An analytical investigation of transient effects on rewetting of heated thin flat plates

The rewetting of a hot surface is a problem of prime importance in the microgravity application of heat pipe technology, where rewetting controls the time before operations can be re-established following depriming of a heat pipe. Rewetting is also important in the nuclear industry (in predicting behavior during loss-of-coolant accidents), as well as in the chemical and petrochemical industries. Recently Chan and Zhang have presented a closed-form solution for the determination of the rewetting speed of a liquid film flowing over a finite (but long) hot plate subject to uniform heating. Unfortunately, their physically unreasonable initial conditions preclude a meaningful analysis of start-up transient behavior. A new nondimensionalization and closed-form solution for an infinitely-long, uniformly-heated plate is presented. Realistic initial conditions (step change in temperature across the wetting front) and boundary conditions (no spatial temperature gradients infinitely far from the wetting front) are employed. The effects of parametric variation on the resulting simpler closed-form solution are presented and compared with the predictions of a 'quasi-steady' model. The time to reach steady-state rewetting is found to be a strong function of the initial dry-region plate temperature. For heated plates it is found that in most cases the effect of the transient response terms cannot be neglected, even for large times.