Estimation of heat-transfer characteristics on the hot surface of glass pane with down-flowing water film

A hybrid inverse scheme of the Laplace transform and finite-difference methods in conjunction with a sequential-in-time procedure, least-squares method and experimental temperature data is applied to solve a 2D transient inverse heat conduction problem in order to estimate the unknown transient total heat flux and overall heat-transfer coefficient on the hot surface of the glass pane with the down-flowing water film exposed to a fire environment. It can be difficult to estimate this overall heat-transfer coefficient because it mainly involves the convection and radiation heat-transfer coefficients and that due to the mass transfer. The functional form of the total heat flux is unknown a priori and is assumed to vary with time and space. Thus, a series of connected cubic polynomial function in space and a linear function in time can be introduced to approximate this unknown surface heat flux during a specific time interval before performing the inverse calculation. Later, the unknown surface heat flux, surface temperature and overall heat-transfer coefficient at a specific time can be estimated from the knowledge of experimental measured temperature data and the given heat-transfer coefficient on the cold surface of the glass pane obtained from the correlation between the local Nusselt number and Rayleigh number. The results show that the effect of the down-flowing water film flow rate on the present estimates cannot be negligible. The overall heat-transfer coefficient on the downstream region of the glass pane can be markedly higher than that on the upstream region.