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.     

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.     

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.     

Inverse solution for a biochemical heat source in a porous medium in the presence of natural convection

The inverse problem approach by conjugate gradient with adjoint equations is adapted to the context of a non-isothermal bioprocess, controlled by internal heat generation from microbial oxidation, as could be found in a composting reactor for instance, to determine the heat source from internal temperature measurements. The volumetric heat source is assumed proportional to the rate of consumption of a substrate by a biomass, as described by a Monod model. Computations are performed for Rayleigh numbers equal to 0.25 and 25, for a representative biochemical reaction under typical boundary conditions, for constant and temperature-dependent model parameters. The influence of noisy input data is also considered. It is found that good solutions can be obtained when heat release and diffusion occur over very different time scales. The variation of the model parameters with temperature must be taken into account, but single sensor solutions are possible at relatively small Rayleigh numbers when convection is present.     

Free convection heat transfer over a horizontal plate at low prandtl number

Boundary layer equations for free convection heat transfer along a semi-infinite horizontal plate are derived by giving more importance to the energy equation. The equations are obtained for low Prandtl number and two separate polynomials are used to approximate the temperature and velocity profiles in these regions. The rate of heat transfer is compared with the available analytical and numerical results based on conventional boundary layer equations.     

空间晶体生长流体效应的实验研究和理论分析

在空间晶体生长实时观察装置上，利用溶液中形成的铌酸钾微晶作示踪粒子，首次在空间高温氧化物熔液内，实时观察和记录了空间表面和力对流效应。利用测量的结果计算了熔体内空间表面张力对流的速度场，并与地面表面张力对流的速度场进行了对比，理论计算与实验结果基本吻合。探讨了空间均匀分布铌酸钾微晶的形成机理。结果表明：表面张务对流在空间晶体生长过程中起主要作用，是形成均匀分布胞状晶体的主要机理。     

Mixed convection heat and Mass transfer in a vertical channel with film evaporation

Numerical results are presented for effects of latent heat transport associated with film vaporization on laminar mixed convection heat and mass transfer in a vertical channel with a half channel width b = 0.01 m. The influences of the inlet liquid mass flowrate and wall temperature on the film vaporization and the associated heat and mass transfer characteristics are examined for air-water and air-ethanol systems with gas Reynolds number Re_g = 2000. Predicted results obtained by including transport in the liquid film are contrasted with those where liquid film transport is neglected, showing that the assumption of an extremely thin film made in Lin et al. (1988) and Yan and Lin (1989) is only valid for systems having small liquid mass flow rates. Additionally, it is found that the interfacial heat flux is predominantly determined by latent heat transfer connected with film evaporation.