Turbulent convective heat transfer of methane at supercritical pressure in a helical coiled tube

The heat transfer of methane at supercritical pressure in a helically coiled tube was numerically investigated using the Reynolds Stress Model under constant wall temperature. The effects of mass flux (G), inlet pressure (P_in) and buoyancy force on the heat transfer behaviors were discussed in detail. Results show that the light fluid with higher temperature appears near the inner wall of the helically coiled tube. When the bulk temperature is less than or approach to the pseudocritical temperature (T _pc ), the combined effects of buoyancy force and centrifugal force make heavy fluid with lower temperature appear near the outer-right of the helically coiled tube. Beyond the T _pc , the heavy fluid with lower temperature moves from the outer-right region to the outer region owing to the centrifugal force. The buoyancy force caused by density variation, which can be characterized by Gr/Re² and Gr/Re^2.7, enhances the heat transfer coefficient (h) when the bulk temperature is less than or near the T _pc , and the h experiences oscillation due to the buoyancy force. The oscillation is reduced progressively with the increase of G. Moreover, h reaches its peak value near the T _pc . Higher G could improve the heat transfer performance in the whole temperature range. The peak value of h depends on P_in. A new correlation was proposed for methane at supercritical pressure convective heat transfer in the helical tube, which shows a good agreement with the present simulated results.     

Exergy transfer in a porous rectangular channel

Present paper is performed to investigate the heat and exergy transfer characteristics of forced convection flow through a horizontal rectangular channel where open-cell metal foams of different pore densities such as 10, 20 and 30 PPI (per pore inches) were situated. All of the bounding walls of the channel are subjected to various uniform heat fluxes. The pressure drop and heat transfer characteristics are presented by two important parametric values, Nusselt number (Nu_H) and friction factor (f), as functions of Reynolds number (Re_H) and the wall heat flux (q). The Reynolds number (Re_H) based on the channel height of the rectangular channel is varied from 600 to 33?000, while the Grashof number (Gr_Dh) ranged from approximately 10⁵–10⁷ depending on q. Based on the experimental data, new empirical correlations are constructed to link the Nu_H. The results of all cases are compared to that of the empty channel and the literature. It is found that the results are in good agreement with those cited in the references. The mean exergy transfer Nusselt number (Nu_e) based on the Re_H, Nu_H, Pr and q for a rectangular channel with constant heat flux is presented and discussed.     

Heat transfer in a small gap between co-axial rotating cylinders

This paper investigates the local heat transfer of a co-axial rotating cylinder. In the inner flow field of the rotating cylinder, the dimensionless parameters include the rotational Reynolds number (Re_Ω) and buoyancy parameter (Gr). The test rig is designed to make the rotating in the inner cylinder and stationary in the outer cylinder. The local temperature distributions of the inner and outer cylinder on axial direction were measured. Under the experimental condition, whereas the ranges of the rotational Reynolds number are 2400 ≤ Re_Ω ≤ 45,000. Experimental results reveal that the rotational Reynolds number's increase is with the heat transfer coefficient distributions increase types. Finally, the local heat transfer rate on the wall are correlated and compared with that in the existing literature.     

Natural convective flow and heat transfer of supercritical CO2 in a rectangular circulation loop

Fluid dynamics and heat transfer of supercritical CO₂ natural convection are important for nuclear engineering and new energy system design etc. In this paper, in order to study the flow and heat transfer behavior of supercritical CO₂ natural circulation system, a computational simulation on a closed natural circulation loop (NCL) model has been carried out. The fluid temperature in the loop varies between 298.15 K and 323.15 K, which is across the CO₂ critical temperature, and the density is found to be in the range of 250–800 kg/m³. The results show a small temperature difference of 25 °C between heating and cooling sources can induce a mass flow with the Reynolds number up to 6 × 10⁴ using supercritical CO₂ fluid. A periodic reversal flow pattern is found and presented in this paper. Enhanced heat transfer phenomenon is also found for the supercritical CO₂ natural convective flow. The mechanisms to this enhancement and the heating effect on the flow are also discussed in detail in the present study.     

Predictions of In-Tube Cooling Heat Transfer Coefficients and Pressure Drops of CO2 and Lubricating Oil Mixture at Supercritical Pressures

The in-tube cooling heat transfer and flow characteristics of supercritical pressure CO₂ mixed with small amounts of lubricating oil differ from those for pure CO₂ due to the entrainment of the lubricating oil as well as the sharp property variations of the supercritical CO₂ working fluid. In-tube gas cooling flow and heat transfer models were developed in this study for CO₂ with entrained polyol ester type lubricating oil in a CO₂ gas cooler at supercritical pressures. A “thermodynamic approach,” which treats the CO₂–oil mixture as a homogenous mixture was used with the heat transfer coefficients and frictional pressure drops evaluated based on the thermophysical properties of the CO₂–oil mixture. Thermophysical property variation correction terms as a function of the wall temperature and the oil concentration were included in the models. The frictional pressure drop correlation predicts more than 90% of the experimentally measured data within ±10%, while the heat transfer coefficient correlation predicts more than 90% of the experimentally measured data within ±20%.     

Convective mass transfer from a horizontal rotating large-diameter cylinder

The local and average convective mass transfer coefficients from the porous medium surface of a horizontal rotating large-diameter cylinder were measured at a constant mass transfer state. Characteristics of local and average Sherwood numbers varying with rotational Reynolds numbers were investigated. Further, the critical Reynolds number (Re_r,cri) was determined and analyzed. Based on the experimental results, equations correlating the average Sherwood number (Sh) and critical Reynolds number (Re_r,cri) with the rotational Reynolds number (Re_r), Schmidt number (Sc) and Grashof number (Gr) have been obtained, respectively.     

Low Reynolds number mixed convection in vertical tubes with uniform wall heat flux

Upward mixed convection of air in a long, vertical tube with uniform wall heat flux has been studied numerically for Re=1000, Re=1500 and Gr?10⁸ using a low Reynolds number k-ε model. The results for the fully developed region identify two critical Grashof numbers for each Reynolds number, which correspond to laminar-turbulent transition and relaminarization of the flow. They also distinguish the Re-Gr combinations that result in a pressure decrease over the tube length from those resulting in a pressure increase. A correlation expressing the fully developed Nusselt number in terms of the Grashof and Reynolds numbers is proposed. It is valid for laminar and turbulent flows in the range 1000?Re?1500, Gr?5×10⁷.     

A correlation for mixed convection heat transfer from converging,parallel and diverging channels with uniform volumetric heat generating plates

A numerical study of steady, laminar, mixed convection heat transfer from volumetrically heat generating converging, parallel and diverging channels is carried out. Air is considered as the working fluid. The maximum angle of deviation (ϕ) of the channel plates from the vertical position for the converging and diverging channels is 2° and − 2°, respectively. A parametric study has been carried out for a wide range of Re_S, Gr_S^⁎, γ and ϕ to investigate their effect on the fluid flow and heat transfer characteristics. A universal correlation, to estimate the non-dimensional maximum temperature occurring in the converging, parallel or diverging channels is presented.     

Study of melt convection and interface shape during sapphire crystal growth by Czochralski method

Global simulation is performed to predict electromagnetic field, heat transfer, melt flow, and interface shape during the different growth stages of sapphire crystal by RF-heated Czochralski (Cz) process. Melt flow in the Cz-sapphire growth system includes Marangoni convection due to the variation of surface tension at the free surface, natural convection due to the complex thermal boundary conditions on the crucible walls, and forced convection due to the crystal rotation. As the crystal grow longer, the effects of the convections on the melt flow, temperature distribution and interface shape varies due to the drop of melt, which can be characterized by Grashof number (Gr) with the melt height as the characteristic length. It is found that as melt height reduces, natural convection gets weaker, and the interface becomes flatter. To examine systematically the effects of the convections on the crystal growth process, three dimensionless parameters, N_σ, Gr/Re² and N_σ2, are further introduced. N_σ denotes the influence of surface tension in the boundary layer as compared with buoyancy in the melt, Gr/Re² is the ratio of convective forces to the normalizing convective velocities with viscosity, and N_σ2 represents the relative strength of Marangoni flow to forced convection. The effects of the parameters on the melt flow and heat transfer are examined, and their relationships to the interface convexities are obtained. The understanding of melt convection and interface shape is not only important for the optimization of a stable sapphire crystal growth, but also critical for an accurate modeling of the growth process.     

Near-Critical Natural Circulation Flows Inside an Experimental Loop: Stability Map and Heat Transfer

The near-critical CO₂-based natural circulation loop (NCL, or thermosyphon) has been proposed in many energy conversion systems, such as the solar heater, waste heat recovery, next-generation nuclear cooling, and so on. There is an increasing need to obtain detailed information about such systems, as it is less verified from a basic system operation viewpoint. This paper presents an experimental investigation of a near-critical CO₂ thermosyphon. The closed thermosyphon is specially designed for high-pressure (in the critical region, from 6.0 MPa to 15.0 MPa), natural circulation flows. The basic transient flow behaviors and parameter behaviors are found to be dependent on initial pressure. The system stability evolution from subcritical oscillating flow to supercritical stable operations is presented. From the experimental data analysis, the stability map for the current supercritical natural circulation loop system is given. It is found that the stability pressure lines will divide the operation into stable, transition, and unstable regions. It is found that the effectiveness of the cooler will greatly affect the system stability, while the heat transfer efficiency is mainly controlled by the heater conditions. Parameter evolutions of the fluid temperature, mass flow rate, and loop pressure are presented in this paper. The heat transfer dependency on operation pressure and evolution mechanisms are also discussed in detail in this paper.     

Free convection effect on mhd coupled heat and mass transfer of a moving permeable vertical surface

The purpose of this paper is to consider numerically the free convection effect on magnetohydrodynamic heat and mass transfer of a continuously moving permeable vertical surface. The surface is maintained at linear temperature and concentration variations. The similar equations were solved by using a suitable variable transformation and employing an implicit finite difference method. Numerical results were graphically given for the Nusselt number and the Sherwood number for various parameters. Generally, it is found that the Nusselt number and the Sherwood number increase for the suction case, increasing the buoyancy ratio N and the buoyancy parameter Gr_T/Re² and for the decrease of magnetic parameter M. Furthermore, the Nusselt (Sherwood) number increases for the decrease (increase) of Schmidt number Sc.     

Study of Variable Turbulent Prandtl Number Model for Heat Transfer to Supercritical Fluids in Vertical Tubes

In order to improve the prediction performance of the numerical simulations for heat transfer of supercritical pressure fluids, a variable turbulent Prandtl number (Pr_t) model for vertical upward flow at supercritical pressures was developed in this study. The effects of Pr_t on the numerical simulation were analyzed, especially for the heat transfer deterioration conditions. Based on the analyses, the turbulent Prandtl number was modeled as a function of the turbulent viscosity ratio and molecular Prandtl number. The model was evaluated using experimental heat transfer data of CO₂, water and Freon. The wall temperatures, including the heat transfer deterioration cases, were more accurately predicted by this model than by traditional numerical calculations with a constant Pr_t. By analyzing the predicted results with and without the variable Pr_t model, it was found that the predicted velocity distribution and turbulent mixing characteristics with the variable Pr_t model are quite different from that predicted by a constant Pr_t. When heat transfer deterioration occurs, the radial velocity profile deviates from the log-law profile and the restrained turbulent mixing then leads to the deteriorated heat transfer.     

Mixed convection heat and mass transfer along a vertical wavy surface

A numerical study of mixed convection heat and mass transfer along a vertical wavy surface has been carried out numerically. The wavy surface is maintained at uniform wall temperature and constant wall concentration that is higher than that of the ambient. A simple coordinate transformation is employed to transform the complex wavy surface to a flat plate. A marching finite-difference scheme is used for present analysis. The buoyancy ratio N, amplitude-wavelength ratio α, and Richardson number (Gr/Re²) are important parameters for this problem. The numerical results, including the developments of skin-friction coefficient, velocity, temperature, concentration, Nusselt number as well as Sherwood number along the wavy surface are presented. The effects of the buoyancy ratio N and the dimensionless amplitude of wavy surface on the local Nusselt number and the local Sherwood number have been examined in detail.     

Mixed convective cooling of a fin in a channel

Mixed convection heat transfer in an inclined parallel-plate channel with a transverse fin located at lower channel wall is investigated numerically. Employing the stream function vorticity transformation, solution of the transformed governing equations for the system is obtained by the control-volume method with non-uniform grid. The results indicate that the optimum aspect ratio of a fin corresponding to the fin with maximum heat transfer rate increases with increasing Re but decreases with K for a fixed fin profile area. Also, the optimum aspect ratio increases with the inclination angle for Gr/Re² = 10; whereas the effects of orientation on the optimum aspect ratio is not pronounced for Gr/Re² < 1. In addition, the optimum aspect ratio of a fin with a smaller fin profile area and Re at Gr/Re² = 0.1 approaches that of analytical solution having the assumption of constant heat-transfer-coefficient.     

An experimental study on convection heat transfer from an array of discrete heat sources

Convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally for air. The lower surface of the channel was equipped with 8×4 flush-mounted heat sources subjected to uniform heat flux; the sidewalls and the upper wall were insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR=2, Reynolds numbers 864≤Re_Dh≤7955, and modified Grashof numbers Gr*=1.72×10⁸ to 2.76×10⁹. From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit.     

Performance of a flat-plate solar thermal collector using supercritical carbon dioxide as heat transfer fluid

Energetic and exergetic performance analyses of flat-plate solar collector using supercritical CO₂ have been done in this study. To take care of the sharp change in thermophysical properties in near critical region, the discretisation technique has been used. Effects of zonal ambient temperature and solar radiation, fluid mass flow rate and collector geometry on heat transfer rate, collector efficiency, heat removal factor, irreversibility and second law efficiency are presented. The optimum operating pressure correlation has been established to yield maximum heat transfer coefficient of CO₂ for a certain operating temperature. Effect of metrological condition on heat transfer rate and collector efficiency is significant and that on heat removal factor is negligible. Improvement of heat transfer rate is more predominant than increase in irreversibility by using CO₂. For the studied ranges, the maximum performance improvement of flat-plate solar collector by using CO₂ as the heat transfer fluid was evaluated as 18%.     

Numerical Investigation of Conjugate Heat Transfer to Supercritical CO2 in a Vertical Tube-in-Tube Heat Exchanger

Conjugate heat transfer to supercritical CO₂ in a vertical tube-in-tube heat exchanger was numerically investigated. The results demonstrate that most models considered are able to reproduce the heat transfer processes qualitatively, and the Abe, Kondoh, and Nagano model shows optimal agreement with the experimental data. The influences of hot fluid mass flux and temperature of the shell side, supercritical fluid mass flux of the tube side, flow direction, and pipe diameter on conjugate heat transfer were investigated based on velocity and turbulence fields. It is concluded that hot fluid mass flux and temperature of the shell side significantly affect heat transfer of the tube side. Mixed convection is the main heat transfer mechanism for the supercritical CO₂ conjugate heat transfer process when the inner diameter of the tube is greater than 1 mm. In addition, density variation is highly significant for heat transfer of supercritical CO₂ while high viscosity hinders the distortion of the flow field and reduces deterioration in heat transfer.     

Laser schlieren measurement of vertical flow past a heated horizontal circular cylinder

Flow past a heated horizontal circular cylinder in the vertically upward direction has been experimentally studied using a monochrome schlieren technique. Both free convection ((Gr)^1/3Re)=0 and mixed convection ((Gr)^1/3Re)=1011, 1055, 1095 and 1133 cases have been studied. The Reynolds number based on the cylinder diameter is set at 102 for the mixed convection, and four heating levels have been utilized with Grashof numbers of Gr=975, 1105, 1240 and 1370. The temperature distribution of the plume, the Strouhal number and the schlieren images have been reported. The vortex shedding frequency decreases with increasing Grashof number and a complete suppression of vortex shedding takes place at Grashof number of 1370. The wake is seen to become visibly narrow during the suppression of vortex shedding. The nondimensional temperature profile inside the plume is a strong function of Grashof number for free convection in comparison to that of mixed convection.     

Heat and mass transfer from a single horizontal tube of an evaporative tubular heat exchanger

In this investigation, water side heat transfer coefficients without air flow from a single horizontal tubes are determined. Mass transfer coefficients are determined with water and air flow from the same tube. The total energy dissipated by inside hot fluid when only water is falling is compared with that when both the air and water flow past the tube. The water side heat transfer coefficient and mass transfer coefficient are given by empirical relations h_w = 6.0(Re_p)^0.18(Re_w)^0.87 and K = 3.5(Re_p)^0.18(Re_a)^0.28 (Re_w)^0.54, respectively. The ratio of energies dissipated with water and air flow and with only water flow increases with Re_w and Re_a and its maximum value is 1.72 in the range of variables used.     

An experimental investigation on characteristics of supercritical CO2‐based solar Rankine system

In this paper, the characteristics of the supercritical CO₂‐based Rankine cycle powered by solar energy are experimentally investigated. In order to study the controlling factors of system performances, in the experimental setups an electrical heating section as well as an evacuated solar collect is utilized. Also, corresponding heat transfer measurements of the supercritical CO₂ fluid in the heating section are conducted. Results show that the collecting efficiency will increase with the CO₂ mass flow rate. The increase in solar radiation and the decrease in condensation temperature in the cycle both can lead to the increase in CO₂ mass flow. It is also found that the CO₂ fluid flow in the heating section is not fully developed and the Local Nusselt number decreases along the flow direction of the testing pipe. The influences of pressure as well as other controlling factors on heat transfer are also analyzed in detail in this paper. Copyright © 2010 John Wiley & Sons, Ltd.