Computation of forced convection in slow flow through ducts and packed beds—II velocity profile in a simple cubic array of spheres

Abstract The velocity profile is calculated for slow three-dimensional flow through a simple cubic array of spheres. The velocity is represented by stream-function expansions which directly satisfy the equation of continuity and the no-slip conditions. The problem is solved by a variational principle which gives a lower bound on the total flow rate. The computed bound is within 0·2 per cent of the experimental results of Martin et al .[6].