# Prediction of Boiling Heat Transfer Coefficient for Micro-Fin Using Mini-Channel
## 1 Introduction
### Flow Boiling in Micro-Fins and Mini-Channels  
Micro-fins have higher heat transfer coefficients than smooth tubes of the same inner diameter, primarily due to the higher surface area provided by the fins. The micro-fin features involve fine grooves inside the tube, with design parameters including the number of fins, fin depth, and fin angle. Previous studies have reported that the surface tension effect results in thinner liquid films within the grooves and around the fins and that liquid is supplied along the grooves up to the tube's top, contributing to enhanced heat transfer. In low mass flow regions, even when there is a flow where the gas and liquid phases are separated vertically, a liquid film still exists between the fins at the top of the tube. The presence of this liquid film enhances the heat transfer because surface tension causes a meniscus liquid film to form on the sides of the fins. However, an annular flow develops at high mass flow rates, forming a uniformly distributed liquid film around the tube circumference. As a result, the heat transfer enhancement is known to be smaller than in low mass flow regions [2; 3; 4]. Previous research suggests that the state of the liquid around the fins significantly affects heat transfer coefficients, especially in terms of the relationship between surface tension and inertial forces. In this study, we considered leveraging data from mini-channels, previously predicted with high accuracy [1], to predict the boiling heat transfer coefficient of micro-fins. The mechanism proposed for improving heat transfer coefficients in both mini-channels and micro-fins involves boiling facilitated by thin liquid films, as illustrated in Figure 1. In mini-channels, slug flow predominates in regions with low flow rates and low qualities. In these regions, the effect of surface tension becomes significant, and the thinning of the liquid film surrounding the gas plug increases the heat transfer coefficient via evaporative heat transfer due to liquid film conduction (liquid film conduction evaporation) [5; 6; 7; 8]. Similarly, in the case of micro-fins, the state of the liquid film around the fins is crucial for evaluating heat transfer characteristics. Therefore, the relationship between surface tension and inertial forces around the fins is important. Additionally, the complex interaction between surface tension and inertial forces complicates the prediction of post-dryout heat transfer coefficient and dryout quality. The most common and widely used approach for predicting the heat transfer coefficient of micro-fins is based on data obtained from several experiments conducted within the geometric and operational ranges of the micro-fins and the refrigerant and operating conditions. [PERSON] et al. [9] proposed a heat transfer prediction model based on experimental data obtained by other researchers using HCFC22, HCFC123, R134a, and CFC12. They introduced the Bond number to account for the effect of surface tension, but the number of fins and fin depth was limited. Additionally, the Cavallini model has been modified by many researchers to include additional refrigerants and operating conditions. [PERSON] et al. [10] conducted R1234 ze(E) experiments and modified the predictive model to a wider range of refrigerants. Further, [PERSON] et al. [11] collected 2221 data points from previous studies and proposed a new predictive model capable of accommodating new refrigerants by modifying the Cavallini model. The data encompassed seven refrigerants: R22, R410A, R407C, R134a, R1234 yf, R1234 ze(E), and CO\({}_{2}\). Although the predictive model accurately predicts the heat transfer coefficient, it defines the point of sharp decrease in heat transfer coefficient as the onset of post-dryout and excludes data points beyond this point from the prediction target.