The paper presents approximate solutions of the momentum-integral equations for swirling flow in a rotating cavity, which is used to model a cover-plate pre-swirl rotating-disc system in a gas-turbine engine. The solutions give the variation of Cm, the moment coefficient on the rotating discs, with βp, the pre-swirl ratio of the cooling air. Cm decreases from the free-disc value at βp = 0 to zero at βp = βp,crit, and becomes negative when βp > βp,crit. Using the Reynolds analogy, the theoretical distribution of Cm is used to calculate Nuav, the average Nusselt number on the heated disc. This shows that Nuav has a minimum value when βp = βp,crit.
The approximate solutions of Cm and Nuav are compared with computed values obtained using an axisymmetric elliptic solver. For most of the conditions considered, the theoretical values of Cm are in good agreement with the computed values. However, unlike the approximate solutions, the computed values of Cm show some dependency on the coolant flow rate. There is reasonable agreement between the theoretical and computed distribution of Nuav provided βp < βp,crit. Near βp,crit there are discontinuities in the computed values, and for larger values of βp, where the Reynolds analogy may be invalid, the theoretical and computed variations of Nuav tend to diverge.