Heat Transfer In Microtubes Research Articles

Numerical and Experimental Study of Flow-Induced Vibrations in Micro-Tube Heat Exchangers

Abstract Thermal management presents an increasing challenge in future engineering systems, especially in applications like combined cycle precooling, waste heat recovery, and innovative propulsion systems. These systems face a growing demand for managing higher heat loads while coping with limited heat sink. Central to these thermal management systems is the heat exchanger, with micro-tube heat transfer emerging as a promising solution for future technologies. Micro-tube heat exchangers are becoming popular owing to their ability to significantly enhance the heat transfer surface area while maintaining a compact core volume. As the demand for high-performance, lightweight heat exchangers escalates, micro-tube heat exchangers are being designed to be increasingly compact yet highly loaded. This trend poses significant challenges to their structural integrity, particularly under harsh operational conditions. Flow-induced vibrations, a critical concern in the design of tubular heat exchangers, can lead to tube failures, compromising the safe operation of engineering systems. While the flow-induced vibrations of conventional-sized heat exchangers have been extensively studied, there is a noticeable gap in the research on similar phenomena in micro-tube heat exchangers. This paper details ongoing research at Reaction Engines Ltd to aid the design of safe and robust heat exchangers, focusing on the flow-induced vibrations in micro-tube heat exchangers and utilizing a cutting-edge laser vibrometry test facility. A predictive model, employing an unsteady flow simulation approach and eigenvalue analysis, has been formulated.

Slip-flow and heat transfer in microtubes with internal fins

The study of the simultaneous development of slip-flow and heat transfer in a microtube with internal fins has been conducted. It was found that rarefaction effects were more pronounced in the entrance region than in the fully developed region for both friction factor and Nusselt number. Minimal influence of the number of fins on rarefaction effects for the friction factor was observed, but a substantial influence on Nusselt numbers was noted. Tubes with larger fin height were found to enhance rarefaction effects on the friction factor, while the opposite was observed for Nusselt number. An evaluation criterion was used to compare the heat transfer and pressure drop in microtubes with and without fins. The results showed that the microtube with fins offers a significant performance advantage, especially in the entrance region and for tubes with a higher number of fins with a larger fin height. This study highlights that microtubes with internal fins have the potential to improve cooling efficiency in electronic circuit cooling applications compared to microtubes without internal fins.

Size effect on compressible flow and heat transfer in microtube with rarefaction and viscous dissipation

In a microtube, the flow and thermal fields have very different features to the conventional tube flows. Fluid properties such as compressibility, viscous dissipation, and rarefaction are important for the flow and heat transfer changes. However, with a decrease in the tube diameter, the relative effect of each of these properties on flow development is unclear. In this study, various compressible microtube flows were numerically investigated for different tube diameters of 1 ∼ 100 μm to examine the size effect on the flow and heat transfer. The slip-flow regime 0.001 < Kn < 0.1, where the continuum-based equations are valid under velocity slip and temperature jump conditions, was selected. The composite effects of compressibility, viscous dissipation, and rarefaction are examined for four cases based on Br and Kn. On the basis of the results, compressible flows were analyzed by varying Kn and the relation Kn ≈ Ma/Re was identified. Furthermore, flow fields related to the Knudsen paradox were examined. The size effect and the effects of viscous dissipation and compressibility on the microtube heat transfer are discussed.

Effects of solid-liquid intermolecular interactions on liquid flow and heat transfer in microtubes

This paper investigates the laminar flow and heat transfer characteristics of liquid in microtubes by considering the solid-liquid intermolecular interactions. We propose an apparent viscosity model of liquid from the wetting theory and the Hamaker theory to account for the interface effect. The numerical simulation considering this model is conducted to study the flow and heat transfer characteristics of liquid in microtubes. Simulation results indicate that the flow and heat transfer characteristics such as velocity distribution, pressure drop, flow friction and heat transfer coefficient deviate from the predictions of the conventional theory. The deviation increases as the hydrophilicity or hydrophobicity increases, and decreases as the diameter of the microtube increases.

Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects

The solution of extended Graetz problem for micro-scale gas flows is performed by coupling of rarefaction, axial conduction and viscous dissipation at slip flow regime. The analytical coupling achieved by using Gram–Schmidt orthogonalization technique provides interrelated appearance of corresponding effects through the variation of non-dimensional numbers. The developing temperature field is determined by solving the energy equation locally together with the fully developed flow profile. Analytical solutions of local temperature distribution, and local and fully developed Nusselt number are obtained in terms of dimensionless parameters: Peclet number, Knudsen number, Brinkman number, and the parameter Kappa accounting temperature-jump. The results indicate that the Nusselt number decreases with increasing Knudsen number as a result of the increase of temperature jump at the wall. For low Peclet number values, temperature gradients and the resulting temperature jump at the pipe wall cause Knudsen number to develop higher effect on flow. Axial conduction should not be neglected for Peclet number values less than 100 for all cases without viscous dissipation, and for short pipes with viscous dissipation. The effect of viscous heating should be considered even for small Brinkman number values with large length over diameter ratios. For a fixed Kappa value, the deviation from continuum increases with increasing rarefaction, and Nusselt number values decrease with an increase in Knudsen number.

The effect of initial flow velocity on the liquid film thickness in micro tube accelerated slug flow

Liquid film thickness is an important parameter for predicting boiling and condensation heat transfer in micro tubes. In the present study, the effect of initial flow velocity on the liquid film thickness in accelerated flows under adiabatic condition is experimentally investigated. The laser focus displacement meter is used to measure the initial liquid film thickness. Circular tube with inner diameter of 1mm was used for the test tube, and water, ethanol and FC-40 are used as working fluids. When the flow is accelerated from small initial velocities under small Bond number condition, initial liquid film thickness is identical to that of steady flow at small capillary numbers, and then deviates from the steady condition and eventually follows that of accelerated flow from zero initial velocity as capillary number is increased. When the flow is accelerated from large initial velocities, initial liquid film thickness deviates from the steady condition earlier and starts to follow that of accelerated flow from zero initial velocity as capillary number is increased. It is found that the initial flow velocity cannot be neglected in accelerated flows especially at large initial flow velocities and at large Bond numbers. Finally, an empirical correlation is proposed for the initial liquid film thickness of accelerated flows that accounts for the initial flow velocities.

Slip flow heat transfer in micro-tubes with viscous dissipation

A numerical study for a steady-state, two-dimensional, laminar convective heat transfer of a rarefied gas in a micro-tube is conducted using first-order slip velocity and temperature jump boundary conditions and taking into account the viscous dissipation and the axial conduction. The numerical model based on the finite volume method was validated using the available data for fully developed slip flow and developing continuum flow. The study reveals significant impact of slip velocity and temperature jump conditions and viscous dissipation on the velocity and temperature profiles at different sections of the micro-tube. The friction coefficient and the Nusselt number are substantially affected by rarefaction and viscous dissipation. The influence of the viscous dissipation depends on whether the fluid is heated or cooled. For the heating case, the Nusselt number distribution exhibits a special behavior characterized by the existence of a singular point where Nusselt number goes to the infinity. The thermal field development continues after the location of this singular point until reaching the fully developed regime. Furthermore, including viscous dissipation for continuum flow results in a significant increase in the Nusselt number regardless the value of the Brinkman number. Applying the temperature jump boundary condition reduces drastically the heat transfer rates along the micro-tube. The axial conduction improves the heat transfer process in the entrance region of the tube for low Peclet numbers and with no temperature jump condition.

Investigation of Convective Heat Transfer with Liquids in Microtubes

Convective heat transfer in microtubes has attracted considerable attention for almost three decades. It is well-known that the solid-liquid interfacial tension plays an important role at the micrometer length scale. In this work, the characteristics of convective heat transfer in microtubes with inner diameters ranging from 0.353 to 1.045 mm were investigated; the effects of interfacial tension on heat transfer were also investigated using nine working fluids (including deionized water, 5 wt % ethanol aqueous solution, 50 wt % ethanol aqueous solution, ethanol, ethyl acetate, cyclohexane, n-hexane, cyclohexanone, and cyclopentanone). The experimental results showed that the performance of convective heat transfer of different working fluids in microtubes varied significantly and was different from that in conventional scale tubes. The results were correlated by an empirical correlation, in which the effect of solid-liquid interfacial tension was taken into account. The agreement between the correlation and the experimental data was found to be satisfactory.

Combined influences of viscous dissipation, non-uniform Joule heating and variable thermophysical properties on convective heat transfer in microtubes

This study presents a comprehensive investigation on hydrodynamic and thermal transport properties of mixed electroosmotically and pressure driven flow in microtubes. Particular emphasis is given to investigating the combined consequences of viscous dissipation, non-uniform Joule heating, and variable thermophysical properties. Analytical solutions are obtained using the Debye–Hückel linearization and constant fluid properties assumption, while a numerical solution is presented for variable fluid properties and non-uniform distribution of Joule heating. The results indicate that, viscous heating effect is pronounced significantly when a favorable pressure gradient exists and cannot be neglected at low values of the dimensionless Debye–Hückel parameter. Moreover, uniform Joule heating assumption, even at low zeta potentials, may reduce the accuracy of the predicted thermal features considerably. The wall shear stress is found to be strongly dependent upon the zeta potential, which is underestimated by the Debye–Hückel linearization. Compared with the constant fluid properties case, decreasing electrical resistivity of the fluid by increasing temperature, amplifies the total energy generation due to the Joule heating and reduces the Nusselt number.

Experimental Study on Single-Phase Gas Flow in Microtubes

An experimental system for single-phase gas flow in microtubes has been developed. The effects of viscous heating and compressibility on the flow and temperature field were studied for a wide range of governing parameters. Also, an analytical/numerical model of the flow was developed. Numerical results for the flow and heat transfer in the slip flow region were found to agree quite well with the experimental data, lending support to the model. The study provides greater physical insight into and understanding the effects of viscous dissipation and compressibility in microtube flow and the associated heat transfer. In addition, the combined experimental and numerical simulation approaches of the process can be used for control and optimization of systems based on microtube heat transfer.

The micro-tube heat transfer and fluid flow of water based Al 2O 3 nanofluid with viscous dissipation

The numerical modeling of the conjugate heat transfer and fluid flow of Al 2O 3/water nanofluid through the micro-tube was presented in the paper. The laminar flow regime was considered along with viscous dissipation effect. The diameter ratio of the micro-tube was D i/ D o = 0.1/0.3 mm with a tube length L = 100 mm. The heat transfer rate was fixed to Q = 0.5 W with three different Br = 0.1, 0.5 and 1. The water based Al 2O 3 nanofluid was considered with various volume concentrations of Al 2O 3 particles ϕ = 1, 4, 6, 9% and two diameters of the particles D p = 10 nm and 47 nm. The analysis was performed on the results for local heat transfer coefficient.

Numerical studies of simultaneously developing laminar flow and heat transfer in microtubes with thick wall and constant outside wall temperature

The effects of wall axial heat conduction in a conjugate heat transfer problem in simultaneously developing laminar flow and heat transfer in straight thick wall of circular tube with constant outside wall temperature are numerically investigated. The results show that the heat transfer process is most sensitive to wall-to-fluid conductivity ratio k sf , and when k sf ⩽ 25 the increasing tube thickness and the decreasing k sf could make the inner wall surface approaching the uniform heat flux condition. It turns out that the basic function of the wall axial heat conduction for the cases studied is to unify the inner wall surface heat flux.

A new model for three-dimensional random roughness effect on friction factor and heat transfer in microtubes

In this paper we propose a novel bottom-up approach to generate a three-dimensional microtube surface with random roughness. This approach starts from four corner points with two defined coordinates and roughness height created by a Gaussian number generator, and then uses a bi-cubic Coons patch to form the curved surface. A computational fluid dynamics solver is used to isolate the roughness effect and solve the three-dimensional N–S equations for the water flow through the generated rough microtubes with diameter D = 50 μm and length L = 100 μm. No-slip, constant heat flux and periodic boundary conditions are applied to achieve the characteristics of fully developed flow. It is found that the wall roughness strongly affects the velocity near the wall and it almost has no effect on the flow at the center. When the mean diameter of a rough microtubes is used as the hydraulic diameter, the friction factor can still be predicted by the conventional flow theory. The temperature has large values at the peaks and small values at the valleys of the microtube surface. However, the roughness has almost no effect on the averaged Nusselt number Nu ¯ because the effects of peaks and valleys counteract each other for the whole microtube. The local Nusselt numbers along the microtube randomly scatter from the theoretical value with a deviation less than 2%. The model has a potential to be used for direct simulations of three-dimensional surface roughness effect on the slip flow.

The effect of bubble acceleration on the liquid film thickness in micro tubes

Liquid film thickness is an important parameter for predicting boiling heat transfer in micro tubes. In the previous study ( Han and Shikazono, 2009a), liquid film thickness under the steady condition was investigated and an empirical correlation for the initial liquid film thickness based on capillary number, Reynolds number and Weber number was proposed. However, under flow boiling conditions, bubble velocity is not constant but accelerated due to evaporation. It is necessary to consider this bubble acceleration effect on the liquid film thickness, since it affects viscous, surface tension and inertia forces in the momentum equation. In addition, viscous boundary layer develops, and it may also affect the liquid film thickness. In the present study, the effect of bubble acceleration is investigated. Laser focus displacement meter is used to measure the liquid film thickness. Ethanol, water and FC-40 are used as working fluids. Circular tubes with three different inner diameters, D = 0.5, 0.7 and 1.0 mm, are used. The increase of liquid film thickness with capillary number is restricted by the bubble acceleration. Finally, an empirical correlation is proposed for the liquid film thickness of accelerated flows in terms of capillary number and Bond number based on the bubble acceleration.

The Nu Number Behavior on Micro-tube Heat Transfer and Fluid Flow of Dielectric Fluid

The numerical modeling of the microchannel heat transfer and fluid flow was analyzed to estimate the thermal behavior of the dielectric fluids with emphasize on Nu number behavior. The geometry of a model is the same as in (Lelea et al., 2004). The diameters of the tube were Di /Do=125.4/300 μm, the total length L=70 mm, Q=0.75 W and only a portion of the tube was heated. The laminar and stationary regime was considered with variable fluid properties. Besides, two different heat flux directions are considered: heating and cooling.

Effects of temperature dependent thermal conductivity on Nu number behavior in micro-tubes

The numerical modeling of the conjugate heat transfer and fluid flow through the micro-tube was presented in the paper. Three different fluids with temperature dependent fluid properties are considered: water and two dielectric fluids, HFE-7600 and FC-70. The diameter ratio of the micro-tube was D i/ D o = 0.1/03 mm with a tube length L = 70 mm, geometry used in [D. Lelea, Nishio S., Takano K., The experimental research on microtube heat transfer and fluid flow of distilled water, International Journal of Heat and Mass Transfer 47 (2004) 2817–2830]. The laminar fluid flow regime is analyzed. Two different heat transfer conditions are considered: heating and cooling. The influence of the temperature dependent thermal conductivity on Nu number is analyzed for these two cases and compared with k = const.

Slip-flow heat transfer in microtubes with axial conduction and viscous dissipation – An extended Graetz problem

This study is an extension of the Graetz problem to include the rarefaction effect, viscous dissipation term and axial conduction with constant-wall-heat-flux thermal boundary condition. The energy equation is solved analytically by using general eigenfunction expansion. The temperature distribution and the local Nusselt number are determined in terms of confluent hypergeometric functions. The effects of the rarefaction, axial conduction and viscous dissipation on the local Nusselt number are discussed in terms of dimensionless parameters such as the Knudsen number, Peclet number and Brinkman number.

TWO-PHASE FLOW AND HEAT TRANSFER IN MICROTUBES UNDER NORMAL AND MICROGRAVITY CONDITIONS

TWO-PHASE FLOW AND HEAT TRANSFER IN MICROTUBES UNDER NORMAL AND MICROGRAVITY CONDITIONS

Experimental and numerical studies of liquid flow and heat transfer in microtubes

Experimental and numerical studies were conducted to reveal the flow and heat transfer characteristics of liquid laminar flow in microtubes. Both the smooth fused silica and rough stainless steel microtubes were used with the hydraulic diameters of 50–100 μm and 373–1570 μm, respectively. For the stainless steel tubes, the corresponding surface relative roughness was 2.4%, 1.4%, 0.95%. The experiment was conducted with deionized water at the Reynolds number from 20 to 2400. The experimental data revealed that the friction factor was well predicted with conventional theory for the smooth fused silica tubes. For the rough stainless steel tubes, the friction factor was higher than the prediction of the conventional theory, and increased as the surface relative roughness increased. The results also confirmed that the conventional friction prediction was valid for water flow through microtube with a relative surface roughness less than about 1.5%. The experimental results of local Nusselt number distribution along the axial direction of the stainless steel tubes do not accord with the conventional results when Reynolds number is low and the relative thickness of the tube wall is high. The numerical study reveals that the large ratio of wall thickness over tube diameter in low Reynolds number region causes significant axial heat conduction in the tube wall, leading to a non-linear distribution of the fluid temperature along the axial direction. The axial heat conduction effect is gradually weakened with the increase of Reynolds number and the decrease of the relative tube wall thickness and thus the local Nusselt number approaches the conventional theory prediction.

A numerical study of single-phase convective heat transfer in microtubes for slip flow

The steady-state convective heat transfer for laminar, two-dimensional, incompressible rarefied gas flow in the thermal entrance region of a tube under constant wall temperature, constant wall heat flux, and linear variation of wall temperature boundary conditions are investigated by the finite-volume finite difference scheme with slip flow and temperature jump conditions. Viscous heating is also included, and the solutions are compared with theoretical results where viscous heating has been neglected. For these three boundary conditions for a given Brinkman number, viscous effects are presented in the thermal entrance region along the channel. The effects of Knudsen and Brinkman numbers on Nusselt number are presented in graphical and tabular forms in the thermal entrance region and under fully developed conditions.