OPTIMAL SPACING OF PARALLEL BOARDS WITH DISCRETE HEAT SOURCES COOLED BY LAMINAR FORCED CONVECTION

Abstract

This paper shows numerically how to select the optimal spacing between boards mounted in a stack of specified volume, so that the overall thermal conductance between the stack and the forced coolant is maximum. Several configurations are considered: boards with uniform flux, flush-mounted discrete sources, and protruding heat sources. The flow is laminar and the pressure difference across the stack is fixed (Δp). It is shown that for all the board geometries and thermal boundary conditions studied, the optimal board-to-board spacing is correlated by (D_opt/l ∼ 2.7(Δpl² / μα)^−¼where l is the effective longitudinal (flow) distance occupied by the discrete sources and the unhealed patches contained between them, and μ and α are the viscosity and thermal diffusivity of the fluid. If U_∞is the free-stream velocity upstream of the stack, the optimal spacing is given by (D_opt/l) ∼ 3.2pr^−¼(U_∞l / v)^−½.