Slow flow past periodic arrays of cylinders with application to heat transfer

Solutions for the slow flow past a square and a hexagonal array of cylinders are determined using a somewhat non-conventional numerical method. The calculated values of the drag on a cylinder as a function of $\text{c}$, the volume fraction of the cylinders, are shown to be in excellent agreement with the corresponding asymptotic expressions for $\text{c ? 1}$ and for $\text{c → c}{}_{\mathrm{<mtext>max</mtext>}}$, the maximum volume fraction. These solutions are then used to calculate the average temperature difference between the bulk and the cylinders which are heated uniformly under conditions of small Reynolds and Péclet numbers.