Reliability-based optimization and design limits of microchannel cooling systems

Abstract Uncertainties are often significant in the operating and design of thermal systems. Any minor variations in the design variables or operating conditions may lead to system failure. In this paper, a microchannel cooling system for a 1 cm x 1 cm electronic chip is studied and optimized under design uncertainties. Numerical simulations are carried out to study the conjugate heat transfer and flow behavior. Three significant design variables or operating conditions are considered: (1) flow rate, (2) channel width or the number of channels, (3) heat flux. The Polynomial Response Surface (PRS) results concerning the design variables are obtained. The objective is to reduce both the pumping power and the thermal resistance under hot-spot temperature and pressure constraints. The standard deviation for the design variables, which are assumed to be normal distributions, are taken as 5% of the mean values. The acceptable probability of failure is chosen as 0.13%, which is the usually accepted level in reliability studies. With varying weights on the two conflicting objectives, the Pareto frontiers are determined and compared with the deterministic cases. The differences further demonstrate the importance of uncertainty in the design variables. This study provides more reliable and realistic design solutions for microchannel cooling systems than if the uncertainties are neglected. This basic approach may be evaluated to the design and formulation of other thermal problems and processes.