The duplex Stirling refrigerator is an integrated refrigerator consists of Stirling cycle engine and Stirling cycle refrigerator used for cooling. The equality of the work generation of the heat engine to the work consumption of the refrigerator is the primary constraint of the duplex Stirling. The duplex Stirling refrigerator is investigated thermodynamically by considering the effects of constructional and operational parameters which are namely the temperature ratios for heat engine and refrigerator, and the compression ratios for both sides. The primary concern is given to the parametric effects on the overall coefficient of performance of the duplex Stirling refrigerator. The given diagrams provide a design bounds and benchmark results that allows seeing the big picture about the cooling load and heat input relation. Moreover they ease to determine the corresponding work rate to the target cooling load. As regard to the obtained results, a definite region for coefficient of performance of the refrigerator and a definite region for the thermal efficiency of the heat engine of the duplex Stirling are identified. (C) 2016 Elsevier Ltd. All rights reserved.