Some considerations on thermal boundary condition of slip flow

The slip effect of gaseous flow in a micro-scale channel is dominant when the characteristic length is less than about 10 μm under atmospheric conditions. The slip flow in a channel whose wall temperature is specified can be analyzed by solving the momentum and energy equations with taking into account the slip velocity and temperature jump. However, when there is slip, the shear work due to the slip at the wall should be included to calculate the heat flux from the wall. Unfortunately, the need of inclusion of the shear work in the heat balance equation has not been physically explained. In this paper, the physical reason of the inclusion of the shear work in the heat balance equation is physically explained from the point of view of both conservation law of energy and the kinetic theory of gases.     

Surface effects in flow boiling of R134a in microtubes

The 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 5 K 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.     

Viscous heating for laminar liquid flow in microtubes

Using de-ionized ultra-filtered water (DIUFW) as the working fluid, the effects of viscous dissipation in micro-tubes with inner diameters of 19.9μm and 44.2μm, respectively, have been studied by experiments, the theoretical analysis and the numerical simulation at laminar state. Based on thermal imaging technology of micro-area, the temperature rise resulted from the viscous dissipation in microtube is measured by employing IR camera with a specially magnifying lens at different Reynolds numbers. A 2-D model adapted to microtube is presented to simulate the viscous dissipation characteristic considering electric double layer effect (EDL). The investigation shows the calculating results are in rough agreement with the experimental data if removing the experimental uncertainties. Based on the experimental and the numerical simulation results, a viscous dissipation number which can describe the law of the viscous heating in microtube is summed up and it explains the abnormity of the flow resistance in microtubes.     

Ground water flow heat losses for seasonal heat storage in the soil

A seasonal heat storage project using ground storage of heat for the heating of 100 solar houses is under consideration for the Netherlands. Losses of heat by conduction and due to natural convection in the groundwater have been studied using a mathematical model. The importance of convection losses depends on soil permeabilities. At permeabilities 10⁻¹¹ m², as for sandy ground, these losses will reduce storage efficiency. Introduction of water impermeable layers reduces the losses     

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 general formula for the evaluation of thermodynamic and aerodynamic losses in nucleating steam flow

Near saturation steam undergoing rapid expansion, with homogeneous nucleation of water droplets, is numerically studied in a series of converging/diverging nozzles with and without shocks. To understand loss mechanisms in such flows a numerical model is presented to calculate thermodynamic losses, which is further used to quantify associated total aerodynamic losses. For the converging/diverging nozzle configuration, the model shows that the overall thermodynamic loss is only mildly influenced by increasing shock strength, while the aerodynamic losses follow that of the single phase flow, and are of the same magnitude as the thermodynamic loss only in the case of very weak shocks. The thermodynamic losses can be attributed to two influences, the homogeneous nucleation event, and the post-shock thermal oscillations in the two-phase system. The calculations rely on a new two-phase CFD model, previously reported, for non-equilibrium phase change with droplet nucleation applicable to general 3D flow configurations.     

Fluid flow in microtubes with axial conduction including rarefaction and viscous dissipation

Graetz problem inside the microtube is revisited considering rarefaction effect, viscous dissipation term and axial conduction in the fluid for uniform wall temperature boundary condition in the slip flow regime. The flow is assumed to be hydrodynamically fully developed, thermally developing, and the velocity profile is solved analytically. The temperature field is determined by the numerical solution of the energy equation. The rarefaction effect is imposed to the problem via velocity-slip and temperature jump boundary conditions. The local and fully developed Nu numbers are obtained in terms of dimensionless parameters; Pe, Kn, Br, κ. Fully developed Nu numbers and the thermal entrance length are found to increase by the presence of the finite axial conduction.     

Friction losses and heat transfer of single-phase flow in a mini-channel

Experimental frictional pressure drop and heat transfer during single phase flow in a vertical mini-channel have been studied with the aim of determining the validity of classical correlations available for conventional size channels. A 1 mm square channel etched in a 420 mm long test section of aluminum has been investigated. The Reynolds number has been varied from 310 to 7780 in order to cover the laminar regime as well as the beginning of the turbulent regime. The heat flux supplied to the fluid varies from 1 kW/m² to 8 kW/m². Experimental frictional pressure drop measurements show that classical correlations accurately apply. Temperature measurements along the channel show that the temperature profile is drastically different from the expected linear behaviour owing to an important longitudinal heat flux in the channel wall. This heat flux mal-distribution which has been recently discussed in the literature is clearly shown and studied in more details by a numerical simulation of the experiment. This numerical work has allowed to make a correction on temperature measurements. Once corrected, the heat transfer measurements are in fair agreement with the classical literature results.     

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.     

Convective heat transfer characteristics of electro-osmotically generated flow in microtubes at high wall potential

Fully-developed convection heat transfer for electro-osmotic flow in a circular microtube has been investigated for arbitrary wall zeta potentials under conditions of imposed wall temperature and imposed wall heat flux. The coupled differential equations governing charge potential, momentum, and energy were solved numerically. It has been determined that elevated values of wall zeta potential produce significant changes in the charge potential, electro-osmotic flow field, temperature profile, and Nusselt number relative to previous results invoking the Debye-Hückel linearization, which is valid only for low wall potentials.     

Couette flow with frictional heating in a fluid with temperature and pressure dependent viscosity

This study investigates the effects of variable viscosity and frictional heating on the laminar flow in a horizontal channel having a wall at rest and a moving wall subjected to a prescribed shear stress. The wall at rest is thermally insulated, while the moving wall is kept at a uniform temperature. This investigation concerns fluids whose viscosity depends exponentially on the pressure and temperature. An appropriate approximation is introduced to analyze the interplay between the dependence of viscosity on the pressure and temperature and the viscous dissipation. It is shown that the nonlinear term in the equation for the balance of energy representing the frictional heating may lead to the existence of dual solutions of the boundary value problem for fixed values of the material parameters that characterize the fluid. The results obtained are compared with those predicted by the generalization of the Oberbeck-Boussinesq approximation for a fluid with pressure and temperature dependent viscosity. It is found that the results for the approximation carried out in this paper and those that stem from the Oberbeck-Boussinesq approximation are markedly different.     

Numerical simulation of laminar flow of water-based magneto-rheological fluids in microtubes with wall roughness effect

Fully developed laminar flows of water-based magneto-rheological (MR) fluids in microtubes at various Reynolds and Hedsrom numbers have been numerically simulated using finite difference method. The Bingham plastic constitutive model has been used to represent the flow behavior of MR fluids. The combined effects of wall roughness and shear yield stress on the flow characteristics of MR fluids, which are considered to be homogeneous by assuming the small particles with low concentration in the water, through microtubes have been numerically investigated. The effect of wall roughness on the flow behavior has been taken into account by incorporating a roughness–viscosity model based on the variation of the MR fluid apparent viscosity across the tube. Significant departures from the conventional laminar flow theory have been acquired for the microtube flows considered.     

基于不确定度的辐射测温优化分析

将基于标定模式的双色测温拓展为基于非标定模式的三色比值辐射测温,以此为出发点,考虑测量不确定度的影响,开展辐射测温的反演算法、光谱组合等优化分析。研究了非标定模式的比值辐射测温与标定模式的双色测温的优劣,对于非标定模式的比值辐射测温,当测量不确定度较大时,通过比较分析,提出了推荐采用的反演算法。同时,针对于具有应用优势的非标定比值辐射测温模式,讨论了光谱组合优化选择的问题,采用遍历模拟的方式,得到了特定条件下的优化光谱组合结果。给辐射测温方法与技术的改进与应用提供重要的指导。     

A variational theory for frictional flow of fluids in inhomogeneous porous systems

For nonlinear steady paths of a fluid in an inhomogeneous isotropic porous medium a Fermat-like principle of minimum time is formulated which shows that the fluid streamlines are curved by a location dependent hydraulic conductivity. The principle describes an optimal nature of nonlinear paths in steady Darcy’s flows of fluids. An expression for the total resistance of the path leads to a basic analytical formula for an optimal shape of a steady trajectory. In the physical space an optimal curved path ensures the maximum flux or shortest transition time of the fluid through the porous medium. A sort of “law of bending” holds for the frictional fluid flux in Lagrange coordinates. This law shows that – by minimizing the total resistance – a ray spanned between two given points takes the shape assuring that its relatively large part resides in the region of lower flow resistance (a ‘rarer’ region of the medium). Analogies and dissimilarities with other systems (e.g. optical or thermal ones) are also discussed.     

Some thermodynamic considerations on the photodecomposition of water mediated by redox reactions and their relation to solar energy utilization

Chemical cycles are considered in which an adiabatic step of quantum absorption by a solute transition metal ion (particularly from the fourth period of the periodic table) in water is followed by chemical isothermal reactions leading to a net decomposition of water. The threshold and the real quantum energy required for the photochemical steps (forming H or OH radicals) in these cycles are calculated and compared with the values hitherto used. It is shown that the Franck-Condon strain photochemical activation energy leads to values of the real hv significantly higher than the threshold values based on the purely thermodynamic cycle calculations. A cycle in which a photocatalyst is oxidized (forming H radical) in the photochemical step requires the highest quantum energy (λ 250 nm). A cycle, in which the absorbing species is an ion pair complex (M³⁺-OH) and the photocatalyst is reduced (forming OH radical) in the photochemical step, requires the lowest quantum energy (λ 340 nm). All cycles of water decomposition involving monophotonic processes leading to free radical intermediate formation from water, appear to be energetically unfavourable for solar energy utilization.     

An evaluation of secondary effects on microchannel frictional and convective heat transfer characteristics

The frictional and convective heat transfer characteristics of rarified flows in rectangular microchannels, with either isoflux or isothermal boundary conditions, are evaluated subject to second-order slip boundary conditions, creep flow, viscous dissipation, and axial conduction effects. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with first- and second-order slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. The results, reported in the form of Poiseuille and Nusselt numbers, are found to be significant functions of aspect ratio, Knudsen number, slip model parameters, Brinkman number, and Peclet number.     

Some considerations of wear and hardfacing materials

This paper is a brief review of various aspects pertaining to Wear Processes and Hardfacing Materials. It attempts to clarify the necessary requirements for realising the correct selection of Hardfacing Materials to mitigate Wear Processes.

It considers such topics as the economics of hardfacing materials where account is taken of various factors such as:

1. (a) cost of repair of replacement;

2. (b) time between scheduled plant shutdowns; and

3. (c) financial overheads, wear processes and testing procedures and material selection for wear resistance.

The effectiveness of surface treatments and coatings in combatting wear are discussed as well as the microstructural influence on wear resistance. Finally outlines for the classification of the various hardfacing materials are assessed.     

Experimental Studies on The Mechanism and Control of Secondary Flow Losses in Turbine Cascades

This paper summarizes the results of the authors' 4 year experimental studies on the secondary flow losses in turbine cascades. Cascade wind tunnel experiments were carried out concerning the influence of aspect ratios, incidence, turning angles and outer endwall divergent angles in order to unveil the evolution mechanism of secondary flow losses in turbine cascades without end clearance. Some methods for controlling the secondary flows are investigated including the blade leaning, blade cambering, endwall convergence and leading edge extension at two ends of the blade.     

Study of the critical heat flux condition with water and R-123 during flow boiling in microtubes. Part I: Experimental results and discussion of parametric effects

Extensive experimentation was performed to obtain flow boiling critical heat flux data in single stainless steel microtubes with diameters from 0.286 to 0.700 mm over a wide range of mass fluxes, inlet subcoolings, and exit pressures for two different working fluids (water and R-123). The effect of different operating parameters – mass flux, inlet subcooling, exit quality, heated length and diameter – were assessed in detail (Part I of the paper). The conventional DNB-type behavior is observed in the high subcooled region, and the typical dryout type behavior is seen in the high-quality saturated region when the flow is completely annular. The flow in transitional flow patterns (churn–annular or slug–annular) causes a peculiar increase of CHF with exit quality. Also, the increased void fraction near the saturated region in subcooled boiling results in increased subcooled CHF values. Part II of the paper deals with comparison of data with existing correlations and development of a new correlation to predict the CHF condition in the subcooled liquid region.     

Analytical solutions of Nusselt number for thermally fully developed flow in microtubes under a combined action of electroosmotic forces and imposed pressure gradients

Closed form expressions are developed for Nusselt number variation in a thermally fully developed microtube flow, under a combined influence of electroosmotic forces and imposed pressure gradients. The analysis takes care of the interaction amongst pressure driven convection and Joule heating effects, in order to obtain the pertinent rate of heat transfer. While separate limiting conditions on the asymptotic Nusselt number can be obtained for pure electroosmotic and solely pressure driven flows, relative influences of electrical potential gradients and imposed pressure gradients acting in tandem are also critically analyzed, as a function of the tube radius normalized with respect to the Debye length. Significant insights are also developed regarding the influence of adverse pressure gradients on the thermal transport, in presence of aiding electroosmotic effects.