Constructal design of non-uniform X-shaped conductive pathways for cooling

Abstract This paper applies constructal design to discover the configuration that facilitates the access of the heat that flows through non-uniform X-shaped pathways of high-conductivity material embedded within a square-shaped heat-generating medium of low-conductivity to cooling this finite-size volume. The objective is to minimize the maximal excess of temperature of the whole system, i.e. the hot spots, independent of where they are located. The total volume and the volume of the material of high thermal conductivity are fixed, but the lengths of the pathways and the angles between the pathways can vary. The configuration was optimized for four degrees of freedom: the two angles between the pathways, and the two ratios between the lengths. It was found numerically that the performance of the non-uniform X-shaped pathways is approximately 10% better than the performance of the uniform X-shaped pathways, i.e. X-shaped with equal lengths and thicknesses. When compared to the configuration calculated for a simpler I-shaped blade (i.e. a single pathway of high thermal conductivity material beginning in the isothermal wall and ending of such a way that there is spacing between the tip of the pathway and the insulated wall) the non-uniform X-shaped pathways configuration performs 56% better.

[1]  Zhihui Xie,et al.  Geometry optimization of T-shaped cavities according to constructal theory , 2010, Math. Comput. Model..

[2]  Y. Azoumah,et al.  Optimal design of tree-shaped water distribution network using constructal approach: T-shaped and Y-shaped architectures optimization and comparison , 2012 .

[3]  Koetsu Yamazaki,et al.  Constructal Design of Cooling Channel in Heat Transfer System by Utilizing Optimality of Branch Systems in Nature , 2007 .

[4]  Fengrui Sun,et al.  Constructal entransy dissipation minimization of an electromagnet , 2009 .

[5]  Maroun Nemer,et al.  A new perspective of constructal networks cooling a finite-size volume generating heat , 2011 .

[6]  G. P. Peterson,et al.  Thermal Control of Electronic Equipment and Devices , 1990 .

[7]  Adrian Bejan,et al.  Design in Nature , 2012 .

[8]  Adrian Bejan,et al.  Constructal design for cooling a disc-shaped area by conduction , 2002 .

[9]  A. Bejan.  Constructal-theory network of conducting paths for cooling a heat generating volume , 1997 .

[10]  Louis Gosselin,et al.  Optimal conduction pathways for cooling a heat-generating body: A comparison exercise , 2007 .

[11]  Fengrui Sun,et al.  Multiobjective constructal optimization of an insulating wall combining heat flow, strength and weight , 2011 .

[12]  C. Biserni,et al.  Constructal design of X-shaped conductive pathways for cooling a heat-generating body , 2013 .

[13]  Qing Li,et al.  Evolutionary topology optimization for temperature reduction of heat conducting fields , 2004 .

[14]  Elizaldo Domingues dos Santos,et al.  Constructal Design of Complex Assembly of Fins , 2011 .

[15]  Khosrow Jafarpur,et al.  Thermal resistance in conductive constructal designs of arbitrary configuration: A new general approach , 2012 .

[16]  Lingai Luo,et al.  Tree-network structure generation for heat conduction by cellular automaton , 2009 .

[17]  W. Aung,et al.  Cooling Technology for Electronic Equipment , 1988 .

[18]  Louis Gosselin,et al.  Constructal heat trees at micro and nanoscales , 2004 .

[19]  W. Li,et al.  Experimental study of unsteady forced convection in a duct with and without arrays of block-like electronic components , 1993 .

[20]  A. Bejan.  Advanced Engineering Thermodynamics , 1988 .

[21]  Enrico Lorenzini,et al.  Constructal H-shaped cavities according to Bejan’s theory , 2007 .

[22]  Fengrui Sun,et al.  On the “area to point” flow problem based on constructal theory , 2007 .

[23]  Fengrui Sun,et al.  Constructal optimization for “disc-to-point” heat conduction without the premise of optimized last-order construct , 2011 .

[24]  Fengrui Sun,et al.  Constructal optimization on T-shaped cavity based on entransy dissipation minimization , 2009 .

[25]  Lotfollah Ghodoossi,et al.  Conductive cooling of triangular shaped electronics using constructal theory , 2004 .

[26]  Adrian Bejan,et al.  Three-dimensional tree constructs of “constant” thermal resistance , 1999 .

[27]  Adrian Bejan,et al.  Distributed energy tapestry for heating the landscape , 2010 .

[28]  Adrian Bejan,et al.  Conduction trees with spacings at the tips , 1999 .

[29]  Fengrui Sun,et al.  Optimization of constructal volume-point conduction with variable cross section conducting path , 2007 .

[30]  A. Bejan.  Shape and Structure, from Engineering to Nature , 2000 .

[31]  Adrian Bejan,et al.  Constructal-theory tree networks of “constant” thermal resistance , 1999 .

[32]  Lotfollah Ghodoossi,et al.  Exact solution for cooling of electronics using constructal theory , 2003 .

[33]  Adrian Bejan,et al.  Disc cooled with high-conductivity inserts that extend inward from the perimeter , 2004 .

[34]  Lotfollah Ghodoossi,et al.  Entropy generation rate in uniform heat generating area cooled by conducting paths: criterion for rating the performance of constructal designs , 2004 .

[35]  A. Bejan,et al.  Constructal tree networks for heat transfer , 1997 .

[36]  XinGang Liang,et al.  Optimization of heat conduction using combinatorial optimization algorithms , 2007 .

[37]  Qing Li,et al.  Evolutionary topology and shape design for general physical field problems , 2000 .

[38]  Chao Bai,et al.  Constructal structure of nanofluids , 2010 .

[39]  Elizaldo Domingues dos Santos,et al.  Constructal Design of Cavities Inserted Into a Cylindrical Solid Body , 2012 .

[40]  LinGen Chen,et al.  “Volume-point” heat conduction constructal optimization based on entransy dissipation rate minimization with three-dimensional cylindrical element and rectangular and triangular elements on microscale and nanoscale , 2012 .

[41]  Adrian Bejan,et al.  Conduction tree networks with loops for cooling a heat generating volume , 2006 .

[42]  Fengrui Sun,et al.  The area-point constructal optimization for discrete variable cross-section conducting path , 2009 .

[43]  Sadegh Poozesh,et al.  Valuable reconsideration in the constructal design of cavities , 2013 .

[44]  Liqiu Wang,et al.  Constructal Allocation of Nanoparticles in Nanofluids , 2010 .

[45]  Pierre Neveu,et al.  Constructal theory through thermodynamics of irreversible processes framework , 2011 .

[46]  N. K. Anand,et al.  Laminar developing flow and heat transfer between a series of parallel plates with surface mounted discrete heat sources , 1994 .

[47]  Fengrui Sun,et al.  Heat-conduction optimization based on constructal theory , 2007 .

[48]  Adrian Bejan,et al.  Constructal trees of circular fins for conductive and convective heat transfer , 1999 .

[49]  J. Meyer,et al.  Three-dimensional multi-scale plate assembly for maximum heat transfer rate density , 2010 .

[50]  Fengrui Sun,et al.  Constructal entransy dissipation rate minimization for heat conduction based on a tapered element , 2011 .

[51]  Fengrui Sun,et al.  Constructal entransy dissipation rate minimization of a disc , 2011 .

[52]  Fengrui Sun,et al.  Constructal entransy dissipation minimization for 'volume-point' heat conduction , 2008 .

[53]  Fengrui Sun,et al.  Constructal entransy dissipation rate minimization for leaf-like fins , 2012 .

[54]  Adrian Bejan,et al.  Design with constructal theory , 2008 .

[55]  A. Bejan,et al.  The optimal spacing of parallel plates cooled by forced convection , 1992 .

[56]  A. Bejan,et al.  Cylindrical trees of pin fins , 2000 .

[57]  J. Meyer,et al.  Thermal characterisation of embedded heat spreading layers in rectangular heat-generating electronic modules , 2009 .

[58]  Mohammad Reza Salimpour,et al.  Constructal design of reverting microchannels for convective cooling of a circular disc , 2011 .

[59]  Jing Fan,et al.  Constructal design of nanofluids , 2010 .

[60]  J. C. Denton,et al.  Analytical solution for heat conduction problem in composite slab and its implementation in constructal solution for cooling of electronics , 2007 .

[61]  Fengrui Sun,et al.  Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective , 2009 .

[62]  J. Meyer,et al.  Heat Removal from Power Electronics in Two Direction Sets Using Embedded Solid State Cooling Layers a Proposed Non-Numerical Calculation Method , 2009 .

[63]  Leroy S. Fletcher,et al.  The Effect of Plate Spacing on Free Convection Between Heated Parallel Plates , 1992 .