In this study, the steady state heat transfer and fluid flow in the annulus section of tube-in tube conically coiled heat exchanger (TTCCHE) is numerically investigated. The flow in the annulus is simulated using the Realizable K-epsilon turbulence model and validated by comparison with published Nusselt numbers. The effect of geometrical and operational parameters of the heat exchanger on the exergy characteristics of the annulus section is obtained. The results allowed for obtaining two correlations for estimation of the annulus section exergy efficiency and coefficient of exergy performance. Furthermore, it was found that the highest values of the turn number and the minimum values of the Reynolds number (d(t,o)/d(c,max)), (P/d(c,max)), Prandt1 number, tube diameter ratio and the cone angle in the studied range maximize the exergy efficiency and coefficient of exergy performance. (C) 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.