The study of flow and heat transfer in a vertical annulus is important due to its applications in the cooling of reactors, industrial heat exchangers, microelectronic devices, and so forth. The aim of the present work is to estimate the operational costs due to entropy generation in an annulus with isoflux boundary conditions. For this purpose, the governing equations are simplified and solved analytically to obtain the entropy generation distribution in the annulus. Using the results obtained by the entropy generation analysis, the operational costs due to entropy generation are calculated for various radius ratios and different quantities of the flow parameters involved in the problem. The results of this study can be helpful in the design of such heat exchangers to reduce the operational costs caused by the irreversibilities.