Constructal design and experimental validation of a non- uniform heat generating body with rectangular cross-section and parallel circular cooling channels

Abstract Non-uniform heat generating phenomenon is omnipresent in real electronic devices. A three-dimensional model with non-uniform heat generation is established in this paper. Both fluid flow and heat transfer behaviors are uncovered with the consideration of constructal theory. Constructal theory enables a heat transfer system to evolve and generate to provide a better flow access for the currents that flow through it. Taking a complex function composed of hot spot temperature and pumping power as the performance indicator, the diameter of cooling channels and the aspect ratio of elemental body are optimized as two degrees-of-freedom. The physical problem is numerically solved by resorting to the finite element method. The optimization was performed by the exhaustive search technique, comparing all results generated by finite element method. The heat generation over the entire body and the volume ratio of cooling channels operate as the prior constraints. On this basis, the optimal geometries of the elemental component are obtained in cases of various heat generating premises. The obtained results demonstrate that the complex function behaves an extreme value for the dimensionless cooling channel diameter. It is observed that the minimum value of the complex function slumps by 29.3% as the number of elements increases from 10 to 30. The overall thermo-fluid performance of the non-uniform heat generating body can be elevated as the elemental body features a square cross-section by releasing the new degree-of-freedom of aspect ratio to morph. Furthermore, alumina ceramics are used as the heat generating substrate and water as the coolant. The validity of the mathematical model is corroborated by experiments. Oriented to industrial applications, it is implied that the coolant entryway should be placed prone to the place where more electronic components or heat generating devices situate. The optimization results can put new suggestions on the thermal design of actual electronic devices from both theoretical and experimental perspectives.

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