An inverse design problem for a three-dimensional U-type compact parallel flow heat exchanger is considered in the present study to determine the optimum design for yielding the uniform tube flow rates by utilizing the Levenberg-Marquardt Method (LMM) and a general purpose commercial code CFD-ACE+. The result reveals that the estimated optimal module of U-type heat exchanger can indeed yield better system uniformity flow rate when comparing with the original design of the heat exchanger. This optimal U-type heat exchanger was designed under the condition that the system flow rate equal to 2 L/min, however, the simulation results also indicated that when the system flow rate varies from 1 L/min to 4 L/min, the heat exchanger can still maintain a good performance in terms of system uniformity flow rate. Finally, when we compare the performance of the optimal U-type heat exchanger with those for four existing type of modified headers, it is found that the optimal module of heat exchanger has the best system uniformity flow rate among those five modules. (c) 2013 Elsevier Ltd. All rights reserved.