Numerical study of turbulent flow and heat transfer of Al2O3–water mixture in a square duct with uniform heat flux

Turbulent flow and convective heat transfer of a nanofluid made of Al₂O₃ (1–4 vol.%) and water through a square duct is numerically studied. Single-phase model, volumetric concentration, temperature-dependent physical properties, uniform wall heat flux boundary condition and Renormalization Group Theory k-ε turbulent model are used in the computational analysis. A comparison of the results with the previous experimental and numerical data revealed 8.3 and 10.2 % mean deviations, respectively. Numerical results illustrated that Nu number is directly proportional with Re number and volumetric concentration. For a given Re number, increasing the volumetric concentration of nanoparticles does not have significant effect on the dimensionless velocity contours. At a constant dimensionless temperature, increasing the particle volume concentration increases the size of the temperature profile. Maximum value of dimensionless temperature increases with increasing x/D_h value for a given Re number and volumetric concentration.     

Experimental study on the heat transfer and pressure drop of a cross-flow heat exchanger with different pin–fin arrays

In this study, convective heat transfer and pressure drop in a cross-flow heat exchanger with hexagonal, square and circular (HSC) pin–fin arrays were studied experimentally. The pin–fins were arranged in an in-line manner. For the applied conditions, the optimal spacing of the pin–fin in the span-wise and stream-wise directions has been determined. The variable parameters are the relative longitudinal pitch (S _L /D = 2, 2.8, 3.5), and the relative transverse pitch was kept constant at S _T /D = 2. The performances of all pin–fins were compared with each other. The experimental results showed that the use of hexagonal pin–fins, compared to the square and circular pin–fins, can lead to an advantage in terms of heat transfer enhancement. The optimal inter-fin pitches are provided based on the largest Nusselt number under the same pumping power, while the optimal inter-fin pitches of hexagonal pin–fins are S _T /D = 2 and S _L /D = 2.8. Empirical equations are derived to correlate the mean Nusselt number and friction coefficient as a function of the Reynolds number, pin–fin frontal surface area, total surface area, and total number. Consequently, the general empirical formula is given in the present form.

Hysteretic heat transfer study of liquid–liquid two-phase flow in a T-junction microchannel

Liquid–liquid two-phase flow in microchannels is capable of boosting the heat removal rate in cooling processes. Formation of different two-phase flow patterns which affect the heat transfer rate is numerically investigated here in a T-junction containing water-oil flow. For this purpose, the finite element method (FEM) is applied to solve the unsteady two-phase Navier–Stokes equations along with the level set (LS) equation in order to capture the interface between phases. It is shown that the two-phase flow pattern in microchannels depends on the flow initial condition which causes hysteresis effect in two-phase flow. In this study, the hysteresis is observed in flow pattern and consequently in the heat transfer rate. The effect of wall contact angle on the hydrodynamics and heat transfer in the microchannel is investigated to gain useful insight into the hysteresis phenomenon. It is observed that the hysteresis is significant in super-hydrophilic microchannels, while it disappears at the contact angle of 75^°. The effect of water to oil flow rate ratio (Q_wat/Q_oil) on the heat transfer is also studied. The flow rate ratio has a negligible effect on the Nusselt number (Nu) in the dripping regime, while the Nu decreases with an increase of Q_wat/Q_oil in the co-flow regime. The thickness of the oil film, velocity, and temperature distribution are studied in the co-flow regime. It is revealed that the normalized slip velocity reduces at higher values of Q_wat/Q_oil, which causes a reduction in the averaged Nu. In dripping regimes, higher flow rate ratios lead to a more frequent generation of droplet/slugs at a smaller size. The passage of the slugs or droplets increases the local Nu. Larger droplets generated at lower flow rate ratios cause a larger increase in the local Nu than smaller droplets. The temperature and velocity field around the droplets are also illustrated to investigate the heat transfer improvement. The generated vortex at the tip of the oil jet causes an increase in the velocity and Nu on the water side.     

The characteristics of gas–solid flow and wall heat transfer in a fluidized bed reactor

Numerical study using computational fluid dynamics has been carried out to investigate the heat transfer characteristics of a laboratory fluidized bed reactor. The fluidized bed reactor of vTI (Johann Heinrich von Thünen-Institute)-Institute of Wood Technology and Wood Biology is modeled. For the simulation of multiphase flow and thermal fields, an Eulerian–Eulerian approach is applied. The flow and thermal characteristics of the reactor are fully investigated for the wide range of superficial gas velocities and two different particle diameters. In particular, the contributions of the gas bubble and emulsion phase flows on the wall heat transfer are scrutinized. From the predicted results, it is fully elucidated that particular near-wall bubble motions mainly govern the wall heat transfer.     

Pool boiling heat transfer characteristics of ZrO2–water nanofluids from a flat surface in a pool

Nucleate pool boiling of ZrO₂ based aqueous nanofluid has been studied. Though enhancement in nucleate boiling heat transfer has been observed at low volume fraction of solid dispersion, the rate of heat transfer falls with the increase in solid concentration and eventually becomes inferior even to pure water. While surfactants increase the rate of heat transfer, addition of surfactant to the nanofluid shows a drastic deterioration in nucleate boiling heat transfer. Further, the boiling of nanofluid renders the heating surface smoother. Repeated runs of experiments with the same surface give a continuous decrease in the rate of boiling heat transfer.     

A study on a flexible wing with up–down vibration in a pulsating flow of cooling air to improve heat transfer efficiency

We investigated a flexible wing that can function as a folding fan by vibrating smoothly on a heated surface, and the effects of this vibration on heat transfer. For flexible up–down vibrations of the wing in a pulsating flow, we propose a novel milli-scale flexible wing shape with a relatively large body and a narrow connecting leg. The shape was optimized such that its deformation became much larger at a low air flow. We performed two-way fluid–structure interaction analyses to predict performance, and an experimental validation was also conducted. The details of flow, heat transfer, and structural deformation are summarized qualitatively. Our results show that the heat transfer coefficient of a heated surface with a single flexible wing was approximately 11.3 % greater than that of a flat plate.     

Effect of variable thermal conductivity models on the combined convection heat transfer in a square enclosure filled with a water–alumina nanofluid

In this numerical study, the effects of variable thermal conductivity models on the combined convection heat transfer in a two-dimensional lid-driven square enclosure are investigated. The fluid in the square enclosure is a water-based nanofluid containing alumina nanoparticles. The top and bottom horizontal walls are insulated, while the vertical walls are kept at different constant temperatures. Five different thermal conductivity models are used to evaluate the effects of various parameters, such as the nanofluid bulk temperature, nanoparticle size, nanoparticle volume fraction, Brownian motion, interfacial layer thickness, etc. The governing stream–vorticity equations are solved by using a second-order central finite difference scheme coupled with the conservation of mass and energy. It is found that higher heat transfer is predicted when the effects of the nanoparticle size and bulk temperature of the nanofluid are taken into account.     

Heat transfer in a rotor–stator system with a radial inflow

The object of the present work is to produce a better understanding of the flow and heat transfer process occurring in a rotor-stator system, with a low aspect ratio and subjected to a superposed radial inflow. The theoretical approach presented in a previous paper (Debuchy et al., Eur. J. Mech. B-Fluids 17 (6) (1998) 791–810) in the framework of laminar, steady, axisymmetric flow is extended to heat transfer effects. The asymptotic model is simplified and new integral relations including temperature are indicated. The experiments, made in a rotor–stator system with a heated stationary disc, are in agreement with the features of the model in the explored range of the gap ratio, Ekman and Rossby numbers. The data include radial and circumferential mean velocity components, air temperature inside the cavity, temperature and temperature-velocity correlations, and also local Nusselt numbers measured on the stationary disc. The flow structure near the axis is found to be strongly affected by the presence of a superposed inflow, as already observed under isothermal conditions. By contrast, the mean temperature, as well as the correlations concerning velocity and temperature are smaller when a radial inflow is assigned.     

Experimental study of the condensation heat transfer characteristics of CO2 in a horizontal microfin tube with a diameter of 4.95?mm

The condensation heat transfer characteristics for CO₂ flowing in a horizontal microfin tube were investigated by experiment with respect to condensation temperature and mass flux. The test section consists of a 2,400?mm long horizontal copper tube of 4.6?mm inner diameter. The experiments were conducted at refrigerant mass flux of 400–800?kg/m²s, and saturation temperature of 20–30?°C. The main experimental results showed that annular flow was highly dominated the majority of condensation flow in the horizontal microfin tube. The condensation heat transfer coefficient increases with decreasing saturation temperature and increasing mass flux. The experimental data were compared against previous heat transfer correlations. Most correlations failed to predict the experimental data. However, the correlation by Cavallini et al. showed relatively good agreement with experimental data in the microfin tube. Therefore, a new condensation heat transfer correlation is proposed with mean and average deviations of 3.14 and ?7.6?%, respectively.     

Simulation of conjugate radiation–forced convection heat transfer in a porous medium using the lattice Boltzmann method

In this paper, a lattice Boltzmann method is employed to simulate the conjugate radiation–forced convection heat transfer in a porous medium. The absorbing, emitting, and scattering phenomena are fully included in the model. The effects of different parameters of a silicon carbide porous medium including porosity, pore size, conduction–radiation ratio, extinction coefficient and kinematic viscosity ratio on the temperature and velocity distributions are investigated. The convergence times of modified and regular LBMs for this problem are 15 s and 94 s, respectively, indicating a considerable reduction in the solution time through using the modified LBM. Further, the thermal plume formed behind the porous cylinder elongates as the porosity and pore size increase. This result reveals that the thermal penetration of the porous cylinder increases with increasing the porosity and pore size. Finally, the mean temperature at the channel output increases by about 22% as the extinction coefficient of fluid increases in the range of 0–0.03.

     

Dynamics of a mass–spring–pendulum system with vastly different frequencies

We investigate the dynamics of a simple pendulum coupled to a horizontal mass?Cspring system. The spring is assumed to have a very large stiffness value such that the natural frequency of the mass?Cspring oscillator, when uncoupled from the pendulum, is an order of magnitude larger than that of the oscillations of the pendulum. The leading order dynamics of the autonomous coupled system is studied using the method of Direct Partition of Motion (DPM), in conjunction with a rescaling of fast time in a manner that is inspired by the WKB method. We particularly study the motions in which the amplitude of the motion of the harmonic oscillator is an order of magnitude smaller than that of the pendulum. In this regime, a pitchfork bifurcation of periodic orbits is found to occur for energy values larger that a critical value. The bifurcation gives rise to nonlocal periodic and quasi-periodic orbits in which the pendulum oscillates about an angle between zero and ??/2 from the down right position. The bifurcating periodic orbits are nonlinear normal modes of the coupled system and correspond to fixed points of a Poincare map. An approximate expression for the value of the new fixed points of the map is obtained. These formal analytic results are confirmed by comparison with numerical integration.     

Effects of heat and mass transfer peristaltic flow of?Williamson fluid in a vertical annulus

In the present investigation, we have studied the effects of mixed convection heat and mass transfer on peristaltic flow of Williamson fluid model in a vertical annulus. The governing equations of Williamson fluid model are simplified using the assumptions of long wavelength and low Reynold’s number. An approximated analytical and numerical solutions are found for the velocity field using (i) Perturbation method (ii) Shooting method. The comparisons of analytical and numerical solutions have been presented. The expressions for pressure rise, velocity against various physical parameter are discussed through graphs.     

Stiffness problem in modeling wave flows of heterogeneous media with a three‐temperature scheme of interphase heat and mass transfer

The numerical modeling of wave flows of heterogeneous media with a threetemperature scheme of interphase heat and mass transfer involves the problem of equation stiffness. A discrete model of improved stability was developed to describe these processes. Test calculations of the interaction of a shock wave with a bounded layer of a mixture of a gas and droplets assuming a discrete model over a wide range of initial data showed that the stability conditions do not depend on the rate of interphase interaction (Cstability).     

Finite differences study of ignition in a methane–air mixture flow

A detailed simulation of the ignition process and premixed flames propagation, taking into account molecular transport, chemical reaction, thermodynamics and convection, is built by making use of the implicit finite difference scheme with the help of the Tridiagonal Matrix Algorithm. The velocity of chemical reaction is expressed by means of Arrhenius form of first order in both fuel and oxygen. The main objective of this work is to define numerically in two cases, u=0.1 m/s and u=0.4 m/s, the ignition temperature of the methane–air mixture with different air excess coefficients in the mixture. In addition, the effect of the thickness of the region ignition and of ignition location on the transient behavior of the flame was studied.     

Study of airflow in a cold-region tunnel using a standard k − ε turbulence model and air-rock heat transfer characteristics: validation of the CFD results

An efficient computational fluid dynamics (CFD) method for simulating the flow and convective heat transfer process of airflow in a tunnel is required to analyze the freezing and thawing of surrounding rock and to apply the results to the design of the insulation layer for a tunnel located in a cold region. Comparisons of experimental data and CFD results using a standard k ? ε turbulence model, a wall function, a thermal function and an adaptive finite element method are presented. Comparison of the results indicated that the proposed model and simulation method are efficient at determining the solid–air interface heat coefficient in a thin and infinitely wide horizontal plate and the hydrodynamic and thermal fields in a 3-D cavity. After demonstrating that the necessary validations are satisfied, this paper presents an analysis of the characteristics of airflow and air–rock heat transfer in a cold-region tunnel.     

Dynamics of a cylindrical shell with elastic bottom filled with a gas–liquid mixture and subject to two-frequency excitation

The paper reports experimental data on the nonlinear dynamic deformation of the elastic bottom of a cylindrical shell and the formation of bubbles and their clusters under two-frequency excitation     

Average and extremal properties of heat transfer and shear stress on a wall surface in Rayleigh–Bénard convection

In this study surface-averaged and extremal properties of heat transfer and shear stress on the upper wall surface of Rayleigh–Bénard convection are numerically examined. The Prandtl number was raised up to 10³, and the Rayleigh number was changed between 10⁴ and 10⁷. As a result, average Nusselt number Nu and shear rate τ/Pr depends on Pr, Ra, and the entire numerical results are distributed between two correlation equations corresponding to small and large Pr. The small and large Pr equations are closely related to steady and unsteady flow regimes, respectively. Nevertheless, a single relation τ/Pr ~ Nu ^3.0 exists to explain the entire results. Similarly the change of local maximal properties Nu _max and τ _max/Pr depends on Pr, Ra, and these values are also distributed between two correlation equations corresponding to small and large Pr cases. Despite such complicated dependence we can obtain a correlation equation as a form of τ _max/Pr ~ Nu _max^2.6, which has not been obtained theoretically.     

Experimental investigation on heat transfer of forced convection condensation of ethanol–water vapor mixtures on a vertical mini-tube

In this paper, condensation heat transfer characteristics of ethanol–water vapor mixtures on a vertical mini-vertical tube with 1.221 mm outside diameter were investigated experimentally. The experiments were performed at different velocities and pressures over a wide range of ethanol mass fractions in vapor. The test results indicated that, with respect to the change of the vapor-to-surface temperature difference, the condensation curves of the heat transfer coefficients revealed nonlinear characteristics, and had peak values. At 2 % ethanol mass fraction in vapor, the condensation heat transfer coefficient value of the ethanol–water vapor mixture was found to have a maximum heat transfer coefficient of 50 kW m^?2 K^?1, which was 3–4 times than that of pure steam. The condensation heat transfer coefficients decreased with increased ethanol mass fraction in vapor. The vapor pressure and vapor velocity had a positive effect on the condensation heat transfer coefficients of ethanol–water vapor mixtures.     

Effect of heat flow on heat‐transfer characteristics for a supersonic spatial flow around a spherically blunted cone

Heattransfer processes for a supersonic spatial flow around a spherically blunted cone were studied by solving direct and inverse threedimensional problems taking into account heat flow along the longitudinal and circumferential coordinates. It is shown that highly heatconducting materials can be used to advantage to decrease the maximum temperatures on the windward side of streamline bodies.     

Detection of liquid–vapor–solid triple contact line in two-phase heat transfer phenomena using high-speed infrared thermometry

Heat transfer in complex physical situations such as nucleate boiling, quenching and dropwise condensation is strongly affected by the presence of a liquid–vapor–solid triple contact line, where intense energy transfer and phase change occur. A novel experimental technique for the detection of the liquid–vapor–solid line in these situations is presented. The technique is based on high-speed infrared (IR) thermometry through an IR-transparent silicon wafer heater; hence the name DEPIcT, or DEtection of Phase by Infrared Thermometry. Where the heater surface is wet, the IR camera measures the temperature of the hot water in contact with the heater. On the other hand, where vapor (whose IR absorptivity is very low) is in contact with the heater, the IR light comes from the cooler water beyond the vapor. The resulting IR image appears dark (cold) in dry spots and bright (hot) in wetted area. Using the contrast between the dark and bright areas, we can visualize the distribution of the liquid and gas phases in contact with the heater surface, and thus identify the liquid–vapor–solid contact line. In other words, we measure temperature beyond the surface to detect phases on the surface. It was shown that even small temperature differences (∼1 °C) can yield a sharp identification of the contact line, within about 100 μm resolution. DEPIcT was also shown to be able to detect thin liquid layers, through the analysis of interference patterns.