Constructal Design Associated to Genetic Algorithm of Asymmetric V-Shaped Pathways

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Emanuel da S. D. Estrada ◽  
Tadeu M. Fagundes ◽  
Liércio A. Isoldi ◽  
Elizaldo D. dos Santos ◽  
Gongnan Xie ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Thermal Resistance ◽  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Geometric Optimization ◽  
Heat Sinks ◽  
Heat Generation Rate ◽  
Conductive Materials ◽  
Constructal Design ◽  
Optimal Shapes

This work relies on constructal design to perform the geometric optimization of the V-shaped pathways of highly conductive materials (inserts) that remove a constant heat generation rate from a body and deliver it to isothermal heat sinks. It is shown numerically that the global thermal resistance of the V-shaped pathway can be minimized by geometric optimization subject to total volume and V-shaped pathways material constraints. Constructal design and genetic algorithm (GA) optimization showed the emergence of an optimal architecture that minimizes the global thermal resistance: an optimal external shape for the assembly of pathways and optimal geometry features for the V-shaped pathway. Parametric study was performed to show the behavior of the minimized global thermal resistance as function of the volume fraction of the V-shaped pathways. First achieved results for ϕ = 0.3 indicated that when freedom is given to the geometry, the thermal performance is improved. Afterward, the employment of GA with constructal design allowed the achievement of the optimal shapes of V-shaped pathways for different volume fractions (0.2 ≤ ϕ ≤ 0.4). It was not realized the occurrence of one universal optimal shape for the several values of ϕ investigated, i.e., the optimal design was dependent on the degrees of freedom and the parameter ϕ and it is reached according to constructal principle of optimal distribution of imperfections.

Constructal Design Applied to the Geometric Optimization of Y-shaped Cavities Embedded in a Conducting Medium

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
G. Lorenzini ◽  
C. Biserni ◽  
L. A. Isoldi ◽  
E. D. dos Santos ◽  
L. A. O. Rocha
Keyword(s):  
Thermal Resistance ◽  
Degrees Of Freedom ◽  
Vertical Direction ◽  
Optimization Procedure ◽  
Power Laws ◽  
Geometric Optimization ◽  
Constructal Design ◽  
Conducting Wall ◽  
Geometric Conditions ◽  
Optimal Shapes

In this paper, we rely on the Constructal method to optimize the geometry of a Y-shaped cavity embedded into a solid conducting wall. The structure has four degrees of freedom. The objective is to minimize the global thermal resistance between the solid and the cavity. The optimization procedure has demonstrated that for larger solids, a cavity shaped as T led to a minimization of the global thermal resistance, while the opposite effect is observed for tall solids, where the optimal shapes are reached when the bifurcated branches deeply penetrates the solid in the vertical direction, according to the Constructal principle of “optimal distribution of imperfections”. The three times minimized global thermal resistance of the Y-shaped cavity has been correlated by power laws as a function of its corresponding optimal configurations. Finally, the performance of the Y-shaped intrusion proved to be superior to that of other basic geometries: the optimized global thermal resistances of the Y-shaped cavities obtained for H/L = 1.0, 2.0, and 5.0 were, respectively 66.61%, 55.37%, and 19.05% lower than the optimal T-shaped cavities under the same thermal and geometric conditions. Furthermore, in comparison with the “finger cavity” shaped as C, the Y-shaped cavities increased the thermal performance in 109.12%, 84.45%, 59.32%, and 20.10% for H/L = 0.5, 1.0, 2.0, and 5.0, respectively.

scholarly journals Computational Modeling and Constructal Design Theory Applied to the Geometric Optimization of Thin Steel Plates with Stiffeners Subjected to Uniform Transverse Load

Metals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 220 ◽  
Author(s):  
Grégori Troina ◽  
Marcelo Cunha ◽  
Vinícius Pinto ◽  
Luiz Rocha ◽  
Elizaldo dos Santos ◽  
...  
Keyword(s):  
Computational Modeling ◽  
Design Theory ◽  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Geometric Optimization ◽  
Steel Plates ◽  
Transverse Load ◽  
Constructal Design ◽  
Thin Steel ◽  
Reference Plate

Stiffened thin steel plates are structures widely employed in aeronautical, civil, naval, and offshore engineering. Considering a practical application where a transverse uniform load acts on a simply supported stiffened steel plate, an approach associating computational modeling, Constructal Design method, and Exhaustive Search technique was employed aiming to minimize the central deflections of these plates. To do so, a non-stiffened plate was adopted as reference from which all studied stiffened plate’s geometries were originated by the transformation of a certain amount of steel of its thickness into longitudinal and transverse stiffeners. Different values for the stiffeners volume fraction (φ) were analyzed, representing the ratio between the volume of the stiffeners’ material and the total volume of the reference plate. Besides, the number of longitudinal (Nls) and transverse (Nts) stiffeners and the aspect ratio of stiffeners shape (hs/ts, being hs and ts, respectively, the height and thickness of stiffeners) were considered as degrees of freedom. The optimized plates were determined for all studied φ values and showed a deflection reduction of over 90% in comparison with the reference plate. Lastly, the influence of the φ parameter regarding the optimized plates was evaluated defining a configuration with the best structural performance among all analyzed cases.

scholarly journals CONSTRUCTAL DESIGN AND SIMULATED ANNEALING EMPLOYED FOR GEOMETRIC OPTIMIZATION OF A Y-SHAPED CAVITY INTRUDED INTO CONDUCTIVE WALL

2015 ◽  
Vol 14 (1) ◽  
pp. 79
Author(s):  
G. V. Gonzales ◽  
E. D. Dos Santos ◽  
L. R. Emmendorfer ◽  
L. A. Isoldi ◽  
E. S. D. Estrada ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Solid Wall ◽  
Internal Heat ◽  
Optimization Methods ◽  
Optimization Method ◽  
Internal Heat Generation ◽  
Geometric Optimization ◽  
Constructal Design ◽  
Optimal Shapes

he problem study here is concerned with the geometrical evaluation of an isothermal Y-shaped cavity intruded into conducting solid wall with internal heat generation. The cavity acts as a sink of the heat generated into the solid. The main purpose here is to minimize the maximal excess of temperature (θmax) in the solid. Constructal Design, which is based on the objective and constraints principle, is employed to evaluate the geometries of Y-shaped cavity. Meanwhile, Simulated Annealing (SA) algorithm is employed as optimization method to seek for the best shapes. To validate the SA methodology, the results obtained with SA are compared with those achieved with Genetic Algorithm (GA) and Exaustive Search (ES) in recent studies of literature. The comparison between the optimization methods (SA, GA and ES) showed that Simulated Annealing is highly effective in the search for the optimal shapes of the studied case.

Genetic Algorithm Applied to Geometric Optimization of Isothermal Y-Shaped Cavities

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Giulio Lorenzini ◽  
Cesare Biserni ◽  
Emanuel da Silva Diaz Estrada ◽  
Elizaldo Domingues Dos Santos ◽  
Liércio André Isoldi ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Degrees Of Freedom ◽  
Geometric Optimization ◽  
Exhaustive Search ◽  
Constructal Design ◽  
Conducting Wall

Constructal design associated with genetic algorithm (GA) is employed to optimize the geometry of an isothermal Y-shaped cavity embedded into a solid conducting wall. The structure has four degrees of freedom (DOF). The main purpose is to minimize the maximum excess of temperature between the solid and the cavity by means of GA and exhaustive search (simulating every geometry combinations). Results showed that GA was well succeeded to find the best shapes which minimize the maximal excess of temperature with a number of simulations strongly lower than that required with exhaustive search, allowing the optimization of cavity under new constraint conditions.

Constructal Design of Particle Volume Fraction in Nanofluids

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
Chao Bai ◽  
Liqiu Wang
Keyword(s):  
Thermal Resistance ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Circular Disk ◽  
Small Scale ◽  
Particle Volume ◽  
Constructal Design ◽  
Dispersed Particles ◽  
Overall Resistance ◽  
Plane Slab

Abstract We perform a constructal design of particle volume fraction of four types of nanofluids used for heat conduction in four systems: a circular disk, a sphere, a plane slab, and a circular annulus. The constructal volume fraction is obtained to minimize system overall temperature difference and overall thermal resistance. Also included are the features of the constructal volume fraction and the corresponding constructal thermal resistance, which is the minimal overall resistance to the heat flow. The constructal nanofluids that maximize the system performance are not necessarily the ones with uniformly dispersed particles in base fluids. Nanofluids research and development should thus focus on not only nanofluids but also systems that use them. The march toward micro- and nanoscales must also be with the sobering reminder that useful devices are always macroscopic, and that larger and larger numbers of small-scale components must be assembled and connected by flows that keep them alive.

Constructal Design of Convective Y-Shaped Cavities by Means of Genetic Algorithm

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
G. Lorenzini ◽  
C. Biserni ◽  
E. D. Estrada ◽  
L. A. Isoldi ◽  
E. D. dos Santos ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Degrees Of Freedom ◽  
Thermal Field ◽  
Optimal Shape ◽  
Exhaustive Search ◽  
Difficult Situation ◽  
Constructal Design ◽  
Conducting Wall ◽  
Dimensionless Heat ◽  
Heat Transfer Parameter

In the present work constructal design is employed to optimize the geometry of a convective, Y-shaped cavity that intrudes into a solid conducting wall. The main purpose is to investigate the influence of the dimensionless heat transfer parameter a over the optimal geometries of the cavity, i.e., the ones that minimize the maximum excess of temperature (or reduce the thermal resistance of the solid domain). The search for the best geometry has been performed with the help of a genetic algorithm (GA). For square solids (H/L = 1.0) the results obtained with an exhaustive search (which is based on solution of all possible geometries) were adopted to validate the GA method, while for H/L ≠ 1.0 GA is used to find the best geometry for all degrees of freedom investigated here: H/L, t1/t0, L1/L0, and α (four times optimized). The results demonstrate that there is no universal optimal shape that minimizes the thermal field for all values of a investigated. Moreover, the temperature distribution along the solid domain becomes more homogeneous with an increase of a, until a limit where the configuration of “optimal distribution of imperfections” is achieved and the shape tends to remain fixed. Finally, it has been highlighted that the GA method proved to be very effective in the search for the best shapes with the number of required simulations much lower (8 times for the most difficult situation) than that necessary for exhaustive search.

Constructal Design of Double-T Shaped Cavity with Stochastic Methods Luus-Jaakola and Simulated Annealing

2017 ◽  
Vol 370 ◽  
pp. 152-161 ◽  
Author(s):  
Gill Velleda Gonzales ◽  
Elizaldo Domingues dos Santos ◽  
Liércio André Isoldi ◽  
Luiz Alberto Oliveira Rocha ◽  
Antônio José da Silva Neto ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Degrees Of Freedom ◽  
Hybrid Methods ◽  
Transfer Problem ◽  
Geometric Optimization ◽  
Stochastic Methods ◽  
Statistical Tool ◽  
Constructal Design ◽  
Cooling Schedule ◽  
Complete Optimization

In this paper it is proposed a comparison between two stochastic methods, Simulated Annealing and Luus-Jaakola algorithms, applied in association with Constructal Design to the geometric optimization of a heat transfer problem. The problem consists in a solid body with an internal uniform heat generation, which is cooled by an intruded cavity that is maintained at a minimal temperature. The other surfaces are kept as adiabatic. The objective is to minimize the maximum excess of temperature (θmax) in the solid domain through geometric optimization of the isothermal double-T shaped cavity. The problem geometry has five degrees of freedom, but in this study four degrees of freedom are evaluated, keeping fixed the ratio H/L (ratio between the height and length of the solid domain) as well as the cavity constraints. The search for the optimal geometry is performed by Simulated Annealing and the Luus-Jaakola algorithm with different configurations or set of main parameters. Each algorithm is executed twenty times and the results for θmax, and corresponding geometry ratios, are recorded. Results of two heuristics are compared in order to select the best method for future studies about the complete optimization of the cavity, as well as, the evaluation of constraints over the thermal performance of the problem. The method employed to compare and rank the different versions of the two algorithms is a statistical tool called multi-comparison of Kruskal-Wallis. With this statistical method it is possible to classify the algorithms in three main groups. Results showed that the Simulated Annealing with hybrid parameters of Cooling Schedule (BoltzExp and ConstExp2) and traditional ones (Exponential) led to the highest probability to find the global optimal shape, while the results obtained with the Luus-Jaakola algorithm reached to several local points of minimum far from the best shape for all versions of the algorithm studied here. However, the Luus-Jaakola algorithm led to the lowest magnitude of maximum excess of temperature, showing that the implementation of hybrid methods of optimization can be an interesting strategy for evaluation of this kind of problem.

Analysis of Geometric Variation of Three Degrees of Freedom through the Constructal Design Method for a Oscillating Water Column Device with Double Hidropneumatic Chamber

2019 ◽  
Vol 396 ◽  
pp. 22-31
Author(s):  
Yuri T.B. Lima ◽  
Mateus das Neves Gomes ◽  
Camila F. Cardozo ◽  
Liércio André Isoldi ◽  
Elizaldo D. Santos ◽  
...  
Keyword(s):  
Water Column ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Design Method ◽  
Geometric Optimization ◽  
Oscillating Water Column ◽  
Constructal Design ◽  
Wave Energy Converters ◽  
Volume Method ◽  
Geometric Variation

This paper presents a biphasic two-dimensional numerical study of sea wave energy converters with operating principle being Oscillating Water Column (CAO) devices with two couples chambers. For the study of the geometric optimization, the Constructal Design method is applied in association with the exhaustive search method to determine the geometric arrangement that leads to the greatest hydropneumatic power available. The objective function is the maximization of hydropneumatic power converted by the device. The constraints of the problem are the inflow volumes of the hydropneumatic chamber (VE1, VE2), the total volumes (VT1, VT2) and the thicknesses of the device columns (e1, e3). The degrees of freedom analyzed were H1/L1(ratio between height and length of the hydropneumatic chamber of the first device), H2/L2 (ratio between height and length of the hydropneumatic chamber of the second device), H2 (height of the column dividing the two devices) and e2 (thickness of the column dividing the devices). In the present work the degree of freedom H6 (depth of immersion of the device) is kept constant and equal to H6 = 9.86 m. The Finite Volume Method (FVM) was used in the numerical solution of the equations employed. For the treatment of the interaction between the air and water phases, the Volume of Fluid (VOF) method was applied. The results show that the maximum hydropneumatic power available was 5715.2 W obtained for degrees of freedom H1/L1 = H2/L2 = 0.2613 and e2 = 2.22 m. The case of lower performance has a power value equal to 4818.5 W with degrees of freedom equal to H1/L1 = H2/L2 = 0.2613 and e2 = 0.1 m.

scholarly journals GEOMETRIC OPTIMIZATION OF “+”-SHAPED CAVITY USING CONSTRUCTAL THEORY

2017 ◽  
Vol 16 (1) ◽  
pp. 75
Author(s):  
P. A. Avendaño ◽  
J. A. Souza ◽  
D. F. Adamatti ◽  
E. D. dos Santos
Keyword(s):  
Solid Body ◽  
Degrees Of Freedom ◽  
Internal Heat ◽  
Thermal Conditions ◽  
Geometric Optimization ◽  
Optimal Performance ◽  
Constructal Theory ◽  
Maximum Temperature ◽  
Constructal Design ◽  
Better Than

In this work it is applied the Constructal Theory for the study of the geometry of an “+”-shaped isothermal cavity inserted in a conductive solid body. Main goal is to minimize the maximum temperature in the solid. The total volume of the solid and the total volume of the cavity are kept fixed while the dimensions of the cavity geometry vary according to constraints and degrees of freedom defined by the Constructal Design. The solid body has internal heat generation and its external surfaces are insulated. Cavity walls are isothermal with constant temperature Tmin. Obtained results indicate that the optimal performance of “+”-shape cavity is 37.2% better that the optimal performance of “C”-shape cavity and 10.8% better than the “T”-shaped cavity for the same thermal conditions.

A Genetic Algorithm Based Multi-Objective Thermal Design Optimization of Liquid Cooled Offset Strip Fin Heat Sinks

2009 ◽  
Author(s):  
Sidy Ndao ◽  
Yoav Peles ◽  
Michael K. Jensen
Keyword(s):  
Genetic Algorithm ◽  
Pressure Drop ◽  
Aspect Ratio ◽  
Power Consumption ◽  
Thermal Resistance ◽  
Thermal Design ◽  
Heat Sinks ◽  
Total Thermal Resistance ◽  
Offset Strip Fin ◽  
Fin Length

A genetic algorithm based multi-objective thermal design optimization of liquid cooled offset strip fin heat sinks is presented. Using water and HFE-7000 as coolants, Matlab’s genetic algorithm and direct search toolbox functions were utilized to determine the optimal thermal design of the offset strip fin heat sink based on the total thermal resistance and power consumption under constant pressure drop. For a relatively small fin length, the total thermal resistance decreases with increasing fin length and aspect ratio α. For larger fin lengths, the total thermal resistance increases with increasing fin length whereas the power consumption continuously increases with increasing fin length and aspect ratio α for a given pressure drop. A plot of the Pareto front indicates a trade-off between the total thermal resistance and pumping power consumption.

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