Constructal structures with and without high-conductivity inserts for self-cooling

Abstract

Here we show how a heat generating domain can be gained self-cooling capability with embedded cooling channels and with and without high-conductivity fins. The volume of the heat generating domain is fixed, so is the overall volume of the cooling channels and high-conductivity inserts. Even though the coolant volume decreases with embedded high-conductivity fins, the peak temperature also decreases with high-conductivity inserts. The peak temperature is affected by the location, shape and complexity of the fins and the volume fraction. This paper documents how these degrees of freedoms should be changed in order to minimize peak temperature. This paper also discusses how the volume fraction affects each fin shape in order to minimize the peak temperature. This paper uncovers that the fins should be distributed non-equidistantly, and that high-conductivity material should be inserted as fins (bulks of high-conductivity materials) rather than uniform distribution in the domain. This paper concludes that the overall thermal conductance of a heat generating domain can be maximized by freely morphing the shape of the high-conductivity material. The optimal design exists for given conditions and assumptions, and this design should be morphed when conditions and assumptions change. This conclusion is in accord with the constructal law. Each optimal design for given conditions and assumptions is the constructal design.

Constructal Design of an Arrow-Shaped High Thermal Conductivity Channel in a Square Heat Generation Body

“…Bejan [ 1 ] stated the constructal law after further studying the formation of urban street networks, and applied it to the optimization of the heat dissipation structure of an electronic device (ED) [ 2 ]. Since the introduction of the constructal theory [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ], it has been applied to design various heat dissipation bodies, such as rectangular [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 ], triangular [ 32 , 33 , 34 , 35 , 36 , 37 ], square [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 ] and discal [ 48 , 49 , 50 , 51 , 52 , 53 ,…”

“…Therefore, based on Refs. [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 ], an HCM with an arrow-shaped HTCC (ASHTCC) in an SHGB will be established in this paper. Aiming at the objective of DMTD, the construct of the ASHTCC in the SHGB will be optimized by using constructal theory.…”