface covered by a layer of fibers is investigated numerically. The flow is initially perpendicular to the surface, and the fibers can bend. The study has two parts. In the first part it is assumed that the fibers are inflexible. It is shown that the effect of the fiber layer on the overall heat transfer can be correlated in terms of the fraction of the external flow that penetrates into the fiber layer. The second part focuses on the effect of fiber bending, which is described by a new dimensionless group: the stiffness number S = EI/(pU 2 ∞ L 4). It is shown that the wall heat transfer, friction and fiber layer flow fraction exhibit a sudden decrease when S drops below a critical value, S c . The critical stiffness number can be correlated as S c = C(H/L)5(D/H)2/(1 -ø), where C is a constant of order 0.4, H and D are the fiber length and diameter, L is the half-length of the solid wall, and ø is the porosity of the fiber layer.
