Numerical studies on heat transfer in Taylor-Couette-Poiseuille flow in a cylindrical annulus with ribs mounted on the rotating inner cylinder are presented. The present study focuses on two different types of ribs, namely, longitudinal ribs and helical ribs. Three-dimensional, steady, incompressible, turbulent fluid flow is solved using a semi-implicit method for pressure linked equations (SIMPLE) algorithm based finite volume method. The numerical solution method is validated using two sets of benchmark experimental data. Extensive numerical computations are carried out at various Reynolds numbers (2100 < Re < 2400) and modified Taylor numbers (30,000 < Tam < 90,000) for annulus with and without ribs. Ribs enhance the transport of heat and momentum by inducing more vorticity and turbulence in the flow. The overall performance is presented in terms of thermal performance factor (TPF), which takes in to account the heat transfer as well as pressure drop in the ribbed annulus. Helical ribs are found to offer superior thermal performance than its longitudinal counterpart.