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چكيده انگليسي :

113 Constructal Design for Cooling a Disc shaped Area by Incomplete High Conductivity Inserts Farrokh Sharifi F Sharifi@me iut ac ir May 3 th 2011 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor M R Salimpour Assist Prof Salimpour@cc iut ac ir AbstractConstructal theory is a means for optimization of resistances in the area point flows In the present study the problemof cooling an adiabatic disc by highly conductive inserts was examined analytically This work was accomplishedusing a fixed amount of highly conductive material distributed as incomplete inserts from the heat sink at the centertoward the perimeter In the present case the length of the inserts was different from the disc radius viz a new degree offreedom was considered and the solution was remarkably different from the complete insert case Using constructaltheory thermal resistances of the radial and tributary configurations were evaluated analytically Firstly it was tried toderive an equation for thermal resistance of the disc for radial configuration of inserts based on the procedureimplemented in constructal studies which have been done previously This was carried out by implementing theoptimized thermal resistance of elemental sectors Then the computed elemental sectors were put together so that theymake branching configuration of inserts in the disc while the thermal resistance of the disc by such architecture ofinserts was calculated The thermal resistance was minimized regarding to the aspect ratio to find the optimal number ofinserts and the radius of the disc From this work It was concluded that for a specific range of R1 R2 the optimal totalthermal resistance for incomplete inserts has considerably better performance in comparison with complete ones in theradial pattern In the present study conductive cooling of a disc was also done by means of incomplete constant andvariable cross section conducting paths embedded in radial and tributary configurations Variational calculus wasinvoked to determine the optimum shape of the cross sections of the inserts Out of the comparison between theobtained thermal resistances of the disc with constant and variable cross sections it was concluded that using variablecross sections reduces thermal resistance but this effect differs in radial and tributary configurations i e increasing thecomplexity of tributary patterns does not always reduce the thermal resistance more effectively in comparison withradial configurations Moreover the thermal conductivities were considered temperature dependent which were variedlinearly and ascending Applying the Kirchhoff transformation the resulting nonlinear partial equations weretransformed to linear ones which would be easier to solve analytically Furthermore the effect of temperature dependency of the thermal conductivities was examined and compared with constant thermal conductivities case underdifferent conditions where a decrease in thermal resistance was observed However the efficiency of this factor indecreasing the thermal resistance was dependent on other parameters The effect of considering variable cross sectionfor the highly conductive material was combined with the temperature dependency of the conductivities where it wasconcluded that under certain circumstances where the effect of temperature dependency of the conductivities is weak the variable cross section can be used to reduce the thermal resistance efficiently Finally as some approximationswere used in analytical solution which the most important of them was the assumption of solving one dimensionalconduction equation for the region with highly conductive material and also the optimization process was implementedbased on constructal theory a numerical solution was performed to validate the analytical results where an acceptableconsistency was observed KeyWords Constructal Highly conductive Incomplete insert Variable cross section V

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