Convective cooling of supercritical carbon dioxide inside tubes: heat transfer analysis through neural networks

In a previous work, convective heating of carbon dioxide was studied with neural networks (NN), obtaining a totally heuristical heat transfer equation from the direct regression of experimental data. In the present work, the analysis focuses on the cooling process, which has a technical relevance in various applications, as for example in transcritical refrigeration cycles. Heat transfer around the critical zone presents a marked enhancement, that follows the peaks in thermophysical properties like thermal conductivity and heat capacity. Similarly, other properties like density and enthalpy, present a strong variation in narrow temperature intervals around the critical point.This constitutes then a highly non-linear phenomenon, for which it is advisable to use a very flexible function approximator like the NNs. NN models were applied both in terms of dimensionless numbers and of physical quantities, obtaining the two corresponding NN architectures. The choice of the optimal number of neurons in the NN hidden layer is discussed. The NN models are then compared with a recent correlation from literature, for which the validation results present an AAD of 27% and a bias of −26% with an evident prediction shifting. On the other hand the NN models in terms of dimensionless numbers and of physical quantities have AAD and bias of 14% and −4%, and of 7% and −2%, respectively, showing a largely better performance.     

Heat and Mass Transfer Analogy Studies of Binary Liquid Mixture in Comparison with Eteanol-n-Heptane Evaporating to Air

An expenmental and theoretical study of heat and mass transfer analogy and a comparison of that to a binary liquid mixture evaporation is presented. Common organic solvents, ethanol and n-heptane, were used to form an alcohol - hydrocarbon mixture. Studies were carried out in a horizontal rectangular channel having air flow velocities of 0.2 - 0.9 m/s. Heat transfer coefficients were measured with a copper plate resistor and mass transfer coefficients with a square pool. The heat and mass transfer analogy is presented for a system having two evaporating compounds with a fixed value of air flow and verified by measuring and comparing mass transfer coefficients for distilled water with air flow velocities of 0.2 - 0.9 mls. An illustrative example of the use of the theory for industrial ventilation is presented.     

Free convection and mass transfer flow of non-newtonian fluid with thermal diffusion effect

An analytical study is performed to examine the thermal diffusion characteristics of free convection and mass transfer flow in a non-Newtonian fluid (Walters, 1962: liquid B') past a uniformly accelerated infinite vertical plate in the presence of thermal diffusion. The expression for the velocity field is obtained by the Laplace transform technique. The influence of the Soret number (a thermal diffusion parameter) on the velocity field is extensively discussed with the help of graphs.     

An experimental and three-dimensional numerical study of natural convection heat transfer between two horizontal parallel plates

In this study, experimental and three-dimensional numerical studies were performed to investigate the effects of plate spacing and temperature difference on natural convection between isothermally heated upward-facing lower horizontal plate and externally insulated horizontal upper plate. Air is used as the heat transfer medium. Rayleigh number varied in the 1108–2.339 × 10⁵ range. Several numerical simulations for three-dimensional steady laminar and turbulent flows heat transfer were carried out using a commercial CFD code Fluent 6.2. Results have shown that there is a good agreement between the numerical and present experimental results as well as with available data in literature.     

Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below

Natural convection in air-filled 2D square enclosure heated with a constant source from below and cooled from above is studied numerically for a variety of thermal boundary conditions at the top and sidewalls. Simulations are performed for two kinds of lengths of the heated source, i.e., a small and a large source corresponding to 20% and 80% of the total length of the bottom wall, respectively. The Rayleigh number varied from 10³ to 10⁷. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number and maximum temperature at the heat source surface. Comparisons among the different thermal configurations considered are reported.     

Simultaneous mass and heat transfer under mixed convection along a vertical cone

Steady laminar binary mixed convection flow along a vertical circular cone under the combined buoyancy effects of thermal and species diffusion is studied analytically. The analysis is confined to mass diffusion processes with low concentration levels. In the analysis the surface of the cone is assumed to be at a uniform temperature and uniform concentration. Numerical results for the local Sherwood number, local Nusselt number and local friction factor are presented. Representative temperature, concentration and velocity profiles are also shown. The analysis covers the diffusion of common gases and vapours into air. Considerations are given to the situations where the buoyancy forces assist and oppose the forced convection flow for various possible combinations of the thermal and species diffusion processes.     

双参数Bézier曲线的升二次扩展

本文以二次Bernstein基函数为例,首次提出了含双参数基函数的新扩展——αβQ—Bern-stein基函数,此类基函数具有新的特点,即基函数的扩展次数一次性升高两次,且包含了二次多项式和带一个参数的三次多项式基函数的所有性质。基于这组基函数定义了αβQ—Bézier曲线,该曲线也含有参数,具有形状可调性,当α与β取某些值时曲线能达到C4连续或在某个端点处C0连续。最后与含两个参数的升一次Bézier曲线进行比较,该曲线具有调节范围广、灵活性更强的优势。     

Continuous finite element schemes for a phase field model in two-layer fluid Bénard–Marangoni convection computations

In this article, we study a phase field model for a two-layer fluid where the temperature dependence of both the density (buoyancy forces) and the surface tension (Marangoni effects) is considered. The phase field model consisting of a modified Navier–Stokes equation, a Cahn–Hilliard phase field equation and an energy transport equation is derived through an energetic variational procedure. An appropriate variational form and a continuous finite element method are adopted to maintain the underlying energy law to its greatest extent. A few examples for Bénard–Marangoni convection in an Acetonitrile and n-Hexane two-layer fluid system heated from above will be computed to justify our phase field model and further show the good performance of our methods. In addition, an interesting experiment will be performed to show the competition between the Marangoni effects and the buoyancy forces.     

Numerical computation for clustering of carbon particles with various sizes under both natural and magnetizing convections

The behavior of carbon particles from 0.01 to diameters in natural convection flow field of air was numerically studied including the effect of the magnetic field and the Brownian motion. One thousand carbon particles were released randomly in a vertical cylindrical enclosure whose height is equal to its radius. The enclosure was heated from below and cooled from above to produce the bulk flow of the natural convection of air in the atmospheric condition. A coil with electric current was set coaxially at the enclosure bottom to produce a magnetic field. Sample computations are carried out for the enclosure of 3 cm high and maximum magnetic field is 2.8 T or less. The results show that the natural convection of air is enhanced by the magnetic field. With the increase in the magnetic strength, more particles go along the fluid streak lines. With the increase in the particle size, more particles get together at the vortex center and cluster.     

EFFECTS OF ASYMMETRIC TEMPERATURE PROFILES ON THERMAL CONVECTION DURING PHYSICAL VAPOR TRANSPORT OF Hg2Cl2

Asymmetric horizontal thermal profiles can change the flow field structure in the physical vapor transport (PVT)of Hg₂Cl₂. It is found that for the ratios of horizontal to vertical thermal Rayleigh numbers Ra_H/Ra ≥ 1·5, the convetive flow structure changes from multicellular to unicellular for the base parametric state of Ra = 2·79 × 10⁴, Pr = 0·91, Le=l·01. Pe = 4·60, Ar= 0·2 and C_r = 1·01. The unicellular flow structure obtained by increasing ∇*_H(Ra_H) is not likely to support the conjecture of the presence of unicellular convective mode in the laser Doppler velocimetry (LDV) experiments for PVT process of Hg₂Cl₂ (Kim el al., 1996). When the six parameters of Ra, Pr, Le, Pe, Ar and C_r are fixed, the dimensional maximum magnitude of the velocity vector |U|_max is proportional to √∇T*_H.