Numerical prediction of periodically fully developed natural convection in a vertical channel with surface mounted heat generating blocks
Natural convection is often employed due to its simplicity and reliability in the cooling of electronic equipment operating at low heat fluxes. In closely packed arrays of circuit boards containing evenly spaced heated components, the buoyancy-induced flow becomes periodically fully developed rather quickly. The dependence of the characteristics of the fully developed natural convection flow on the type of imposed thermal boundary conditions is discussed. The mathematical formulation for periodically fully developed natural convection with thermally active throughflow is presented in the context of the flow through an insulated channel with heated blocks mounted on one of the walls. This represents a generalization of the theory of fully developed natural convection between parallel plates subjected to uniform heat flux that is available in the literature. The decomposition of the temperature field into a periodic part and a linearly varying part has implications in the discretization of the temperature field and is elaborated. The solution procedure for the discretization equations that addresses the constraint imposed on the periodic part of the temperature field is then described. Computations are carried out for the periodically fully developed natural convection in the channel geometry considered. The values of the channel length and module heating are varied to illustrate the utility of the proposed formulation and the solution procedure in analyzing a class of periodically fully developed natural convection flows encountered in electronics cooling applications.
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