Optimal Geometric Arrangement of Staggered Vertical Plates in Natural Convection

Abstract

This paper documents the geometric optimization of an assembly of staggered vertical plates that are installed in a fixed volume. The heat transfer is by laminar natural convection. The objective is to maximize the overall thermal conductance between the assembly of plates and the surrounding fluid. The geometric parameters that vary are the horizontal spacing between adjacent columns of plates, the number of plates mounted in each vertical column, the plate dimensions, and the stagger between columns. The optimization is performed numerically and experimentally in the range Pr = 0.72 and 103 ≤ RaL ≤ 106, where RaL is the Rayleigh number based on the vertical dimension of the assembly (L). The results for the optimal horizontal spacing are correlated using formulas derived from the theory of the intersection of asymptotes (Bejan, 1984, 1995).