Comparative numerical study of single and two-phase models of nanofluid heat transfer in wavy channel

The main purpose of this study is to survey numerically comparison of two- phase and single phase of heat transfer and flow field of copper-water nanofluid in a wavy channel. The computational fluid dynamics （CFD） prediction is used for heat transfer and flow prediction of the single phase and three different two-phase models （mixture, volume of fluid （VOF）, and Eulerian）. The heat transfer coefficient, temperature, and velocity distributions are investigated. The results show that the differences between the temperature fie].d in the single phase and two-phase models are greater than those in the hydrodynamic tleld. Also, it is found that the heat transfer coefficient predicted by the single phase model is enhanced by increasing the volume fraction of nanoparticles for all Reynolds numbers; while for the two-phase models, when the Reynolds number is low, increasing the volume fraction of nanoparticles will enhance the heat transfer coefficient in the front and the middle of the wavy channel, but gradually decrease along the wavy channel.     

Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial- and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height.     

Direct Numerical Simulation of particulate flow with heat transfer

Numerical simulations of heat transfer in non-isothermal particulate flows are important to better understand the flow pattern. The complexity of numerical algorithms coupling the heat and mass transfer and the considerable computational resources required limit the number of such direct simulations that can be reasonably performed. We suggest a Distributed Lagrange Multiplier/Fictitious Domain (DLM/FD) method to compute the temperature distribution and the heat exchange between the fluid and solid phases. The Boussinesq approximation is considered for the flow/temperature fields coupling. We employ a Finite Element Method (FEM) to solve the fluid flow conservation equations for mass, momentum and energy. The motion of particles is computed by a Discrete Element Method (DEM). On each particle, heat transfer is solved using a FEM. For each class of particles, we generate a single FEM grid and translate/rotate it at each time step to match the physical configuration of each particle. Distributed Lagrange multipliers for both the velocity and temperature fields are introduced to treat the fluid/solid interaction. This work is an extension of the method we proposed in Yu et al. (2006). Two two-dimensional (2D) test cases are proposed to validate the implementation by comparing our computational results with those reported in the literature. Finally, the sedimentation of a single sphere in a semi-infinite channel is presented and the results are discussed.     

Untersuchung von Schwingungen einer Zweiphasenströmung durch Druckabfall und Dichtewellen mit Hilfe finiter Differenzen

The previous experimental analysis has indicated the existence to two major modes of oscillations, i.e., Density-Wave (high frequency) and Pressure-Drop (low frequency) Oscillations in single channel, electrically heated, forced convection upflow systems. In this work the stability of such a system is investigated theoretically and the results are compared with experimental findings obtained by the authors. The Homogeneous Phase Equilibrium model is used to describe the two-phase flow characteristics. The friction between the pipe wall and the expanding fluid is modeled using the Moody friction factor assuming an effective two-phase viscosity. Gravitational forces are included and heat transfer into the fluid is assumed to be the function of the wall temperature, fluid temperature and heat transfer coefficient which is also assumed to be a function of the flow rate. Though simple, this model is found to be very satisfactory in simulating both modes of oscillations with acceptable accuracy. The physical nature of each mode is different and distinct, therefore, separate solution methods are developed for each case. The Steady-State Flow Characteristics are obtained for various heat inputs and inlet temperatures by solving the conservation equations together with the equation of state by using an Implicit Finite- Difference technique. In the analysis of low frequency oscillations it is assumed that the quasi-steady state conditions prevail in the heater. The system equations obtained with this assumption are solved under constant exit pressure and constant container pressure boundary conditions using the finite-difference technique. Two methods of approach are adapted in solving the non-linear hyperbolic equations which describe the system at low mass flow rates where the density-wave type oscillations are observed. They are the Explicit Integral Momentum method (EIM) and the Explicit Finite-Difference method (EFD). A comparison of the results with experiments and other mathematical models is discussed.     

Heat transfer correlation for boiling flows in small rectangular horizontal channels with low aspect ratios

In the present experimental study, a correlation is proposed to represent the heat transfer coefficients of the boiling flows through horizontal rectangular channels with low aspect ratios. The gap between the upper and the lower plates of each channel ranges from 0.4 to 2 mm while the channel width being fixed to 20 mm. Refrigerant 113 was used as the test fluid. The mass flux ranges from 50 to 200 kg/m² s and the channel walls were uniformly heated up to 15 kW/m². The quality range covers from 0.15 to 0.75 and the flow pattern appeared to be annular. The modified Lockhart–Martinelli correlation for the frictional pressure drop was confirmed to be within an accuracy of ±20%. The heat transfer coefficients increase with the mass flux and the local quality; however the effect of the heat flux appears to be minor. At the low mass flux condition, which is more likely to be with the smaller gap size, the heat transfer rate is primarily controlled by the liquid film thickness. A modified form of the enhancement factor F for the heat transfer coefficient in the range of Re_LF200 well correlates the experimental data within the deviation of ±20%. The Kandlikar's flow boiling correlation covers the higher mass flux range (Re_LF>200) with 10.7% mean deviation.     

Effectiveness of a multi-channel volumetric air receiver for a solar power tower

In this study, the heat transfer performance of a multi-channel volumetric air receiver for a solar power tower was numerically analyzed. The governing equations, including the solar radiation heat flux, conduction, convection and radiation heat transfer for a single channel, were solved on the basis of valid related references and a methodology that can predict the temperature distribution of the receiver wall and the heat transfer fluid for specific dimensions and input conditions. Furthermore, a mathematical model of the effectiveness of the receiver was derived from an analysis of the temperature profiles of the wall and the heat transfer fluid. The receiver effectiveness as an appropriate criterion to assess economic feasibility regarding geometric size was investigated, as it would be applied to the design process of the receiver. The main parameters for the thermal performance simulations described in this paper are the air mass flow rate, receiver length and the influence of these parameters on the heat transfer performance from the viewpoint of receiver efficiency and effectiveness.     

Research on heat transfer of two-phase dispersed flow in narrow annular channel

Narrow channel heat transfer technique is a new developing heat transfer technique in recent years. As the temperature of droplet, steam and wall are decided by forced convection heat transfer between the steam and the wall, between the droplet and the wall, between the steam and the droplet and radiation heat transfer, which makes heat transfer mechanism of dispersed flow be difficultly interpretative. Dispersed flow in narrow annular channel is analyzed in the paper, investigating the influence of all kinds of heat transfer processes on dispersed flow, building annular channel dispersed flow model using thermodynamic non-equilibrium model. Calculation results show heat transfer is mainly controlled by heat transfer process between steam and wall. When temperature is low, radiation can be ignored on heat transfer coefficient calculation. The calculation of model can provide a reference for engineering application of steam generator, refrigeration system and so on.     

Numerical simulation of flow boiling for organic fluid with high saturation temperature in vertical porous coated tube

A semi-analytical model is developed for the prediction of flow boiling heat transfer inside vertical porous coated tubes. The model assumes that the forced convection and nucleate boiling coexist together in the annular flow regime. Conservations of mass, momentum, and energy are used to solve for the liquid film thickness and temperature. The heat flux due to nucleate boiling consists of those inside and outside micro-tunnels. To close the equations, a detailed analysis of various forces acting on the bubble is presented to predict its mean departure diameter. The active nucleation site density of porous layer is determined from the pool boiling correlation by introducing suppression factor. The flow boiling heat transfer coefficients of organic fluid (cumene) with high saturation temperature in a vertical flame-spraying porous coated tube are studied numerically. It is shown that the present model can predict most of the experimental values within ±20%. The numerical results also indicate that the nucleate boiling contribution to the overall heat transfer coefficient decreases from 50% to 15% with vapor quality increasing from 0.1 to 0.5.     

Adverse and favorable mixed convection heat transfer in a two-side heated square channel

Experimental heat transfer measurements and analysis for mixed convection in a vertical square channel are presented. Water flow directions are selected such that buoyancy assists or opposes the bulk flow pressure gradient. Unlike most previous experiments with symmetrically heated circular tubes, the present configuration uses an asymmetric heating condition (two sides heated and two sides insulated) and shows significant increase in the Nusselt number for both assisted and opposed flow conditions. Observed heat transfer coefficient distributions are different from the symmetrically heated channels; and this difference in heat transfer coefficient is attributed to the formation of buoyancy driven large-scale flow structures. In general, opposed flow shows higher heat transfer coefficients, and the Nusselt number ratio is observed to increase as Gr/Re or Gr/Re² ratios increase for both assisted and opposed flow conditions. A correlation based on the buoyancy parameter predicts the heat transfer pattern well in both assisted and opposed mixed convection. The range of Reynolds numbers discussed (Re=400–10,000) is of importance for direct numerical simulations and the details provided here can serve as the benchmark data required for complicated buoyancy affected turbulence simulations.     

Rarefied gas flow in a channel with specular‐diffuse boundary conditions for arbitrary knudsen numbers. Onsager relations

The problem of a rarefied gas flow in a channel for arbitrary Knudsen numbers has been solved analytically for the first time in the case where the scattering of gas molecules on the channel walls can be described by speculardiffuse boundary conditions. The mean free path of gas molecules is assumed to be constant, i.e., the collision frequency is proportional to molecular velocity. The gas moves under the action of a streamwise temperature gradient. Exact relations for heat and mass fluxes and for meanmass velocity are obtained. It is shown that the Onsager relations are valid within the entire range of Knudsen numbers in the problem of heat and mass transfer in a channel. The dependence of heat and mass fluxes on the Knudsen number (channel thickness) is analyzed. A comparison with available results is performed.     

Heat and mass transfer at rotary heat exchangers in consideration of the condensation potential

In many industrial processes as well as in air conditioning systems heat and moisture is transferred by rotary heat exchangers from the warm exhaust air flow to the cold supply air flow. Rotary heat exchangers are classified as sorption rotors, hygroscopic rotors and condensation rotors. Basic mechanisms of heat and moisture transfer are presented. By means of the condensation potential as the difference between the moisture content of the warm air flow and the moisture content of the cold air flow at saturation the humidity transfer at the different rotor types is investigated. The condensation potential as a reference parameter provides the possibility to describe the influence of various air conditions in exhaust air and supply air flow on the humidity transfer of different rotary heat exchangers and to compare these rotors with each other. In order to give an overview of relevant design parameters, the influence of the speed of turning, the flute height of the rotor matrix and the velocity of the air flow regarding the heat and mass transfer is considered.     

On selection of reference temperature of heat transfer coefficient for complicated flows

Convective heat transfer coefficient is closely related with flow and thermal conditions. To define heat transfer coefficient, a reference temperature needs to be properly selected, which can be the fluid bulk mean temperature for internal flows or the temperature at the far field for external flows. For complicated flows, the adiabatic wall temperature is commonly adopted as the reference temperature, while other options can also be applied. This paper analyzed some of the potential selections of the reference temperature for different flow settings, including film cooling, jet impingement with cross flows, and a mixing flow in a straight duct with or without internal heat source. It is observed that heat transfer coefficient changes dramatically with selection of reference temperatures. In case of constant wall temperature, using adiabatic wall temperature as reference temperature can result in negative heat transfer coefficient, which means the heat flux has a different direction with the defined driving temperature difference. To avoid the inconsistency due to the reference temperature, an innovative method is proposed to calculate the heat transfer coefficient of complicated flows.     

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.     

Numerical Study of Heat Transfer in a Rectangular Channel with Porous Covering Obstacles

A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered. The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with the increase of Reynolds number.     

Heat and mass transfer characteristics of a new combined absorber-evaporator exchanger operating near the triple point of water

The present experimental study investigates the controlling mechanism involved in a new combined vertical film-type absorber-evaporator exchanger operating near the condition of the triple point of water. This peculiar exchanger plays the most important role in the VFVPE process that can be utilized in many industrial applications, water pollution prevention, desalination, and purification of chemicals, for example. The method of analogy of the heat and mass transfer near the film surface is used to calculate the interfacial concentration and temperature, and thus determining the heat and mass transfer coefficients. It is shown that the working temperature level has the negligible effect on the characteristics of the mass transfer. The mass transfer coefficients are higher than those obtained in the case of isothermal absorption due to the convective effect arisen from vapor absorption in the falling solution film. The water flow rate in the evaporator side has a minor effect on the performance of this combined exchanger. The overall mean heat transfer coefficient remains nearly constant in the lower range of the solution flow rate of the absorber; however, it would increase with increasing solution flow rate in the higher range. The correlating equations for both the heat and mass transfer coefficients are suggested.     

Effects of radiation on turbulent natural convection in channel flows

A computational study has been carried out to analyse complex interaction of radiation with turbulent natural convective flow of dry and humid air in open-ended channels. Transient flow simulations are undertaken in the channel with one uniformly heated wall and adiabatic side walls for different values of emissivity of active walls with and without participating medium. To adequately present turbulence and radiation, a computational model included large eddy simulations for the turbulent flow coupled with discrete ordinates method for radiation transfer. Spectral line-based weighted-sum-of-grey-gases for the absorption properties of water vapour has been adopted. Complex three-dimensional vortical structures are identified which directly affect the temperature distribution on the heated wall. Including wall to wall radiation resulted in significant changes in the heat transfer, reaching 14 °C temperature drop at the hot wall with wall emissivity of 0.9. Mixing and cooling rates in this case were increased by up to 25%. Including gas radiation for the humid air with the water vapour molar fraction of 0.02 corresponding to saturated conditions at inlet temperature of 25 °C did not have a significant effect on the mean flow and temperature values comparing with wall to wall radiation. However, turbulent statistics have changed significantly resulting in a delayed transition to turbulence near the active wall of the channel and increased turbulent activity near the cold wall. The model developed in the present study is also applicable in fire management, where the aim is to reduce the damage that occurs when a PV module is exposed to high temperatures.     

Experimental investigation of vapor bubble growth during flow boiling in a microchannel

Experiments were conducted to analyze flow boiling characteristics of water in a single brass microchannel of 25 mm length, 201 μm width, and 266 μm depth. Different heat flux conditions were tested for each of two different mass flow rates over three different values of inlet fluid temperature. Temporal and spatial surface temperature profiles were analyzed to show the relative effect of axial heat conduction on temperature rise along the channel length and the effect of flow regime transition on local surface temperature oscillation. Vapor bubble growth rate increased with increasing wall superheat. The slower a bubble grew, the further it was carried downstream by the moving liquid. Bubble growth was suppressed for increased mass flux while the vapor bubble was less than the channel diameter. The pressure spike of an elongating vapor bubble was shown to suppress the growth of a neighboring bubble by more than 50% of its volume. An upstream progression of the Onset of Bubble Elongation (OBE) was observed that began at the channel exit and progressed upstream. The effects of conjugate heat transfer were observed when different flow regime transitions produced different rates of progression for the elongation sequence. Instability was observed at lower heat fluxes for this single channel experiment than for similar studies with multiple channels.     

Periodic boiling in parallel micro-channels at low vapor quality

Based on experimental investigations the present study evaluates instability and heat transfer phenomenon under condition of periodic flow boiling of water and ethanol in parallel triangular micro-channels. Tests were performed in the range of hydraulic diameter 100–220 μm, mass flux 32–200 kg/m² s, heat flux 120–270 kW/m², vapor quality x = 0.01–0.08. The period between successive events depends on the boiling number and decreases with an increase in the boiling number. The initial film thickness decreases with increasing heat flux. When the liquid film reached the minimum initial film thickness CHF regime occurred. Temporal variations of pressure drop, fluid and heater temperatures were periodic. Oscillation frequency is the same for the pressure drop, for the fluid temperature at the outlet manifold, and for the mean and maximum heater temperature fluctuations. All these fluctuations are in phase. The CHF phenomenon is different from that observed in a single channel of conventional size. A key difference between micro-channel heat sink and single conventional channel is amplification of parallel-channel instability prior to CHF. The dimensionless experimental values of the heat transfer coefficient are presented as the Nusselt number dependence on the Eotvos number and the boiling number.     

Buoyancy effects on mixed convection heat and mass transfer in a duct with sudden expansions

The present paper deals with the study of heat and mass transfer by mixed convection in an inclined duct preceded with a double step expansion. The control volume based finite element method was used to solve the set of non-dimensional equations for the vorticity, stream function, energy and species conservation. Numerical simulations are carried out for different combinations of the Lewis number, thermal and mass diffusion Grashof numbers for different inclinations. Streamlines, temperature and concentration distributions are presented and discussed. The results show the effect of the secondary flow induced by buoyancy forces and the presence of the double step expansion on the heat and mass transfer mechanism. It is found that the recirculation vortices induced by the expansion can be present along the channel and the flow structure can be wavy. For the vertical orientation, asymmetric fields are observed for the different simulated cases.     

Boiling heat transfer,pressure drop,and flow pattern in a horizontal square minichannel

This study experimentally investigated the flow boiling heat transfer, pressure drop, and flow pattern in a horizontal square minichannel with a hydraulic diameter of 2.0 mm, and the effects of mass flux, vapor quality, heat flux, and refrigerant properties on the flow boiling characteristics were clarified. The heat transfer coefficient and pressure drop of R32 and R1234yf were measured in a mass flux range of 50–400 kgm⁻²s⁻¹ at a saturation temperature of 15 °C. The flow pattern of the square minichannel outlet was observed and was classified as plug, wavy, churn, and annular flows. The heat transfer coefficients in the square minichannel were larger than those in the circular minichannel with a similar hydraulic diameter at low mass flux conditions. The heat transfer coefficients of R32 indicated higher values compared with those of R1234yf at same mass flux and qualities. An empirical heat transfer model taking into account the forced convection, nucleate boiling, and thin liquid film evaporation was developed for horizontal square and circular minichannels. The frictional pressure drop of R32 was 1.5–2 times higher than that of R1234yf at same mass flux and vapor quality condition, and the effect of channel shape on the frictional pressure drop was small unlike the boiling heat transfer.