The present study is aimed at shape design of a millimeter-scale air channel for increasing heat transfer to the air from the heated channel wall and reducing pressure drop between the inlet and the outlet. The approach is developed by combining a direct problem solver with an optimization method. A two-dimensional theoretical model is used to develop a direct problem solver, which provides the numerical predictions of the thermal and flow fields associated with the varying shape profile during the iterative optimization process. Meanwhile, the simplified conjugate-gradient method (SCGM) is used as the optimization method which Continuously updates the shape until the objective function is minimized. In this paper, a method based oil a point-by-point technique for constructing the shape profile is employed. This method is particularly suitable for determining the irregular profiles that cannot be approximated by the polynomial functions. The optimal shapes at different inlet velocities are obtained. It is found that the search process is robust and always leads to the same optimal solution regardless of the initial guess. (C) 2007 Elsevier Ltd. All rights reserved.