Hollow fiber membrane (HFM) modules have recently drawn considerable attention in membrane distillation (MD) because of their high packing density compared to other type of modules. In this work, a mathematical model is developed to study the impact of design and process parameters on both permeate flux and energy efficiency of hollow fiber membrane modules. The membrane module is integrated with a heat exchanger to utilize the heat of waste brine. Also, a solar collector is integrated in the system to increase the temperature of feed stream before entering the module. The simulation data were in good agreement with the experimental results. We found that the close-packed configuration provides the maximum permeate flux and energy efficiency for the module when the inter-spacing parameter, the ratio of the fiber radius to the center-to-center distance between neighboring fibers, is properly adjusted. The simulation results suggested that the permeate flux for this system can be enhanced as high as 18% by choosing the close-packed configuration and adjusting the inter-spacing parameter such that neighboring fibers are not in contact with each other.