Vertical ground heat exchangers are one of the most important parts of geothermal utilization systems. In order to understand the effect of simultaneous variation of design parameters; a three dimensional computational fluid dynamics simulation was carried out. Based on the effective parameters on the heat exchanger efficiency and the total heat transfer efficiency in cooling mode, and with the aid of the second-order Response Surface Model, two functions for the total heat transfer efficiency and the heat exchanger efficiency were derived. The effects of different design parameters on the response variables were examined. Based on the Response Surface Model, it was found that the dimensionless inlet fluid temperature and the dimensionless pipe diameter significantly affect the response variables, while the response variables are weakly affected by dimensionless depth. Finally, an optimization was performed and the optimum heat exchanger is defined using the model equations. (C) 2011 Elsevier B.V. All rights reserved.