Mathematical Modeling of Closed-End Pulsating Heat Pipes Operating with a Bottom Heat Mode

Abstract

The mathematical model of a closed-end pulsating heat pipe (CEPHP) with a bottom heat mode at different inclination angles was constructed. The closed-end pulsating heat pipe was modeled with specified assumptions that were observed visually (i.e., the scaling factor for geometrical size and the frequency of bubble generation inside the liquid slugs). The solution for all of the basic governing equations of liquid film, liquid slugs, and vapor plugs, in which the effects of surface tension, viscous friction of the working fluid, and perfect gas were included, has been numerically obtained by solving a series of ordinary differential equations by means of the explicit method. However, the solution for the momentum equation of liquid slugs was numerically obtained by solving a series of partial differential equations by using the implicit method. Results from the model clearly simulated the dynamics of the internal working fluid in the CEPHP. Moreover, the results were compared with existing experimental data, and good agreement was found with an error range of ± 13%. It was also noted that the maximum heat transfer rate of the CEPHP with bottom heat mode occurred at the highest evaporator temperature (150°C for this study) and inclination angles of 70–80 degrees from horizontal axis. The boiling frequencies in this range of inclination angles were observed by visual experiment and seen to be at their highest values. This has been justified by the higher amount of liquid in the evaporator section as well as the change in flow pattern to a stratified flow (inclination tube).