Cooling of a two-dimensional space with one or more streams making one or more passes

This is a study of a fundamental problem in electronic cooling; namely, conduction in a two-dimensional (2-D) domain cooled by one or more streams that make one or more passes. The fundamental objective is to determine the relation between the chosen cooling patterns and the temperature distribution in the domain, with particular emphasis on the maximum and minimum temperatures. The practical objective is to develop a consistent method of evaluating the cooling performance of various flow patterns, so that the trends of performance improvement are visible, and the selection of the best cooling pattern can be made with minimum additional computation. The method begins with a general analytical treatment based on the use of finite cosine Fourier transforms, and ends with an efficient numerical implementation of the analytical formulation. The results show that cooling patterns with more cold inlets maintain lower hot-spot temperatures. Furthermore, patterns where adjacent flow passes are oriented in counterflow guarantee more uniform temperature distributions than patterns with adjacent passes in parallel flow. The distribution of temperature is also illustrated experimentally for 15 cases using three different flow patterns.