Analysis of the liquid film formed beneath a vapour bubble growing at a heated wall without neglect of evaporative thermal resistance

The ability to predict various aspects of boiling is important for both safety and design of water-cooled reactors. Component-scale modelling is necessarily done by semi-mechanistic, semi-empirical approaches, generally based on heat flux partitioning. This needs to be informed by multiple detailed experimental observations of boiling behavior. Such measurements are difficult to make, and much effort is being applied to microscopic computational modelling of the detailed boiling process. Aims of such activities include the mechanistic prediction of growth and detachment of one bubble during nucleate boiling, and the quantification of the associated heat transfer partitioning (evaporation, microconvection, quenching). We here study a subset of the full problem, and focus on the thermal response of the boiling substrate to the early growth of a single vapour bubble during pool boiling of water at atmospheric pressure. In such conditions, a thin liquid film ("microlayer") is left behind beneath the bubble as this expands. The microlayer evaporates due to the temperature difference between the solid-liquid and vapour-liquid interface. Its thickness being small, of order of microns, the local evaporation rate per unit area of bubble base can be high, up to one kilogram per second. Microlayer evaporation can therefore be important in early stages of bubble growth. In this contribution, thermal response of the boiling substrate to microlayer evaporation is studied with a twodimensional, axisymmetric transient conduction model, coupled with an algebraic sub-model of the liquid film. The flow of heat through the microlayer is modelled as conduction in the liquid and with a pseudo-convective "evaporative" heat transfer coefficient at the liquid-vapor interface, accounting for the interface superheat driving the evaporation process. Thermal coupling (conjugate heat transfer) between microlayer and solid substrate is obtained with a time dependent non-homogeneous Neumann boundary condition, derived from the algebraic microlayer submodel and applied at the top surface of the solid computational domain. The thermal resistance associated to the evaporative heat transfer mechanism is shown to depend on a highly uncertain parameter, termed an "evaporation coefficient". After some exploratory calculations of the likely importance of the evaporative resistance in the present context, the model is employed to interpret some recent microlayer measurements. Satisfactory agreement between computed and measured evolution of the microlayer profile is obtained if small values (between 0.01 and 0.10) of the evaporation coefficient are used. The order of magnitude of the predicted evaporation rate from the microlayer is consistent with experimental observations.