Heat and Mass Transfer Issues in Mini-Gaps

1. Introduction

The transfer of large heat fluxes is one of the most significant issues in modern technology. During the operation of devices, the generation of excessive heat can cause undesirable temperature increases in the elements of machines. High temperatures must be reduced by various means to ensure proper and long-lasting operation of the apparatus and user safety. Today, more and more sophisticated technologies are being supported to prevent exceeding the maximum operational temperature. Furthermore, the trend toward miniaturization of mechanical and electronic equipment components is still growing. The rapid improvement in microelectronic devices is accompanied by a high increase in heat generation, which would decrease their efficiency and useful lifetime.

In recent years, the range of applications for heat transfer through mini-gaps with different geometries has broadened considerably, extending to a new generation of systems. The trend toward miniaturization of the components of mechanical and electronic equipment has been the driving force behind the development of increasingly better cooling technologies that are designed to prevent maximum allowable operating temperatures from being exceeded. These are the main reasons why mini-channel heat exchangers are becoming increasingly popular, as they help to remove large heat fluxes under single-phase and two-phase flow, providing effectiveness. The changes of phase that accompany flow, especially the boiling process, allow for high heat flux at a low temperature difference between a heated wall surface and the working fluid. What is simultaneously needed for mini-channel heat exchangers occurs in a slight heat transfer area. Theoretical analyses, experimental measurements, and practical applications have been performed to help us understand heat and mass transfer phenomena in mini-gaps. The results of these studies provide us with information on the design of cooling systems that use mini-channel devices and can be applied to cooling, thermostabilization, and thermoregulation. Despite the growing number of new studies dealing with heat and mass transfer in mini-gaps, the results refer mainly to a narrow range of parameters. The results concerning heat and mass transfer during fluid flow along mini-gaps are inconsistent or even contradictory. Studies focusing on systems with an enhanced structure have attracted attention because of their potential to enhance heat transfer.

Therefore, heat transfer during flow with a change of phase in mini-channels turned out to be a necessary solution to achieve high heat fluxes with reasonably miniature geometrical dimensions and a temperature at a not very high level within the heat exchanger device. It is worth underlining that innovative methods to achieve the effectiveness of heat transfer processes in mini-heat devices are still being sought.

2. An Overview of the Articles Concerning Heat Transfer during Flow in Mini-Channels Published in Special Issues on ‘Heat and Mass Transfer Issues in Mini-Gaps’

The special issue entitled “Heat and Mass Transfer Issues in Mini-Gaps” and its continuation titled “Heat and Mass Transfer Issues in Mini-Gaps 2021–2022” cover studies carried out to better understand the heat transfer mechanisms during flow in channels of small dimensions. In general, the special issue focuses on such topics as heat transfer characteristics during convection but also realized with change of phase (boiling and condensation processes), two-phase flow, and heat transfer enhancement to help us understand heat and mass transfer phenomena in mini-gaps. The published work involved theoretical analyses and the results of experimental measurements. Guidelines for practical applications have also been developed. Nine published articles published in special issues on ‘Heat and Mass Transfer Issues in Mini-Gaps’ are briefly described in this section.

The main objective of [1] was boiling heat transfer during FC-72 flow in a mini-channel heat sink oriented vertically or horizontally. The key objective was to develop mathematical calculation methods for the identification of the boiling heat transfer coefficient based on data from my own research. The experimental setup comprised a test section with three or five mini-channels, oriented at a different angle from the horizontal plane, and selected to provide a variety of databases. During the experiments, an infrared camera was used to measure the temperature of the outer foil surface that constitutes the heated common wall of the mini-channels. The selected sets differed in experimental thermal and flow parameters, number of mini-channels, spatial position of the test section, and thickness of the heated foil. It was proposed that the mathematical model assume a steady-state heat transfer process and a laminar, incompressible flow of the fluid in an asymmetrically heated central mini-channel. Data from experiments in the subcooled boiling region was used for calculations. FEM calculations carried out simultaneously by the Trefftz functions and ADINA software were conducted to find the temperature field in the flowing fluid and in the heated wall. Numerical computations due to ADINA software included testing the effect of the mesh density on the values of the heat transfer coefficient. In the 2D approach, the heat transfer coefficient was determined using the Robin condition. The results were illustrated by graphs of the foil and fluid temperatures versus the distance from the mini-channel inlet. Local heat transfer coefficients were the main results from the FEM calculations using the Trefftz functions and the ADINA software. For comparison, the results of the calculations according to the 1D approach were presented. The temperature distributions in the heater and fluid obtained from the FEM computations performed by ADINA software were also shown. The values of the heat transfer coefficient obtained from the 2D approach did not exceed 9.9%. The resulting heat transfer coefficients from the 1D approach were usually lower than those of the 2D approach. The average relative difference between the 1D and 2D approaches reached 12.8%. Example boiling curves indicating nucleation hysteresis were shown. The course of the boiling curves was typical for refrigerants, indicating nucleation hysteresis. The authors indicated that the construction of a compact heat exchanger with a group of rectangular mini- and microchannels with enhanced surfaces can improve the heat transfer process. Such devices, which enable the effective cooling of components during operation, can be applied in several industries, such as microelectronics.

The continuation of the topic covered in [1] was article [2], in which the investigation of FC-72 boiling heat transfer was carried out in a set of mini-channels with a rectangular cross section. The set consisted of seven mini-channels with 1 mm of depth. The temperature of the common heated wall of the channels was measured with an infrared camera. Flow structures were captured by a high-speed camera. The main consideration was the application of modified surfaces to the heated wall during experiments that covered subcooled and saturated boiling regions. Seven modified surface enhancements were used during experiments, mainly electro-machining texturing, and laser surface texturing, iron powder soldering, while four of them were produced by emery papers of various paper roughnesses. The heat transfer coefficient was calculated using a simple 1D approach. The authors noticed that the highest temperature of the heated wall and the lowest heat transfer coefficient were detected for the porous heated wall surface. The heat transfer coefficients in the subcooled boiling increased with distance from the inlet and were scientifically higher for the saturated boiling region, compared to the subcooled boiling. Furthermore, the electro-machining textured surface gained the highest values of the heat transfer coefficient compared to other tested surfaces. During the analysis of the boiling curve curse, it was stated that for small mass fluxes and downward flow, the highest temperature differences at boiling initation were detected. Flow patterns were captured, while upward and downward flow were recognized. Finally, the authors underlined that using specific microstructural surfaces of well-defined roughness could help obtain heat transfer enhancement.

The authors of one study (i.e., [3]) dealt with the gas flow in the axisymmetric mini-gaps bound by the surface of the top of the labyrinth seal tooth and the surface of the body. The analysis of the results included experimental investigations and numerical calculations. The experiments focused on the gas flow at six clearance heights; the experiments were performed at a wide range of pressure drops. Based on experimental data, the mass flow in the clearance was determined. The flow coefficient as a function of the pressure ratio upstream and downstream of the seal was calculated with the Saint-Venant dependence. It was noted that the values of the flow coefficient for the clearance heights differ. The drop values of the flow coefficient as a function of the pressure for six heights of the clearance create two groups of curves. Two groups were distinguished: the first comprising clearances of 0.362 and 0.542 mm, and the second with clearances of 0.752, 1.067, 1.549, and 2.058 mm. The value of the flow coefficient was in the range of 0.6 (for the small pressure drop) to 0.85 (for the pressure ratio close to the critical one). Furthermore, a numerical analysis of the gas flow was provided with the aid of Fluent software to help interpret the coefficient results that change in the clearance geometry. The author stated that the change in the flow coefficient results from the increase of the strong recirculation zone on the top of the tooth in the end part of the clearance. In addition, a significant growth of the recirculation zone is influenced by a considerable extension of the low-pressure area in the vicinity of the front edge of the tooth. At a clearance height of 0.752 mm, the reverse flow was clearly noticeable. It was indicated that for small clearances, the recirculation zone grows slightly and limits the flow by creating the convergent-divergent nozzle; it grows considerably for large clearances. The authors indicated that seals are applied to minimize leakage. It is important to keep the flow coefficient as low as possible. The basis for determining the change in seal integrity during operation for staggered and stepped seals could be found in this work.

The results of experimental research on pool boiling on enhanced surfaces were reported in articles [4,5]. The authors of [4] presented the results of heat transfer based on the experimental data collected in the test section with open microchannels within heated surfaces. The various types of open microchannels were presented in the state-of-the-art. In the experimental section, a pool boiling measurement stand was described. In this work, the authors focused on pool boiling heat transfer of water on surfaces of rectangular microchannels with a depth of 0.2 to 0.5 mm and a width of 0.2 to 0.4 mm. The tested surface was made of copper, and as a working fluid, water was applied. Parallel microchannels are made by machining and are spaced with a pitch that is equal to twice the width of the microchannel. Experiments were carried out under atmospheric pressure. The essential aim was to investigate the effects of the geometric dimensions of the surface and the surface extension coefficient on the heat transfer coefficient and the critical heat flux. The authors noted that there was an increase in the heat flux and the heat transfer coefficient for surfaces with microchannels. The surface gave more than a four-fold increase in the heat transfer coefficient compared to the plain, smooth surface with water as the boiling liquid. In particular, 2.5–4.9 times higher values of the heat transfer coefficient were achieved for the heat flux range of 992 to 2188 kW/m² compared to the smooth surface. An improvement in maximum heat flux of more than 245% was observed. The highest values of the heat transfer coefficient and critical heat fluxes were obtained using microchannels with the smallest widths (0.2–0.3 mm). All surfaces analyzed allowed for a significant increase in the critical heat flux compared to the plain smooth surface: from 1.3 to 2.5 times. The heat transfer coefficient determined based on experimental investigations was compared with the coefficients obtained for various other structures known from the literature. Based on the visualization of a bubble formation cycle, the diameters of departing bubbles were determined. The proposed modified Zuber correlation allowed for the determination of the dependence of the departing bubble frequency on the diameter of the microchannel surfaces with an error not exceeding 20%. Static computational models were proposed to determine the bubble departure diameter. These two methods of bubble diameter calculation were proposed in relation to the two types of determining the vapor-liquid-microchannel contact line. Both calculation methods provided acceptable accuracy for high enough heat fluxes (above 100 kW/m²) to assume almost complete filling of the microchannel with vapor. A similar topic on pool boiling research on enhanced surfaces, as in [4], was reported in [5]. The author applied copper heat transfer surfaces with milled parallel grooves with a depth of 0.3 mm and a width ranging from 0.2 to 0.5 mm in increments of 0.1 mm for straight channels and channels inclined with respect to the vertical by 30 and 60, respectively. The study was carried out with Novec-649 as a working fluid at atmospheric pressure. A smooth surface and surfaces with straight and inclined microchannels were investigated. The main objective was to recognize the most favorable microchannel geometry to achieve the highest heat transfer coefficients and critical heat flux. Generally, surfaces with straight microchannels gave the best results. Furthermore, with the increasing width of the microchannel, a trend in the efficiency of heat transfer was noticed. The application of microsurfaces with a width of 0.5 mm indicated an increase of 385% in the heat transfer coefficient compared to the smooth surface. It was concluded that the highest heat transfer coefficients were obtained at the largest microchannel surface extensions, that is, the surfaces with the smallest microchannel widths, contributing to a significant number of active nucleation sites at their bottoms and lateral surfaces.

Articles [6,7] relate to the use of turbulent impinging jets as methods to enhance heat transfer in heat exchangers. The main objective of [6] was to analyze the phenomenon of jet impingement and investigate the influence of the inlet flow conditions on the thermal performance of the impinged surface. Numerical simulations were performed using the OpenFOAM program. The authors used the RANS based on Hanjalic’s ζ-f model for numerical modeling of turbulent conditions. The velocity profile and turbulence intensity at the jet site of discharge were focused on in the analyses. A qualitative analysis of the heat transfer enhancement was performed in relation to the inlet conditions. Two types of conditions were discussed, assuming the flow developed. The mean velocities achieved the same values, and the near-wall turbulence kinetic energy did not differ by more than ~5%. The stagnation region, where the thermal effects are the most intense and affected by the conditions, was indicated as essential. According to the authors’ findings, at the difference in the stagnation point, the Nusselt number reached 10%. However, its discrepancy in relation to inlet conditions was up to 23%. Furthermore, the authors claimed that the conditions near the impinged wall (described as related to turbulence flow) and at this wall (related to thermal performance) differed significantly. A correlation between the values of the turbulence kinetic energy rate and the Nusselt number was described. The turbulence kinetic energy rate budget near the wall and the enstrophy flux distribution were discussed. In [7], the thermal and hydrodynamic conditions influencing the surface of air jet impingement were the main objectives of the authors. Single-jet impingement on the concave and convex surfaces was investigated for various geometries. The numerical simulations were also performed in OpenFOAM with the application of the ζ-f turbulence model. According to the authors, conspicuous differences were observed between convex and concave surface impingements. The differences were caused by the shape of the geometry, which determined the flow characteristics and the resulting heat transfer performance. The origins of these differences were investigated in the turbulence characteristics close to the impinged surface of the stagnation zone and its vicinity. It was emphasized that they pay special attention to the stagnation point. Furthermore, the shape of the geometry impacts the size of the stagnation zone, resulting in different flow characteristics when the wall jet starts to form after impingement. The distribution of the Nusselt number was related to the turbulence’s kinetic energy near the heated wall. An attempt was made by the authors to interconnect the rates of turbulence dissipation and enstrophy in the assumed models.

The article [8] showed the results of an experimental and modeling investigation of fluid flow distribution in dividing headers of tubular-type equipment. It is worth underlining that flow maldistribution causes an undesirable effect of a nonuniform pressure field in a heat exchanger. The authors of [8] focused on modeling the flow distribution through analytical, numerical, and experimental aspects and finding the most suitable distribution model. Various modeling approaches were examined for a set of header geometries. Two analytical distribution models were examined using three distinctive geometrical configurations. The flow distribution obtained using analytical models and the results of CFD analyses were compared with the results based on the conducted experiments. The modified Model BJ achieved the best fit with experimental data in two modeled configurations with a cross-sectional ratio of 0.5 and 2.0. It was stated that the selected analytical model used for modeling flow distribution in mini-scale systems can also be utilized for conventional systems. The industrial example showed the importance of flow maldistribution and its implementation into design procedures. The analytical method (Model BJ) was used to evaluate flow rates in the tubular system of the steam superheater. Thermal analysis was performed using the composite modeling system. It was concluded that investigations involving a mini-scale system and a conventional-size heat exchanger confirmed the applicability of the proposed distribution model and the accuracy of the composite modeling system.

The work [9] presented the characteristics of loop heat pipes with two different wicks, one made of sintered stainless steel and the other of ceramic. The evaporator has a flat-rectangular assembly under gravity-assisted conditions. The influence of these two wicks was tested and used to experimentally analyze the performance of the loop heat pipe. Water was used as a working fluid. The performance of the loop heat pipes was analyzed in terms of temperatures and thermal resistance. The purpose of the tested loop heat pipes was to cool elements of electronics/microelectronics, such as processors. The authors indicated conditions for maintaining a stable operation: heat flux (ranges) and maximum temperature, which are important for safe electronics work.

3. Conclusions

As the Guest Editor of the Special Issue entitled “Heat and Mass Transfer Issues in Mini-Gaps”, and the author of a review article based on the successfully invited works, I hope that published articles will be of interest to a wide range of readers, as the topic is important and worth further scientific attention.