An inverse design problem to determine the optimum variables for a three-dimensional Z-type compact parallel flow heat exchanger is considered in this study using the Levenberg-Marquardt Method (LMM) and a general purpose commercial code CFD-ACE+ to obtain the uniform tube flow rates. Five different optimization design problems are examined to demonstrate the validity of the study. The results obtained from the LMM are justified based on numerical experiments. It is concluded that the estimated optimal tube diameters and entrance length of the header can indeed effectively eliminate the eddy flow in the first tube due to the circulation of the vortex flow near the header inlet. As a result, the non-uniformity observed in the flow rate of the system can be minimized and the tube flow rate in the heat exchanger is nearly uniform. Additionally, the results reveal that if constraints are placed on both the desired system non-uniformity and the inlet gage pressure, different initial guesses of the design variables will yield almost the same design for the heat exchanger. The sensitivity analysis technique is then used to reduce the number of design variables and to shorten the computational time. The results indicate that an acceptable design with nearly uniform tube flow rates for Z-type compact parallel flow heat exchangers can be obtained using sensitivity analysis, saving 41% of computational time. (C) 2012 Elsevier Ltd. All rights reserved.