Role of viscous heating in entransy analyses of convective heat transfer

The entransy theory is widely used and found to be effective in thermal analyses and optimizations. Some researchers considered the entransy variation due to viscous heating as part of entransy dissipation and analyzed convective heat transfer based on the differential relationship between entropy and entransy. However, it has been pointed out that the derivation of the differential relationship between entropy and entransy is incorrect. In this paper, the convective heat transfer processes with viscous heating is reconsidered and analyzed from the viewpoint of the energy conservation and the entransy balance equation. It is shown that the influence of the viscous heating is equivalent to that of an inner heat source. Therefore, the contribution of viscous heating to system entransy should not be treated as part of entransy dissipation, but entransy flow into the system. Two-stream parallel and counter flow heat exchangers with viscous heating and a thermal insulation transportation problem of heavy oil are taken as examples to verify the theoretical analyses intuitively. In the examples, the numerical results show that the entransy dissipation rates could be negative when the influence of the viscous heating on the system entransy is treated as part of the entransy dissipation. This is obviously unreasonable. Meanwhile, when the entransy contribution from the viscous heating to the system entransy is treated as entransy flow into the system, it is shown that the entransy dissipation rate is always positive, and the heat transfer processes can be well explained with the entransy theory.