Forced convection from a microstructure on a flat plate

In this work, a cooling of a flat microelectronic structure with single-phase forced convection is investigated. The axial conduction, usually neglected in boundary layer theory, is considered here since the length of the heated element is in the same order of magnitude as the thickness of the boundary layer. The microstructure represents a package of chips mounted flush with the surface of the plate, and uniformly heated with a constant heat flux. The differential method is used to reduce the governing partial differential equations to ordinary differential ones, which are solved numerically by the use of a computational code developed by the authors. This code is based on Keller-Box method. The temperature profiles and Nusselt numbers are plotted at several locations on the heated element and are given as functions of the Reynolds number at the beginning of heated microstructure and of the ratio of unheated to heated length. Furthermore, the average Nusselt numbers on the heated length are computed for Prandtl numbers in the range 0.7 <= Pr <= 7,000. The results are compared to the boundary layer solution of unheated starting length problem. The results will be used as a baseline for successively more complex situations of cooling in electronics.