Abstract
The geometry of a heat generating volume cooled by forced convection is optimized by applying the entransy dissipation extremum principle and constructal theory, while the optimal spacing between the adjacent tubes and the optimal diameter of each tube are obtained based on entransy dissipation rate minimization. The results of this work show that the optimal constructs based on entransy dissipation rate minimization and maximum temperature difference minimization, respectively, are clearly different. For the former, the porosity of the volume of channels allocated to the heat generating volume is 1/2; while for the latter, the larger the porosity is, the better the performance will be. The optimal construct of the former greatly decreases the mean thermal resistance and improves the global heat transfer performance of the system compared with the optimal construct of the latter. This is identical to the essential requirement of the entransy dissipation extremum principle that the required heat transfer temperature difference is minimal with the same heat transfer rate (the given amount of heat generated in the heat generating volume) based on the entransy dissipation extremum principle.
Highlights
The necessity to cool electronic devices escalates with the continued increase in chip integration level, packaging density and operating frequency, all leading to a steep increase in the generated heat density
Wang et al [37] designed tree-shaped vascularization and developed a method to control the maximum temperature of the heat generating volume using nothing more than natural convection
Based on Ref. [27], this paper will combine constructal theory with the entransy dissipation extremum principle and re-optimize the uniformly heated volume cooled by forced convection, to obtain the optimal construct corresponding to the minimization of entransy dissipation rate, and compare it with the construct corresponding to the minimization of maximum temperature difference
Summary
The cuboid volume has a frontal area A, length L and heat generation rate q′′′(W/m3) in a solid material of thermal conductivity ks. The heat generated is removed from the volume by the coolant in multiple channels cooled by forced convection. The coolant is a single phase fluid with constant specific heat cp and thermal conductivity kf. The heat generated inside the shaded square with side S is conducted entirely into the flow channel situated at its center. This shaded square element is based on the area A as constructed.
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