Constructal design of a cooling channel with semi-circular sidewall ribs in a rectangular heat generation body

A cooling channel model with semi-circular sidewall ribs in a rectangular heat generation body (HGB) is considered in this paper. With fixed volumes of the cooling channel and ribs, constructal design of the cooling channel is implemented with the objective of weighted sum function composed of the heat transfer and flow performances. Multi-objective optimization is further conducted by considering the two performance indexes. The results reveal that the quadratic minimum weighted sum function of the rectangular HGB can be gained by choosing the optimal width-to-height ratio of the cooling channel and the optimal radius of the sidewall ribs. The weighted sum function is augmented by 8.5% after constructal optimization. The comprehensive heat dissipation performance of the rectangular HGB is elevated by employing the suitable number of the sidewall ribs and mass flow rate of the coolant. The smallest deviation index is 0.267, which is gained by the LINMAP decision method, and the corresponding optimal construct can be selected as the design scheme of the cooling channel in a rectangular HGB. Multi-objective optimization provides a Pareto optimal solution set for the comprehensive performance of the rectangular HGB, which provides the heat dissipation designers of various electronic devices with new guidelines.