A machine learning approach to the prediction of heat-transfer coefficients in micro-channels

The accurate prediction of the two-phase heat transfer coefficient (HTC) as a function of working fluids, channel geometries and process conditions is key to the optimal design and operation of compact heat exchangers. Advances in artificial intelligence research have recently boosted the application of machine learning (ML) algorithms to obtain data-driven surrogate models for the HTC. For most supervised learning algorithms, the task is that of a nonlinear regression problem. Despite the fact that these models have been proven capable of outperforming traditional empirical correlations, they have key limitations such as overfitting the data, the lack of uncertainty estimation, and interpretability of the results. To address these limitations, in this paper, we use a multi-output Gaussian process regression (GPR) to estimate the HTC in microchannels as a function of the mass flow rate, heat flux, system pressure and channel diameter and length. The model is trained using the Brunel Two-Phase Flow database of high-fidelity experimental data. The advantages of GPR are data efficiency, the small number of hyperparameters to be trained (typically of the same order of the number of input dimensions), and the automatic trade-off between data fit and model complexity guaranteed by the maximization of the marginal likelihood (Bayesian approach). Our paper proposes research directions to improve the performance of the GPR-based model in extrapolation.Comment: 7 pages, 2 figures, to be published in the proceedings of the 17th International Heat Transfer Conference 2023 (IHTC-17

Single-phase laminar flow heat transfer from confined electron beam enhanced surfaces

An experimental investigation of the thermal-hydraulic characteristics for single-phase flow through three electron beam enhanced structures was conducted with water at mass flow rates from 0.005 kg/s to 0.045 kg/s. The structures featured copper heat transfer surfaces, approximately 28 mm wide and 32 mm long in the flow direction, with complex three-dimensional (3D) electron beam manufactured pyramid-like structures. The channel height varied depending on the height of the protrusions and the tip clearance was maintained at 0.1-0.3 mm. The average protrusion densities for the three samples S1, S2, and S3 were 13, 11, and 25 per cm2 with protrusion heights of 2.5, 2.8, and 1.6 mm, respectively. The data gathered were compared to those for a smooth channel surface operating under similar conditions. The results show an increase up to approximately three times for the average Nusselt number compared with the smooth surface. This is attributed to the surface irregularities of the enhanced surfaces, which not only increase the heat transfer area but also improve mixing, disturb the thermal and velocity boundary layers, and reduce thermal resistance. The increase in heat transfer with the enhanced surfaces was accompanied by an increase of pressure drop, which has to be considered in design.The authors would like to acknowledge Dr Anita Buxton and Dr Bruce Dance of TWI for their contribution to this project and also EPSRC and TSB for funding the EngD programme and sponsoring the ASTIA collaborative research project that helped to develop the Electron Beam enhanced surfaces respectively

Pool boiling on modified surfaces using R-123

This article has been made available through the Brunel Open Access Publishing Fund.Saturated pool boiling of R-123 was investigated for five horizontal copper surfaces modified by different treatments, namely, an emery-polished surface, a fine sandblasted surface, a rough sandblasted surface, an electron beam-enhanced surface, and a sintered surface. Each 40-mm-diameter heating surface formed the upper face of an oxygen-free copper block, electrically heated by embedded cartridge heaters. The experiments were performed from the natural convection regime through nucleate boiling up to the critical heat flux, with both increasing and decreasing heat flux, at 1.01 bar, and additionally at 2 bar and 4 bar for the emery-polished surface. Significant enhancement of heat transfer with increasing surface modification was demonstrated, particularly for the electron beam-enhanced and sintered surfaces. The emery-polished and sandblasted surface results are compared with nucleate boiling correlations and other published data. © 2014 Syed W. Ahmad, John S. Lewis, Ryan J. McGlen, and Tassos G. Karayiannis Published with license by Taylor & Francis

Heat transfer correlation for flow boiling in small to micro tubes

This article is available open access under a Creative Commons license (http://creativecommons.org/licenses/by-nc-nd/3.0/) Copyright © 2013 The Authors. Published by Elsevier Ltd. All rights reserved.There is a large discrepancy in the open literature about the comparative performance of the existing macro and microscale heat transfer models and correlations when applied to small/micro flow boiling systems. This paper presents a detailed comparison of the flow boiling heat transfer coefficient for R134a in stainless steel micro tubes with 21 macro and microscale correlations and models. The experimental database that was used in the comparison includes the data for 1.1 and 0.52 mm diameter tubes, mass flux range of 100–500 kg/m2 s and system pressure range 6–10 bar obtained in the course of this study. The effect of the evaporator heated length on the comparative performance of the correlations and models was investigated using three different lengths of the 1.1 mm diameter tube (L = 150, 300 and 450 mm). This comparative study demonstrated that none of the assessed models and correlations could predict the experimental data with a reasonable accuracy. Also, the predictability of most correlations becomes worse as the heated length increases. This may contribute in explaining the discrepancy in the comparative performance of the correlations from one study to another. A new correlation is proposed in the present study based on the superposition model of Chen. The database used in developing the correlation consists of 5152 data points including the current experimental data and data obtained previously with the same test rig, fluid and methodology for tubes of diameter 4.26, 2.88, 2.01 mm. The new correlation predicted 92% of the data within the ±30% error bands with a MAE value of 14.3%

Surface effects in flow boiling of R134a in microtubes

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 ElsevierThe inner surfaces of microtubes may be influenced strongly by the process of making them due to manufacturing difficulties at these scales compared to larger ones, e.g. the surface characteristics of a seamless cold drawn tube may differ from those of a welded tube. Accordingly, flow boiling heat transfer characteristics may vary. In addition, there is no common agreement between researchers on the criteria of selecting tubes for flow boiling experiments. Instead, tubes are usually ordered from commercial suppliers, in many cases without taking into consideration the manufacturing method and its effect on the heat transfer process. This may explain some of the discrepancies in heat transfer characteristics which are found in the open literature. This paper presents a comparison between experimental flow boiling heat transfer results obtained using two different metallic tubes. The first one is a seamless cold drawn stainless steel tube of 1.1 mm inner diameter while the second is a welded stainless steel tube of 1.16 mm inner diameter. Both tubes have a heated length of 150 mm and the flow direction is vertically upwards. The tubes were heated using DC current. Other experimental conditions include: 8 bar system pressure, 300 kg/m2 s mass flux, about 5K inlet sub-cooling and up to 0.9 exit quality. The results are presented in the form of local heat transfer coefficient versus local quality and axial distance. Also, the boiling curves of the two tubes are discussed. The results show a significant effect of tube inner surface morphology on the heat transfer characteristics

Compressible flows in micro-channels: an enhanced quasi-2D Fanno-based numerical model

Fanno theory provides an analytical model for the prediction of confined viscous compressible flows under the hypotheses of constant cross-section channel and adiabatic flow. From theory, differentials of flow characteristic quantities can be expressed in function of Mach number and friction factor. Yet, the theory does not assess how to evaluate friction, whereas classical formulas for friction prediction in channels are derived under the hypothesis of incompressible flow and are no longer valid in case of compressible flows. Compressibility deforms the velocity profiles in the channel by making them more flat. As a consequence friction is increased compared to the incompressible case. At the same time, the change in the velocity profiles affects the average dynamic pressure and the bulk temperature along the channel. Correlations, function of Mach and Reynolds numbers, are required for quantifying these changes and improve the prediction of the Fanno model. In the present paper, the impact of compressibility on laminar and turbulent flows in micro-channels is assessed on the basis of a series of CFD simulations, and correlations are presented for friction, average dynamic pressure, and bulk temperature. The correlations are proven to enhance the accuracy of the Fanno model predictions

Compressible flows in micro-channels: an enhanced quasi-2D Fanno-based numerical model

Fanno theory provides an analytical model for the prediction of confined viscous compressible flows under the hypotheses of constant cross-section channel and adiabatic flow. From theory, differentials of flow characteristic quantities can be expressed in function of Mach number and friction factor. Yet, the theory does not assess how to evaluate friction, whereas classical formulas for friction prediction in channels are derived under the hypothesis of incompressible flow and are no longer valid in case of compressible flows. Compressibility deforms the velocity profiles in the channel by making them more flat. As a consequence friction is increased compared to the incompressible case. At the same time, the change in the velocity profiles affects the average dynamic pressure and the bulk temperature along the channel. Correlations, function of Mach and Reynolds numbers, are required for quantifying these changes and improve the prediction of the Fanno model. In the present paper, the impact of compressibility on laminar and turbulent flows in micro-channels is assessed on the basis of a series of CFD simulations, and correlations are presented for friction, average dynamic pressure, and bulk temperature. The correlations are proven to enhance the accuracy of the Fanno model predictions