Nucleate boiling is recognized as an ideal and effective technique applied in almost all of the engineering disciplines due to its high heat transfer rate associated with nucleate boiling incipience. In earlier decades, these applications included design of efficient heat exchanger, and the cooling of high power, high-density systems such as nuclear reactors. More recently, this interest derives from heat dissipation problems created by the microelectronics industry's success in greatly increasing circuit integration density and certain space technology problems such as thermal management and design requirement of efficient, compact devices.

Nevertheless, the problem's inherent complexity has limited the theoretical understanding of the mechanism of nucleate boiling heat transfer enhancement, and its use to predict the rate of heat transfer from a solid interface to a liquid. Current proposed mechanisms are mainly divided into 4 categories: The bubble agitation model, the liquid-vapor exchange model, the bulk convection model and the micro-layer model. Many numerical simulations have been based on these models. However, none of these models recognizes the importance of the three-phase contact line at the edge of the vapor-bubble on the solid heating surface. Sadhal was perhaps the first to treat contact line explicitly for an ideal, semi-infinite geometry and found an exact solution of the quasi-static heat conduction for a bubble suspended or attached to a solid surface with semi-infinite, 3-dimensional liquid and solid phases. His results suggest that the appearance of the contact line upon nucleate boiling causes a huge heat enhancement even though the case of both solid and the liquid being semi-infinite is of limited physical interest. We believe the appearance of the contact line is the heart of the issue. We therefore employ an axisymmetric boundary integral equation method to simulate bubble growth due to heat conduction and liquid evaporation given the existence of a contact line. We use various models for the motion of the contact line as the bubble grows and simulate up to the point where the bubble would begin to deform due to gravity. We hope to advance the understanding of mechanism of nucleate boiling heat transfer enhancement.

We model the transport process by the quasi-steady heat conduction equation for the growth of a single bubble at the interface of solid and liquid media each of finite extent. We define an axisymmetric, cylindrical region with the bubble at its center and implement an axisymmetric boundary integral equation method to numerically solve the quasistatic problem simulation. This formulation assumes small Reynolds, thermal Peclet, Capillary and Bond numbers. We also apply zero heat flux boundary conditions at the radius of the cylindrical cell in order to mimic the effect of bubble-bubble interactions. We calculate the heat flux as a function of wall superheat and a function of bubble density and compare these correlations to well-known, but poorly understood plots that have long been in the literature. Our simulations suggest temperature profile on the solid-liquid interface is highly non-uniform and time-dependent. This is not the same as most numerical simulation works but is in agreement with the experiment. We also show the singularity of Laplace's equation at the contact line acts to effectively enhance the heat transfer relative to the bubble-free condeiton and the bubble plays as a major heat sink that monopolizes a considerable amount of the heat in its vicinity.

As noted, we couple the solution of the quasi-static problem with three simple, somewhat ad hoc contact line motion models to simulate the growth of an incipient bubble due to conduction until at least one of our assumptions is no longer valid. These models are (1) the contact line is pinned; (2) the contact line maintains its equilibrium contact angle and (3) a kinematic contact line motion that locally evaporates liquid to advance the contact line by virtue of the heat conducted to the contact line region in the current time step. The effects of different parameters such as conductivity ratio of the liquid and solid, wall superheat and bubble density on bubble growth are examined to reveal the fundamental mechanism We found that, after an initial, short parameter- and model-dependent growth phase, the radius of the bubble as a function of time approaches an apparently universal time to the 1/2 power, which is in agreement with laser-doppler experimental data. We have a simple theory that can explain this growth behavior.