Innovative Approaches to Heat and Mass Transfer: a New Semi-mechanistic Wall Boiling Heat Transfer Model

Heat and mass transfer are at the heart of so many things we take for granted in engineering. Think about it: cooling a laptop, designing a battery or even keeping energy systems efficient all depend on these processes working smoothly. While we’ve come a long way in understanding them, however, there are still challenges that researchers and engineers struggle with, especially when things get complicated. Systems with unique shapes, rapid temperature changes, or extreme conditions don’t behave in ways that are easy to predict, and that’s where the difficulty lies. A lot of traditional research relies on making things simpler than they are, and assume that real-world systems behave like perfect versions of themselves. But they don’t. Heat doesn’t flow evenly; fluids don’t always move as expected. Add in complications like phase changes—say, when water turns into steam—and things get even trickier. When engineers try to design high-tech equipment, even small errors in understanding these processes can mean reduced efficiency, wasted energy, or even system failures. Then there’s the challenge of keeping up with modern technology. High-performance electronics, for instance, generate so much heat that managing it has become a major engineering hurdle. If processors overheat, they fail—it’s as simple as that. And it’s not just electronics. Large energy systems such as nuclear power plants and traditional thermal power plants also require precise thermal control to operate at optimal efficiency and ensure safety. As devices expectations for efficiency grow, finding new ways to manage heat and mass transfer becomes even more essential.

Flow boiling heat transfer is a highly efficient thermal management technique utilized in various industrial applications, such as nuclear reactors, refrigeration, and air-conditioning systems. Its high efficiency is attributed to latent heat during phase change and bubble-induced turbulence. In the Computational Fluid Dynamics (CFD) fields, accurate prediction of flow boiling heat transfer relies heavily on robust wall boiling heat transfer models. Existing wall boiling heat transfer models employed in CFD simulations mainly originate from the widely adopted RPI model, which divided total wall heat flux into three components, including liquid convection heat flux, evaporation heat flux, and quenching heat flux. However, the RPI model, as well as its improved versions, requires a large number of microscopic bubble dynamics parameters, such as the nucleation site density, bubble departure frequency, bubble sliding diameter, and so on. Most of these parameters are calculated by using the empirical correlations, which are obtained through visual low-pressure experimental measurements. The empirical correlations themselves have large uncertainties under high-pressure conditions. In addition, the RPI model introduces different underlying bubble dynamics models, resulting in poor convergence of the model under some working conditions. Thus, although the wall boiling heat transfer model in CFD methodology has been discussed by many researchers with different forms, there exists a pressing need for its further development, aiming to characterize the flow boiling mechanism by several heat flux terms while ensuring the independence of each partitioning from the bulk flow parameters.

Seeing the gaps in what’s understood and what’s needed, researchers Dr. Xiang Zhang, Professor Xu Cheng from the Karlsruhe Institute of Technology (KIT), and Professor Wei Liu from Kyushu University decided to take a deeper dive into the problem. They wanted to look beyond the traditional wall boiling heat transfer models and developed a new robust semi-mechanistic wall boiling heat transfer model. In their idea, the model should be designed to yield a straightforward expression for heat flux partitioning and underpinned by mechanism foundation. Their work, published in the International Journal of Heat and Mass Transfer, combines bubble growth mechanism analysis, theoretical derivation and experimental validations to propose a new wall boiling heat transfer model. The new model uses local flow field parameters and physical property parameters at the grid level, which is easy to be implemented in three-dimensional CFD simulations, solves the problem of the traditional wall boiling model’s dependence on bubble dynamics parameters, and enhances the stability of numerical calculations of flow boiling under different working conditions. Their findings aren’t just academic but also practical and can offer solutions for engineers designing the advanced devices and systems.

To derive the new model, they started by making some basic assumptions: (1) The heat transferred from the wall to the microlayer underneath the bubble in subcooled flow boiling is equivalent to the corresponding part of heat observed in saturated pool boiling. (2) In saturated pool boiling, all the heat transferred from the wall to the liquid thermal boundary layer is assumed to be totally transferred to the bubble. (3) The process of bubble growth is assumed to be thermal-controlled. (4) The temperature distribution within the liquid thermal boundary layer is assumed to follow a linear function. (5) The morphology of the growing vapor bubbles on the heated wall are assumed to be hemispherical.

Their new semi-mechanistic wall boiling heat transfer model divides the total wall heat flux (q_w) into two components: the liquid convection heat flux (q_fc) that can be obtained by wall function approach in CFD, and the nucleate boiling heat flux (q_nb) that can be derived using the famous Forster-Zuber model. By analyzing the mechanism of bubble growth, two correction factors are deduced to modified these heat flux. The one is the correction factor (F1) for convection term considering the effects of bubble influenced area and bubble induced convection enhancement. The other one is the correction factor for boiling term to excluded the liquid convective part already included in the Forster-Zuber model. Their new wall boiling heat transfer model is expressed as:

The results obtained through various validation tests underscores the new model’s accuracy and potential for widespread use in industrial and research settings. The new model offers a new approach to treat the wall boiling heat transfer and to be easily adopted in CFD simulations. A new model might sound small, but the impact is big: more robust simulations within different conditions and simpler composition with clear physical meaning provide a powerful tool for the advanced industrial heat exchanger designs, which can save a lot of time and economic costs.