A compact fin-tube heat exchanger is used to transfer current fluid heat inside the tubes into the air outside. In this study, entropy production and optimized Reynolds number for finned-tube heat exchangers based on the minimum entropy production have been investigated. As a result, the total entropy of compact heat exchangers, which is the summation of the production rate of fluid entropy inside the tube, and the entropy production rate of fluid in the air, is minimum due to the changes in the Reynolds number of the fluid inside the tubes. Based on thermodynamic analysis and study of parameters affecting the entropy production, one expression is proposed for the optimal Reynolds number. The expression is a function of the thermodynamic properties of the fluid in the pipe, fluid thermodynamic properties of air, the effects of ambient temperature, input temperature of the cooling fluid, and geometrical dimensions of the heat exchanger. According to this optimization, effective information for the design of a compact finned-tube heat exchanger would be obtained. Therefore, in practical conditions, using optimal Reynolds number, the system has the lowest irreversibility, and as a result, the best exergy will be accessible. Finally, an empirical correlation is proposed for the optimum Re number that can predict Re_opt with less than 0.6 % error.