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Here we show that there is a complete analogy between the configuring of heat and fluid flow and the configuring of the “flow of stresses”. The common principle is the avoidance of flow strangulations. This endows the flow systems (fluid, heat, stresses) with high density: for example, strongest for a fixed volume, or lightest for a fixed load. Examples treated in detail are “ducts” for the flow of stresses (slender bars in tension of compression), bifurcated bars shaped as Y and V, and slender and tapered plates (adhesive joints, tendons, ligaments), which are shown to be analogous to convection boundary layers. The design value of the “flow of stresses” concept is emphasized: to facilitate the flow of stresses (and the flow of fluid and heat) is to generate the configuration of the flow system, in accord with the constructal law.
We already have discussed one form of mixed convection in a horizontal layer, namely, the onset of convection with throughflow when the heating is from below (see Sect 6.10). In this chapter, we discuss some more general aspects of mixed convection. Since we have...
In this paper the cooking of meat is modeled as a process of time-dependent conduction through a constant-property medium that shrinks as its temperature increases. The overall shrinkage is the integrated result of shrinking that is distributed volumetrically through the piece of meat and depends on the temperature history at every point. The meat temperature history and associated shrinkage are determined numerically. The geometric configuration is the one-dimensional conducting slab with convective heating on both sides. Means for calculating the required cooking time are reported in the form of dimensionless charts for the temperature in the midplane of the meat slab. A numerical example shows that the cooking time calculated by accounting for meat shrinkage is appreciably shorter than the time estimate based on the classical Heisler chart for conduction in a constant-volume slab.
We already have discussed one form of mixed convection in a horizontal layer, namely the onset of convection with throughflow when the heating is from below (see Sect. 6.10). In this chapter we discuss some more general aspects of mixed convection. Since we have...
This paper shows that the internal geometric configuration of a component can be deduced by optimizing the global performance of the installation that uses the component. The example chosen is the counterflow heat exchanger that serves as condenser in a vapor-compression-cycle refrigeration system for environmental control of aircraft. The optimization of global performance is achieved by minimizing the total power requirement or the total entropy generation rate. There are three degrees of freedom in the heat exchanger configuration, which is subjected to two global constraints: total volume, and total volume (or weight) of wall-material. Numerical results show how the optimal configuration responds to changes in specified external parameters such as refrigeration load, fan efficiency, and volume and weight. In accordance with constructal theory and design [1], it is shown that the optimal configuration is robust: major features such as the ratio of diameters and the flow length are relatively insensitive to changes in the external parameters.
This paper describes the constructal route to the conceptual design of a two-stream heat exchanger with maximal heat transfer rate per unit volume. The flow structure has multiple scales. The smallest (elemental) scale consists of parallel-plates channels the length of which matches the thermal entrance length of the small stream that flows through the channel. This feature has two advantages: it eliminates the longitudinal temperature increase (flow thermal resistance) that would occur in fully developed laminar flow, and it doubles the heat transfer coefficient associated with fully developed laminar flow. The elemental channels of hot fluid are placed in crossflow with elemental channels of cold fluid. The elemental channel pairs are assembled into sequentially larger flow structures (first construct, second construct, etc.), which have the purpose of installing (spreading) the elemental heat transfer as uniformly as possible throughout the heat exchanger volume. At length scales greater than the elemental, the streams of hot and cold fluid are arranged in counterflow. Each stream bathes the heat exchanger volume as two trees joined canopy to canopy. One tree spreads the stream throughout the volume (like a river delta), while the other tree collects the same stream (like a river basin). It is shown that the spacings of the elemental and first-construct channels can be optimized such that the overall pumping power required by the construct is minimal. The paper concludes with a discussion of the advantages of the proposed tree-like (vascularized) heat exchanger structure over the use of parallel small-scale channels with fully developed laminar flow.
This paper considers the basic thermodynamic optimization problem of extracting the most power from a stream of hot exhaust when the contact heat transfer area is fixed. It shows that when the receiving (cold) stream boils in the counterflow heat exchanger, the thermodynamic optimization consists of locating the optimal capacity rate of the cold stream. At the optimum, the cold side of the heat transfer surface divides itself into three sections: liquid preheating, boiling and vapor superheating. Numerical results are developed for a range of design parameters of applications with either water or toluene on the cold side. It is shown that the optimal design is robust, because several of the design parameters have only a weak effect on the optimal design.
The second law of thermodynamics is used as a basis for evaluating the irreversibility (entropy generation) associated with simple heat transfer processes. In the first part of this paper, the irreversibility production is analyzed from the local level, at one point in a convective heat transfer arrangement. The second part of the paper is devoted to a limited review of second law analysis applied to classic engineering components for heat exchange. In this category, the paper includes such topics as: heat transfer augmentation techniques, heat exchanger design, and thermal insulation systems. Analytical methods for evaluating and minimizing the irreversibility associated with textbook-type components of heat transfer equipment are presented.
This article reveals the thermodynamics of human sustainability on earth: (i) Production of power increases and, necessarily, the consumption of source energy increases (fuel, food, area covered by solar panels and windmills). Greater efficiency and energy conservation do not translate into less fuel consumption. (ii) Consequently, the world population will continue to increase monotonically. (iii) The power generated, consumed, and dissipated by the world population will continue to increase because every individual and group makes decisions in the direction of achieving greater wealth. The scatter in the data (the diversity) is because more advanced societies facilitate greater human movement per unit of fuel consumed. The way forward consists of making consistent steps on several paths: (a) Greater efficiency, (b) Cleaner power generation, (c) More economical distribution of power on the globe, and (d) Greater flow connectivity (empowering) of the pockets of populations that, unlike advanced societies, do not benefit from greater movement (access) per unit of fuel consumed. Any idea that moves a population toward greater movement (access) counts: increasing power plant efficiency, power & refrigeration, transportation evolution, energy in buildings, climate evolution and prediction, and reshaping the coastline.
In this paper, we extend the constructal optimization method to cylindrical assemblies of pin fins. The assembly is arranged as a tree with one stem and many radial branches. The optimization consists of maximizing the global conductance subject to fixed total volume and amount of fin material. The length scale of the spacing between adjacent elemental fins is selected based on earlier results regarding the forced convection of compact electronic packages. The optimized features of the tree construct are the external shape (height/diameter) and the internal ratio between the stem diameter and the diameter of the elemental fins. The paper shows how the geometric optimum responds to changes in the remaining parameters of the design: the volume fraction occupied by fin material, the free stream velocity, and the Prandtl number. The optimized geometry is relatively robust. It is shown that optimized trees with tapered fins have slightly larger global conductances, but nearly the same external and internal aspect ratios. This last comparison also shows that the more efficient trees look more natural.
This paper describes the optimization of a tree-shaped system of insulated pipes for the distribution of a stream of hot water over an area. The area is covered uniformly by users who must receive the same flow rate of hot water. The network of pipes is developed in steps. Each step consists of attaching to an existing network an extension (one new user) that is placed in the position that maximizes the temperature of the water received by the new user. The network grows `one-by-one', i.e., by one new user at a time. Networks with up to 16 users are optimized in this manner, and their geometric features and thermo-fluid performance are documented. These one-by-one trees of hot water flows are compared with corresponding `constructal' trees that are obtained in steps of pairing (doubling), i.e., connecting together two identical area constructs of the same size. It is shown that although the constructal trees perform the best (uniform water delivery at the highest temperature), the one-by-one trees approach the same level of performance as they become more complex. It is also shown that the geometry of the insulated tree structure is relatively insensitive to how the insulation is distributed over all the pipes. The thermal performance of the structure is relatively insensitive to how finely the distribution of pipe sizes and insulation radii is optimized.
In this paper “constructal theory,” is used to predict the formation of geometric shape and structure in finite-size fluid systems subjected to heating from below. Two classes of system are considered as tests: (i) single-phase fluid layers, and (ii) porous layers saturated with single-phase fluids. It is shown that the minimization of thermal resistance across the layer can be used to account for the appearance of organized macroscopic motion (streams) on the background of disorganized motion (diffusion). By optimizing the shape of the flow, it is possible to predict analytically the main structural and heat transfer characteristics of the system, e.g., the onset of convection, the relation between Nusselt number and Rayleigh number, the geometric shape of the rolls, and the decreasing exponent of RaH as RaH increases. The convective flow structure emerges as the result of a process of geometric optimization of heat flow path, in which diffusion is assigned to length scales smaller than the smallest macroscopic flow element (elemental system). The implications of this test of constructal theory are discussed in the context of the wider search for a physics law of geometric form generation in natural flow systems.
This is a study of the evolving design of a composite material with inserts that are free to be configured and distributed through the base material. Several classes of shapes of inserts are considered competitively: parallel plates, staggered plates, forks, chains and diamonds. The architecture evolves in two directions (with two objectives), high thermal conductance and mechanical strength (stiffness). Relative to the base material, the inserts have higher thermal conductivity and lower modulus of elasticity. As a consequence, better architectures emerge from the tradeoff between thermal conductance and strength, for example, chain and diamond shaped inserts. The two-objective performance further improves when the inserts are distributed nonuniformly through the base material, such that the high conductivity inserts are not placed in the regions with the highest stresses.
This article reports an analytical study of natural convection in a wedge-shaped horizontal space filled with a fluid-saturated porous medium. The study focuses on the detrimental effect of natural convection on the insulation value of an attic-shaped porous layer in “winter” conditions (cold roof, warm ceiling). The study reveals the most basic features of the temperature field and flow pattern established in the porous layer. The study addresses two distinct flow regimes: (a) the shallow attic limit (H/L→0, RaH = finite, but fixed) and (b) the boundary layer regime which consists of a boundary layer driven by the sloped (roof) wall plus a core flow moving slowly along the horizontal (ceiling) wall. Heat-transfer results are developed for both flow regimes.
The laws of classical thermodynamics refer to systems as black boxes, without configuration. Nature is different: it has "designedness" everywhere and at all scales (pattern, configuration, rhythm). The generation of configuration is a phenomenon of all physics, and it is covered by the constructal law: for a finite‐size flow system to persist in time (to live) it must evolve such that it provides easier access to its currents. The constructal law is predictive across the board, in inanimate, animate and human flow systems. Examples are the scaling laws of all river basins, the speeds and frequencies of all kinds of animal locomotion, and the zipfian distribution of hierarchical city sizes and numbers on the globe. The constructal law accounts for the numerous and often contradictory ad‐hoc statements of self‐optimization, e.g. minimization and maximization of entropy generation, minimization and maximization of flow resistance, minimization of time and cost, maximization of utility, and the axiom of uniform stresses in animal bones and botanical trees.
