Constructal Optimization for Cooling a Non-Uniform Heat Generating Radial-Pattern Disc by Conduction

Abstract

A heat conduction model in a radial-pattern disc by considering non-uniform heat generation (NUHG) is established in this paper. A series of high conductivity channels (HCCs) are attached on the rim of the disc and extended to its center. Constructal optimizations of the discs with constant and variable cross-sectional HCCs are carried out, respectively, and their maximum temperature differences (MTDs) are minimized based on analytical method and finite element method. Besides, the influences of the NUHG coefficient, HCC number and width coefficient on the optimal results are studied. The results indicate that the deviation of the optimal constructs obtained from the analytical method and finite element method are comparatively slight. When the NUHG coefficient is equal to 10, the minimum MTD of the disc with 25 constant cross-sectional HCCs is specifically reduced by 48.8% compared to that with 10 HCCs. As a result, the heat conduction performance (HCP) of the disc can be efficiently improved by properly increasing the number of HCCs. The minimum MTD of the disc with variable cross-sectional HCC is decreased by 15.0% when the width coefficient is changed from 1 to 4. Therefore, the geometry of variable cross-sectional HCC can be applied in the constructal design of the disc to a better heat transfer performance. The constructal results obtained by investigating the non-uniform heat generating case in this paper can contribute to the design of practical electronic device to a better heat transfer performance.

Performance Optimization of a Condenser in Ocean Thermal Energy Conversion (OTEC) System Based on Constructal Theory and a Multi-Objective Genetic Algorithm

“…Constructal theory [ 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 ] was put forward by Professor Bejan in 1996. The corresponding constructal law [ 27 , 28 ] is “For a finite-size flow system to persist in time (to live), its configuration must change in time such that it provides easier and easier access to its currents.” The structural designs for living and non-living systems can be performed by applying constructal theory, including the structural designs of HEs.…”

Constructal Design of Elliptical Cylinders with Heat Generating for Entropy Generation Minimization

“…Research aiming to optimize electronic device and heat sink designs to enhance their heat dissipation has attracted the interest of many scholars [ 1 , 2 ]. In recent years, extensive and in-depth investigations for heat transfer optimization in the light of constructal theory [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] and entropy generation minimization [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 ,…”

“…Bejan, who investigated the universal physical mechanism of various natural dendritic structures [ 4 , 5 , 6 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 24 ], found the constructal law and proposed constructal theory from analyzing the formation and evolution of street network configurations in major cities around the world as an example in 1996 [ 3 ]. Constructal theory was firstly applied to design an optimal network of high conductivity material for electronics cooling, and the constructal law was found correspondingly [ 4 ].…”

“…Constructal theory was firstly applied to design an optimal network of high conductivity material for electronics cooling, and the constructal law was found correspondingly [ 4 ]. The constructal law [ 4 ] stated that, “For a finite-size flow system to persist in time (to live), its configuration must change in time such that it provides easier and easier access to its currents.” For everything in nature, society and engineering, the configuration evolution in time follows this deterministic physics law [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ]. Constructal theory not only accounts for and predicts the flow pattern/configuration evolution in nature and society, but also provides theoretical guidelines for the flow pattern/configuration design in various disciplines.…”

“…For heat transfer optimization, the studies following constructal law can be classified as single-objective optimization, multi-objective optimization and multi-disciplinary optimization by optimization objectives; and these also can be classified as heat conduction optimization, convective heat and mass transfer optimization and various device and component optimization by study objects, and so on [ 4 , 5 , 6 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 24 ]. It has also been applied to the designs of cavities and fin heat sinks [ 24 , 61 , 62 , 63 ], channel heat sinks [ 64 , 65 ], heat exchangers [ 66 , 67 , 68 , 69 ], nonuniform heat generating units [ 70 , 71 ], evaporators [ 72 , 73 , 74 ], boiler superheater [ 75 ], tubular arrangements [ 76 , 77 ], dual-pressure turbine [ 78 , 79 ], etc., in recent years.…”