Cooling of stacks of plates shielded by porous screens

This paper addresses the question of how to cool a stack of parallel, heat-generating boards when the flow is impeded by electromagnetic screens placed upstream and downstream of the stack. Four separate designs are considered: (1) forced convection cooling of a stack with board-to-board spacing selected to minimize the stack-coolant thermal resistance; (2) forced convection cooling of stack with fixed board-to-board spacing; (3) natural convection cooling of a vertical stack with spacing selected to minimize the overall thermal resistance; and (4) natural convection cooling of a vertical stack with fixed spacing. The optimal spacings in designs (1) and (3) are determined by intersecting the known asymptotic solutions for stacks with small spacings and stacks with large spacings. The results of parts (1) and (2) are extended to applications where the stack is cooled by immersion in a free stream. We show that the effect of the screen is controlled by a single dimensionless group, which is identified for each class of designs; namely, forced versus natural convection, and high- versus low-screen Reynolds number. Engineering results are reported for the design of screens made of wire meshes, or perforated plate with square (sharp) edges.