Entropy generation in transpiration cooling of concentric spherical shells

The present paper deals with transpiration cooling of two concentric spherical shells. The analysis includes the calculation for the radial distribution of temperature and volumetric entropy generation, and the total rate of entropy generation in the thermal system. Standard air is considered as the cooling fluid. Results showed that the entropy generation increases with increasing temperature difference between the sphere surfaces. Variation of either mass flow rate or radius ratio affects volumetric entropy distribution and the total rate of entropy generation of the processes. The increase of mass flow rate or radius ratio increases the total rate of entropy generation. The performance of the system is analyzed by calculating irreversibility to heat transfer ratio at both inner and outer sphere surfaces. It was found that irreversibility to heat transfer ratio at the inner sphere surface increases with increasing mass flow rate, or decreasing radius ratio. The opposite is true for the outer sphere surface.