Optimization of heat‐transfer rate into time‐periodic two‐dimensional Stokes flows

The periodic boundary displacement protocol leading to the optimum wall‐to‐fluid heat‐transfer rate, or to the most efficient mixing rate, in 2‐D annular Stokes flows is determined by calculating the steady periodic velocity and temperature fields. To obtain the steady periodic state one usually solves the dynamical system obtained after the spatial coordinates have been discretized. Here, we calculate the steady periodic state using an implicit method based on the discretization of the time coordinate over a period and the asymptotic regime is enforced by the periodicity condition in the computed temperature field. The obtained system of equations is solved using a Newton‐type iterative algorithm with invariant Jacobian. At each iteration step, the sparse linearized system is solved using a multi‐grid algebraic technique of rapid convergence. From a computational point of view and for the problem considered here, this method is an order of magnitude faster than the one based on a spatial discretization. Copyright © 2006 John Wiley & Sons, Ltd.