Inverse heat transfer problems are important in numerous scientific research and engineering applications. This paper proposes a network-based method utilizing the nonlinear autoregressive with ...exogenous inputs (NARX) neural network, which can achieve real-time identification of thermal boundary conditions for nonlinear transient heat transfer processes. With the introduction of the NARX neural network, the proposed method offers two key advantages: (1) The proposed method can obtain inversion results using only surface temperature time series. (2) The heat flux can be estimated even when the state equation of the system is unknown. The NARX neural network is trained using the Bayesian regularization algorithm with a dataset comprising exact surface temperature and heat flux data. The neural network takes current and historical surface temperature measurements as inputs to calculate the heat flux at the current time. The capability of the NARX method has been verified through numerical simulation experiments. Experimental results demonstrate that the NARX method has high precision, strong noise resistance, and broad applicability. The composition of the input data, the surface temperature measurement noise, and the boundary heat flux shape have been studied in detail for their impact on the inversion results. The NARX method is a highly competitive solution to inverse heat transfer problems.
•A robust saturated-interface-volume phase change model is developed.•The model is compared to previous analytical, numerical, and experimental studies.•A three-dimensional flow boiling problem is ...studied using the cost-effective model.•Flow boiling transport mechanisms can be revealed in complex domains with the model.
High-fidelity simulation of flow boiling in microchannels remains a challenging problem, but the increasing interest in applications of microscale two-phase transport highlights its importance. In this paper, a volume of fluid (VOF)-based flow boiling model is proposed with features that enable cost-effective simulation of two-phase flow and heat transfer in realistic geometries. The vapor and liquid phases are distinguished using a color function which represents the local volume fraction of the tracked phase. Mass conservation is satisfied by solving the transport equations for both phases with a finite-volume approach. In order to predict phase change at the liquid–vapor interface, evaporative heat and mass source terms are calculated using a novel, saturated-interface-volume phase change model. This phase change model is formulated to anchor the interfacial temperature at saturation within each iteration, and thereby acts as a robust constant-temperature boundary condition. Unlike other available phase-change models, the source terms are coupled with the local temperature explicitly; therefore, numerical oscillations around the interface temperature are not observed during iterations within a time step, which reduces the numerical cost. In addition, the reference frame is set to move with the vapor slug to artificially increase the local velocity magnitude in the thin liquid film region in the relative frame. This reduces the influence of numerical errors resulting from calculation of the surface tension force, and thus suppresses the development of spurious currents. As a result, non-uniform meshes may be used which can efficiently resolve high-aspect-ratio geometries and flow features. The overall numerical expense is significantly reduced. The proposed saturated-interface-volume model is first validated against a one-dimensional Stefan problem, and then used to simulate the growth of a vapor bubble flowing in a heated, 2D axisymmetric microchannel. The bubble motion, bubble growth rate, liquid film thickness, and local heat transfer coefficient along the wall are compared against previous numerical studies. A three-dimensional flow boiling problem is studied to demonstrate the cost effectiveness of the present approach and to highlight the transport mechanisms it can reveal in more complex domains.
Evaporation rates are predicted and important transport mechanisms identified for evaporation of water droplets on hydrophobic (contact angle ∼110°) and superhydrophobic (contact angle ∼160°) ...substrates. Analytical models for droplet evaporation in the literature are usually simplified to include only vapor diffusion in the gas domain, and the system is assumed to be isothermal. In the comprehensive model developed in this study, evaporative cooling of the interface is accounted for, and vapor concentration is coupled to local temperature at the interface. Conjugate heat and mass transfer are solved in the solid substrate, liquid droplet, and surrounding gas. Buoyancy-driven convective flows in the droplet and vapor domains are also simulated. The influences of evaporative cooling and convection on the evaporation characteristics are determined quantitatively. The liquid–vapor interface temperature drop induced by evaporative cooling suppresses evaporation, while gas-phase natural convection acts to enhance evaporation. While the effects of these competing transport mechanisms are observed to counterbalance for evaporation on a hydrophobic surface, the stronger influence of evaporative cooling on a superhydrophobic surface accounts for an overprediction of experimental evaporation rates by ∼20% with vapor diffusion-based models. The local evaporation fluxes along the liquid–vapor interface for both hydrophobic and superhydrophobic substrates are investigated. The highest local evaporation flux occurs at the three-phase contact line region due to proximity to the higher temperature substrate, rather than at the relatively colder droplet top; vapor diffusion-based models predict the opposite. The numerically calculated evaporation rates agree with experimental results to within 2% for superhydrophobic substrates and 3% for hydrophobic substrates. The large deviations between past analytical models and the experimental data are therefore reconciled with the comprehensive model developed here.
In the pursuit of enhancing thermal management for miniaturized electronic devices, our study delves into the impact of entry effects on Ledinegg instability and flow maldistribution within parallel ...microchannels. Utilizing a coupled model that incorporates phase change and pressure drop dynamics in boiling flow, we examine microchannels characterized by a 50 length-to-diameter ratio and a 200 μm hydraulic diameter. Our findings unveil a significant influence of entry effects, which narrow the total flow excursion interval, thereby bolstering system stability. Specifically, as the heat flux escalates from 5 W/cm2 to 120 W/cm2, the entry effects increasingly mitigate flow instability and maldistribution in parallel channels, diminishing the total flow rate range susceptible to flow instability by 4.73% and 47.52%, while narrowing the total flow rate range corresponding to uneven flow distribution by 4.70% and 46.75%, respectively. Furthermore, entry effects expand the inlet subcooling range necessary for stabilizing the parallel channel system by 38.89% and 1000%. This research not only underscores the importance of considering entry effects in microchannel design but also opens avenues for further exploration into enhancing thermal management solutions.
Bubble flow in confined geometries is a problem of fundamental and technological significance. Among all the forms, bubble breakup in bifurcated microchannels is one of the most commonly encountered ...scenarios, where an in-depth understanding is necessary for better leveraging the process. This study numerically investigates the non-uniform breakup of a bubble slug in Y-shaped microchannels under different flow ratios, Reynolds numbers, and initial bubble volumes. Overall, the bubble can either breakup or non-breakup when passing through the bifurcation and shows different forms depending on flow regimes. The flow ratio-Reynolds number phase diagrams indicate a power–law transition line of breakup and non-breakup. The bubble takes longer to break up with rising flow ratios yet breaks earlier with higher Reynolds numbers and volumes. Non-breakup takes less time than the breakup patterns. Flow ratio is the origin of non-uniform breakup. Both the Reynolds number and initial volume influence the bubble states when reaching the bifurcation and thus affect subsequent processes. Bubble neck dynamics are analyzed to describe the breakup further. The volume distribution after breaking up is found to have a quadratic relation with the flow ratio. Our study is hoped to provide insights for practical applications related to non-uniform bubble breakups.
This study investigates the heat and mass transfer characteristics of a binary mixture (R134a/R245fa) evaporated in a porous medium. The Eulerian model coupled with the multiphase VOF model and ...species transport equations is employed to establish a multi-component evaporation model. The effects of heat flux ranging from 200 kW/m2 to 500 kW/m2, porosity ranging from 0.4 to 0.6, and mass fraction ratios (R134a/R245fa) of 3:7, 5:5, and 7:3 are explored. The results indicate that an increase in heat flux contributes to an increase in the evaporation rate. For the overall evaporation rate, the evaporation rates of R134a and R245fa improve by 11.3%, 6.9%, and 16.3%, respectively, while the maximum improvement in heat transfer coefficient is only 1.4%. The maximum evaporation rate is achieved at intermediate porosity in the porous medium, and the highest heat transfer coefficient is obtained at a porosity of 0.4. With the increase in mass fraction, the evaporation rate of the corresponding species also increases, while the overall evaporation rate and heat transfer coefficient remain almost unchanged.
•Evaporation of water droplet on inclined surfaces is numerically investigated.•Transport details and underlying mechanisms are revealed.•Influence of the inclination angle is quantitatively ...determined.•Inclination–induced flow transition is systematically studied.
A three-dimensional numerical model is developed to explore the evaporation of a small water droplet sessile on inclined surfaces. Important transport mechanisms, including evaporative cooling, heat transfer, vapor diffusion and natural convections in both liquid and gas domains are taken into account. The accuracy of the present model is first validated by comparing the total evaporation times and volume evolution curves obtained by the present model with those measured from experiments in the literature. The transport details and evaporation characteristics are then investigated. Under the influence of the combining effect of natural convection and evaporative cooling, the overall evaporation rate increases first as the inclination angle gets enlarged till ∼75°, and then decreases with further increase of the inclination angle. The flow field in the gas domain is converted from symmetry to asymmetry with the increase of the inclination angle, and the flow intensity near the droplet is also enhanced, which accelerates the evaporation. At the same time, the local evaporation flux distribution at gas-liquid interface changes from symmetry to asymmetry and the location of the lowest evaporation flux moves from the droplet apex to its waist (on the higher side of the droplet). The total evaporation times of droplets evaporating on vertical surfaces are shorter than those on horizontal surfaces by up to ∼9.38% when the substrate temperature is 40 °C higher than the ambient. The flow behavior inside the droplet is also discussed. With the increase of the inclination angle (0°∼180°), the flow pattern inside the droplet changes from double-vortex flow to single-vortex flow and to double-vortex flow again. The flow velocity magnitude is remarkably increased with the inclination angle increases from 0° to 90°
The process of evaporation from a meniscus into air is more complicated than in enclosed chambers filled with pure vapor. The vapor pressure at the liquid–gas interface depends on both of the ...evaporation and the vapor transport in the gas environment. Heat and mass transport from an evaporating meniscus in an open heated V-groove is numerically investigated and the results are compared to experiments. The evaporation is coupled to the vapor transport in the gas domain. Conjugate heat transfer is considered in the solid walls, and the liquid and gas domains. The flow induced in the liquid due to Marangoni effects, as well as natural convection in the gas due to thermal expansivity and vapor concentration gradients are simulated. The calculated evaporation rates are found to agree reasonably well with experimentally measured values. The convection in the gas domain has a significant influence on the overall heat transfer and the wall temperature distribution. The evaporation rate near the contact lines on either end of the meniscus is high. Heat transfer through the thin liquid film near the heated wall is found to be very efficient. A small temperature valley is obtained at the contact line which is consistent with the experimental observation.
Plenty of studies have been made to have a comprehensive understanding of heat and mass transport at an evaporating meniscus. Recently in this journal Gazzola et al. (
2009
) reported an asymmetrical ...flow pattern generated at a convex meniscus while the boundary conditions were symmetrical. In their experiment a vertical micro well was filled up with liquid and the meniscus was held convex above the well outlet. The flow pattern at the meniscus was found having only one single vortex, which was distinct from those symmetrical paired vortexes in literatures (Buffone and Sefiane
2004
). In the present work a simulation is conducted to clarify the mechanisms behind the abnormality. Factors including liquid evaporation, vapor transport, and Marangoni effect are considered. It is found that for a convex meniscus as that in the experiment, symmetrical flow pattern is not stable. The transition of symmetry to asymmetry occurs and this is greatly affected by random perturbations. After the asymmetrical flow pattern is established, the perturbations have relatively minor effects on the flow pattern.
•Dynamics and phase change heat transfer of an isolated vapor bubble traveling through a heated T-shaped branching microchannel are investigated.•A numerical model is developed and validated by ...coupling VOF and the saturated-interface-volume phase change model.•Even under very low heat flux, the bubble dynamics and heat transfer characteristics are significantly altered owing to the evaporation.•The influence of inlet Reynolds number is studied and the underlying mechanisms are revealed.
While flow boiling problem has been extensively investigated in the last decades, the transport details of boiling flow in heated T-shaped branching microchannels have not yet been revealed with high-fidelity simulations. The present paper reports a numerical study of the saturated boiling of an isolated vapor bubble traveling through a heated T-shaped branching microchannel. The evolution of liquid-vapor interface is captured with the volume of fluid (VOF) method, while the saturated-interface volume phase change model is employed to simulate heat and mass exchange on the interface. The numerical model is first validated with literatures, and then is utilized to simulate the bubble dynamics and phase change heat transfer. The numerical results indicate that even a very low wall heat flux can exert great influences on the bubble dynamics and heat transfer characteristics. When the bubble travels through the heated main channel (HMC), the bubble keeps growing and the heat transfer coefficient of the HMC keeps increasing. After the bubble nose leaves the HMC and enters the heated branching channel (HBC), the bubble gradually breaks into two bubbles. The bubble breakup process is found to have a great impact on the heat transfer characteristics of the HBC. As a result, the heat transfer coefficient of the HBC is improved more significantly compared with that of the HMC. At last, the influence of inlet Reynolds number (Re) on bubble dynamics and heat transfer characteristics is revealed. The bubble breakup regime is found to change significantly with Re ranging from 76 to 612. The overall heat transfer enhancement gradually decreases with increasing Re. This study provides a new insight into the bubble motion in T-shaped branching microchannels.
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