From Heat Transfer Principles to Shape and Structure in Nature: Constructal Theory

2000 ◽  
Vol 122 (3) ◽  
pp. 430-449 ◽  
Author(s):  
Adrian Bejan
Keyword(s):  
Heat Transfer ◽  
Body Size ◽  
Heat Flow ◽  
Power Plants ◽  
Degrees Of Freedom ◽  
Fluid Flows ◽  
Constructal Theory ◽  
Void Space ◽  
Engineering Theory ◽  
Body Heat

This lecture reviews a relatively recent body of heat transfer work that bases on a deterministic (constructal) principle the occurrence of geometric form in systems with internal flows. The same principle of global optimization subject to constraints allow us to anticipate the natural (animate and inanimate) flow architectures that surround us. The lecture starts with the example of the optimal spatial distribution of material (e.g., heat exchanger equipment) in power plants. Similarly, void space can be allocated optimally to construct flow channels in the volume occupied by a heat generating system. The lecture continues with the optimization of the path for heat flow between a volume and one point. It shows that when the heat flow can choose between at least two paths, low conductivity versus high conductivity, the optimal flow structure for minimal global resistance in steady flow is a tree. Nearly the same tree is deduced by minimizing the time of discharge in the flow from a volume to one point. Analogous tree-shaped flows are constructed in pure fluid flows, and in flow through a heterogeneous porous medium. The optimization of trees that combine heat transfer and fluid flow is illustrated by means of two-dimensional trees of plate fins. The method is extended to the superposition of two fluid trees in counterflow, as in vascularized tissues under the skin. The two trees in counterflow are one tree of convective heat currents that effect the loss of body heat. It is shown that the optimized geometry of the tree is responsible for the proportionalities between body heat loss and body size raised to the power 3/4, and between breathing time and body size raised to the power 1/4. The optimized structures are robust with respect to changes in some of the externally specified parameters. When more degrees-of-freedom are allowed, the optimized structure looks more natural. The lecture outlines a unique opportunity for engineers to venture beyond their discipline, and to construct an engineering theory on the origin and workings of naturally organized systems. [S0022-1481(00)02403-8]

The Reynolds Analogy Applied to a Cylinder Rotating in Air

1954 ◽  
Vol 58 (519) ◽  
pp. 205-208 ◽  
Author(s):  
Y. R. Mayhew
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Heat Flow ◽  
Solid Surface ◽  
Fluid Flows ◽  
Flat Plates ◽  
Reynolds Analogy ◽  
Transfer Data ◽  
Turbulent Fluid ◽  
Flow Through

When a turbulent fluid flows past a solid surface whose temperature differs from that of the fluid, the shear stress at the surface and the heat flow from it can be related by means of the Reynolds analogy. This analogy has been improved by Prandtl, Taylor, von Kármán and others, and its validity has been tested for flow through tubes and past flat plates by several investigators. In this note the analogy is checked against shear stress data and heat transfer data for a cylinder rotating in “still” air, when the flow is turbulent.

scholarly journals Constructal theory of design in engineering and nature

2006 ◽  
Vol 10 (1) ◽  
pp. 9-18 ◽  
Author(s):  
Adrian Bejan
Keyword(s):  
Body Size ◽  
Honey Bees ◽  
Finite Size ◽  
The Body ◽  
Constructal Theory ◽  
Flow Structures ◽  
Engineering Theory ◽  
Heart Beating ◽  
Size Constraints ◽  
Source Sink

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.

scholarly journals Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3827
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Shape Functions ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Steady State Heat ◽  
Steady State Heat Transfer

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.

scholarly journals The use of a solution of the inverse heat conduction problem to monitor thermal stresses

2019 ◽  
Vol 108 ◽  
pp. 01003
Author(s):  
Jan Taler ◽  
Piotr Dzierwa ◽  
Magdalena Jaremkiewicz ◽  
Dawid Taler ◽  
Karol Kaczmarski ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Power Plants ◽  
Thermal Stresses ◽  
Thermal Power ◽  
Temperature Fields ◽  
Thick Wall ◽  
Fluid Temperature ◽  
Unsteady Temperature

Thick-wall components of the thermal power unit limit maximum heating and cooling rates during start-up or shut-down of the unit. A method of monitoring the thermal stresses in thick-walled components of thermal power plants is presented. The time variations of the local heat transfer coefficient on the inner surface of the pressure component are determined based on the measurement of the wall temperature at one or six points respectively for one- and three-dimensional unsteady temperature fields in the component. The temperature sensors are located close to the internal surface of the component. A technique for measuring the fastchanging fluid temperature was developed. Thermal stresses in pressure components with complicated shapes can be computed using FEM (Finite Element Method) based on experimentally estimated fluid temperature and heat transfer coefficient

Solid Media Thermal Storage Development and Analysis of Modular Storage Operation Concepts for Parabolic Trough Power Plants

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Doerte Laing ◽  
Wolf-Dieter Steinmann ◽  
Michael Fiß ◽  
Rainer Tamme ◽  
Thomas Brand ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Power Plants ◽  
Heat Storage ◽  
Storage Systems ◽  
Storage System ◽  
Sensible Heat ◽  
Economic Optimization ◽  
Parabolic Trough ◽  
Solid Media ◽  
Exergetic Analysis

Cost-effective integrated storage systems are important components for the accelerated market penetration of solarthermal power plants. Besides extended utilization of the power block, the main benefits of storage systems are improved efficiency of components, and facilitated integration into the electrical grids. For parabolic trough power plants using synthetic oil as the heat transfer medium, the application of solid media sensible heat storage is an attractive option in terms of investment and maintenance costs. For commercial oil trough technology, a solid media sensible heat storage system was developed and tested. One focus of the project was the cost reduction of the heat exchanger; the second focus lies in the energetic and exergetic analysis of modular storage operation concepts, including a cost assessment of these concepts. The results show that technically there are various interesting ways to improve storage performance. However, these efforts do not improve the economical aspect. Therefore, the tube register with straight parallel tubes without additional structures to enhance heat transfer has been identified as the best option concerning manufacturing aspects and investment costs. The results of the energetic and exergetic analysis of modular storage integration and operation concepts show a significant potential for economic optimization. An increase of more than 100% in storage capacity or a reduction of more than a factor of 2 in storage size and therefore investment cost for the storage system was calculated. A complete economical analysis, including the additional costs for this concept on the solar field piping and control, still has to be performed.

A Computational Study of the Interaction of Melting Soil With Moisture Transport in the Native Soil

1998 ◽  
Author(s):  
Will Schreiber ◽  
John Kuo
Keyword(s):  
Heat Transfer ◽  
Heat Flow ◽  
Moisture Transport ◽  
Moving Boundary ◽  
Computational Study ◽  
Fluid Motion ◽  
Computer Code ◽  
General Purpose ◽  
Simple Method ◽  
Porous Soil

Abstract The current paper describes a computer model designed to analyze the moisture transport in the unmelted, porous soil neighboring a convecting melt. The time-dependent fluid and heat flow in the soil melt is simulated implicitly using the SIMPLE method generalized to predict viscous fluid motion and heat transfer on boundary-fitted, non-orthogonal coordinates which adapt with time. TOUGH2, a general-purpose computer code for multiphase fluid and heat flow developed by K. Pruess at Lawrence Berkekey Laboratory, has been modified for use on time-adaptive, boundary-fitted coordinates to predict heat transfer, moisture and air transport, and pressure distribution in the porous, unmelted soil. The soil melt model is coupled with the modified TOUGH2 model via an interface (moving boundary) whose shape is determined implicitly with the progression of time. The computer model’s utility is demonstrated in the present study with a special two-dimensional study. A soil initially at 20°C and partially-saturated with either a 0.2 or 0.5 relative liquid saturation is contained in a box two meters wide by ten meters high with impermeable bottom and sides. The upper surface of the soil is exposed to a 20°C atmosphere to which vapor and air can escape. Computation begins when the soil, which melts at 1700°C, is heated from one side (maintained at constant temperatures ranging from 1700°C to 4000°C). Heat from the hot wall causes the melt to circulate in such a way that the melt interface grows more rapidly at the top of the box than at the bottom. As the upper portion of the melt approaches the impermeable wall it creates a bottle neck for moisture release from the soil’s lower regions. The pressure history of the trapped moisture is examined as a means for predicting the potential for moisture penetration into the melt. The melt’s interface movement and moisture transport in the unmelted, porous soil are also examined.

scholarly journals Thermal conductivity of sandstones from Biot’s coefficient

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. D173-D185 ◽  
Author(s):  
Tobias Orlander ◽  
Eirini Adamopoulou ◽  
Janus Jerver Asmussen ◽  
Adam Andrzej Marczyński ◽  
Harald Milsch ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flow ◽  
Cross Section ◽  
Geometric Mean ◽  
Well Log ◽  
Biot’S Coefficient ◽  
Model Predictions ◽  
The Cross ◽  
Rock Texture

Thermal conductivity of rocks is typically measured on core samples and cannot be directly measured from logs. We have developed a method to estimate thermal conductivity from logging data, where the key parameter is rock elasticity. This will be relevant for the subsurface industry. Present models for thermal conductivity are typically based primarily on porosity and are limited by inherent constraints and inadequate characterization of the rock texture and can therefore be inaccurate. Provided known or estimated mineralogy, we have developed a theoretical model for prediction of thermal conductivity with application to sandstones. Input parameters are derived from standard logging campaigns through conventional log interpretation. The model is formulated from a simplified rock cube enclosed in a unit volume, where a 1D heat flow passes through constituents in three parallel heat paths: solid, fluid, and solid-fluid in series. The cross section of each path perpendicular to the heat flow represents the rock texture: (1) The cross section with heat transfer through the solid alone is limited by grain contacts, and it is equal to the area governing the material stiffness and quantified through Biot’s coefficient. (2) The cross section with heat transfer through the fluid alone is equal to the area governing fluid flow in the same direction and quantified by a factor analogous to Kozeny’s factor for permeability. (3) The residual cross section involves the residual constituents in the solid-fluid heat path. By using laboratory data for outcrop sandstones and well-log data from a Triassic sandstone formation in Denmark, we compared measured thermal conductivity with our model predictions as well as to the more conventional porosity-based geometric mean. For outcrop material, we find good agreement with model predictions from our work and with the geometric mean, whereas when using well-log data, our model predictions indicate better agreement.

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