Energy equation of swirling flow in a cylindrical container

The energy equation which includes the substantial derivative of pressure and the viscous dissipation terms was solved numerically to verify whether it can correctly calculate the energy conversion from kinetic to thermal energy in an irreversible process. The fluid temperature was obtained for a swirling flow in a cylindrical container with a constant initial angular velocity. The fluid in the container came to a halt after a short time because of the viscosity. The kinetic energy of the fluid was converted into thermal energy which resulted in an increase of the fluid temperature. The governing equations were discretized using the control volume based power-law scheme of Patankar and the discretized equations were solved by using a line-by-line method. The results showed that the kinetic energy at its initial state was converted into thermal energy with a conversion rate of 99.4%.