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Deyi Shang - One of the best experts on this subject based on the ideXlab platform.
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Effects of Various Physical Conditions on Heat Transfer of the Free Convection Film Condensation
Heat and Mass Transfer, 2012Co-Authors: Deyi ShangAbstract:In this chapter, the Film Condensation of saturated water vapor is taken as an example for analyzing the effects of various physical conditions on heat transfer. The effects of four physical conditions including Boussinesq approximation (i.e. ignoring variable physical properties), shear force at the liquid–vapor interface, inertia force of the condensate Film, and the thermal convection of the condensate Film on the heat transfer coefficient of the Film Condensation are deeply investigated. It is found that the variable physical properties and thermal convection cause larger effect on heat transfer of laminar free convection Film Condensation, meanwhile, the effect of the variable physical properties is even larger than that of the thermal convection. It follows that it is necessary to consider variable physical properties for investigation on heat transfer of free Film Condensation. Compared with the variable physical properties and thermal convection, the effect of the Interfacial shear force and inertia force will be much smaller on heat transfer of laminar free convection Film Condensation, meanwhile, the effect of the inertia force is little bit smaller than that of the interfacial shear force.
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Complete Mathematical Model of Laminar Free Convection Film Condensation of Pure Vapour
Heat and Mass Transfer, 2012Co-Authors: Deyi ShangAbstract:In this chapter, the work is focused on constitution of mathematical models of the laminar free convection Film Condensation of superheated vapor, while, the Film Condensation of saturated vapor is only regarded as its special case. The new similarity analysis method is successfully applied for similarity transformation of the governing partial differential equations of laminar free convection Film Condensation of superheated vapor with consideration of coupled effects of variable physical properties of liquid and vapor Films. In the transformed governing ordinary differential equations, the dimensionless velocity components of liquid and vapor Films have definite physical meanings, and then the solutions of the governing models can be understood easily. In the analysis and similarity transformation of the mathematical models, the interfacial balance equations between the liquid and vapor Films are considered in detail, such as mass flow rate balance, velocity component balance, shear force balance, temperature balance, and energy balance. Therefore, such mathematical model is serious theoretically and has its application value in practice.
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Heat and Mass Transfer of Laminar Free Convection Film Condensation of Vapor–Gas Mixture
Heat and Mass Transfer, 2012Co-Authors: Deyi ShangAbstract:The theoretical equations on heat and mass transfer are set up for laminar free Convection Film Condensation of vapor–gas mixture. In the theoretical equations only dimensionless wall temperature gradient and condensate mass flow rate parameter are no-given variables respectively for prediction of heat and mass transfer rates. The laminar free Convection Film Condensation of water vapor in presence of air on a vertical flat plate is taken as example for the numerical solutions on condensate heat and mass transfer, including those on the dimensionless temperature gradient and mass flow rate parameter. Both by decreasing the bulk vapor mass fraction and the reference wall subcooled grade, the wall dimensionless temperature gradient will increase at accelerative pace. Both decreasing the bulk vapor mass fraction and the reference wall subcooled grade will cause decreasing the condensate mass flow rate parameter at accelerative pace. These phenomena demonstrate the decisive effect of the non-condensable gas on condensate heat and mass transfer of the laminar forced Film Condensation of vapor–gas mixture. The system of the rigorous key solutions on the wall dimensionless temperature gradient and the condensate mass flow rate parameter is formulated to the simple and reliable equations for the laminar free Convection Film Condensation of water vapor–air mixture. Coupled with these formulated equations, the theoretical equations on the condensate heat and mass transfer can be respectively used for reliable and simple prediction of heat and mass transfer rate on laminar free Convection Film Condensation of water vapor–air mixture. Additionally, it is found that the condensate heat transfer rate is dominated by the wall subcooled temperature\(t_\text{w}-t_{\text{s},\,\text{int}}\) and the wall temperature gradient, the condensate mass flow rate is dominated by the condensate mass flow rate parameter, and the condensate heat transfer rate is identical to the condensate mass flow rate. Due to the quite different condensate mechanisms, the condensate heat and mass transfer rate of the laminar free Convection Film Condensation from vapor in presence of non-condensable gas is quite different from that of pure vapor, even for \(C_{\text{mv},\infty } \rightarrow 0.\)
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Velocity, Temperature, and Concentration Fields on Laminar Free Convection Film Condensation of Vapor–Gas Mixture
Heat and Mass Transfer, 2012Co-Authors: Deyi ShangAbstract:A set of physical matching conditions at the liquid–vapor interface are considered and rigorously satisfied for getting reliable solutions related to the three-point boundary value problem on the laminar free convection Film Condensation of vapor–gas mixture. With the example on the laminar free convection Film Condensation of water vapor–air mixture, a system of the interfacial vapor saturation temperature \(T_{{s},\mathrm{int}}\) is found out, which only depends on the bulk vapor mass fraction for a special bulk temperature. The numerical solutions of the interfacial vapor saturation temperature \(T_{{s},\mathrm{int}}\) are further formulated into an equation for its reliable prediction. A system of rigorous numerical results is successfully obtained, including velocity and temperature fields of the condensate liquid Film, as well as the velocity, temperature, and concentration fields of the vapor–gas mixture Film. With increasing the vapor mass fraction (or decreasing the gas mass fraction) in the bulk, the condensate liquid Film thickness, the condensate liquid velocity, and vapor–gas mixture velocity at the liquid–vapor interface will increase at an accelerative pace. It proved that the noncondensable gas in the vapor–gas mixture has a decisive effect on the laminar free convection Film Condensation from vapor–gas mixture. The wall temperature has also a decisive effect on the laminar free convection Film Condensation from vapor–gas mixture. With increasing wall temperature, the condensate liquid Film thickness, the condensate liquid velocity, as well as velocity of the vapor–gas mixture at the liquid–vapor interface will decrease. However, with increasing the wall temperature, the thicknesses of the momentum, temperature, and concentration boundary layers of the vapor–gas mixture will increase.
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Heat and Mass Transfer on Laminar Forced Film Condensation of Vapour–Gas Mixture
Theory of Heat Transfer with Forced Convection Film Flows, 2010Co-Authors: Deyi ShangAbstract:Through the heat and mass transfer analyses, the equations of condensate heat and mass transfer rates are provided, where only dimensionless wall temperature gradient, interfacial vapour saturation temperature and defined condensate mass flow rate parameter are non-given conditions. The defined mass flow rate parameter depends on condensate liquid Film thickness as well as the interfacial condensate liquid velocity components. Then, the laminar forced Film Condensation of water vapour in the presence of air on a horizontal flat plate is taken as an example, and a system of numerical results of the wall dimensionless temperature gradient and mass flow rate parameter are obtained. It is found that although decreasing the bulk vapour mass fraction (i.e. increasing the bulk gas mass fraction) causes increase of the wall dimensionless temperature gradient, it decreases the condensate mass flow rate parameter. However increasing the reference wall subcooled grade causes decrease of the wall temperature gradient and increase of the condensate mass flow rate parameter. These phenomena are closely related to the effect of the non-condensable gas on the Condensation. The system of the rigorous key solutions of the wall dimensionless temperature gradient and condensate mass flow rate paramater is formulated using the simple and reliable equations for the laminar Film Condensation of water vapour–air mixture on a horizontal flat plate. In combination with the provided theoretical heat transfer equation, the formulated equation of the wall dimensionless temperature gradient and condensate mass flow rate parameter can be used for simple and reliable evaluation of the condensate heat transfer rate. The interfacial vapour saturation temperature, necessary for correct prediction of laminar Film Condensation of vapour–gas mixture, is deeply investigated here. By taking the laminar forced Film Condensation of water vapour–air mixture as an example, three methods are reported for evaluation of the interfacial vapour saturation temperature: (1) the numerical calculation method, (2) prediction with the formulation equation and (3) prediction by solving the condensate mass–energy transformation equation. The calculated results of the interfacial vapour saturation temperature related to different methods are well coincident. It proves that the similarity analysis method, the similarity mathematical model, the numerical calculation and treatment method of variable physical properties reported in this chapter are valid for extensive investigation of heat and mass transfer of laminar forced Film Condensation of vapour–gas mixture. The author believes that the analysis and calculation methods reported in this work can be conveniently extended to investigate other different types of laminar forced Film Condensation from vapour–gas mixture.
Cha'o-kuang Chen - One of the best experts on this subject based on the ideXlab platform.
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laminar Film Condensation from a downward flowing steam air mixture onto a horizontal circular tube
Applied Mathematical Modelling, 2009Co-Authors: Cha'o-kuang Chen, Yanting LinAbstract:Abstract This investigation develops a numerical model of laminar Film Condensation from a downward-flowing steam-air mixture onto a horizontal circular tube. The significant non-similarity of the coupled two-phase flow laminar Film Condensation is such that the boundary layer governing conservations of momentum, species and energy in the mixture and liquid phases are solved by finite-volume methods. Numerical analysis of both the local condensate Film thickness and heat transfer characteristics elucidated the simultaneous effects of inlet-to-wall temperature difference and inlet air concentration, the Reynolds number of the mixture, and the dimensionless parameter, F , by adopting a unified condensate parameter. The local Nusselt number and liquid Film thickness increase as both the non-condensable air mass fraction and the tube temperature decreases. The numerical results on local heat transfer and Film thickness for low/no non-condensable gas (air) agree closely with the theoretical results of Yang [Sheng-An Yang, Superheated laminar Film Condensation on a nonisothermal horizontal tube, J. Thermophys. Heat Transfer 11(4) (1997) 526–532], Fuji [T. Fujii, H. Uehare, C. Kurata, Laminar Filmwise Condensation of flowing vapor on a horizontal tube, Int. J. Heat Mass Transfer 15 (1972) 235–246] and Homescu and Panday [D. Homescu, P.K. Panday, Forced convection Condensation on a horizontal tube: Influence of turbulence in the vapor and liquid phases, J. Heat Transfer Trans. ASME 121(4) (1999) 874–885]. Meanwhile, the comparison of average heat transfer coefficient with the experimental data from Rose and Lee [W.C. Lee, J.W. Rose, Forced convection Film Condensation on a horizontal tube with and without non-condensing gases, Int. J. Heat Mass Transfer 27(4) (1984) 519–528] demonstrates reasonably good agreement with the parameter F ( = gdh fg μ L / ⌊ k L U 0 2 ( T 0 - T W ) ⌋ , the ratio of gravity to mixture velocity) and G (= ( T 0 - T W ) ( k L / h fg μ L ) ( ρ L μ L / ρ m μ m ) , the suction effect).
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Forced Convection in Film Condensation on a Horizontal Elliptical Tube
Heat Transfer Engineering, 2006Co-Authors: Cha'o-kuang ChenAbstract:The aim of the present study is to investigate Film Condensation on an isothermal elliptical tube employing the model of Sarma et al. (1998). The study also considers the transition from laminar to turbulent Film. The paper then presents analytical analysis for the local dimensionless Film thickness and heat transfer characteristics for different degrees of tube eccentricity. Finally, the results developed in this study are compared with those generated by previous theoretical and experimental research. It is noted that the correlation between the two sets of data is quite satisfactory.
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Turbulent Film Condensation on a vertical wedge
Applied Thermal Engineering, 2004Co-Authors: Cha'o-kuang ChenAbstract:Abstract The present paper develops for the study of turbulent Film Condensation on a vertical wedge plate. It begins by considering the case of vapour flow past an isothermal wedge. Potential flow theory is used to determine the high tangential velocity of the vapour, and the Colburn analogy is used to define the local liquid–vapour interfacial shear which occurs when the high velocity vapour flows across the wedge surface. The paper then presents a discussion of the results obtained for the local dimensionless Film thickness and heat transfer characteristics. Finally, the results developed in this study are compared with those generated by previous theoretical results.
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Turbulent Film Condensation on a horizontal elliptical tube
Journal of Heat Transfer, 2003Co-Authors: Cha'o-kuang ChenAbstract:This is an investigation of turbulent Film Condensation on a horizontal elliptical tube. The high tangential velocity of the vapor flow at the boundary layer is determined from potential flow theory. The Colburn analogy is used to define the local liquid-vapor interfacial shear which occurs for high velocity vapor flow across an elliptical tube surface
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Turbulent Film Condensation on a half oval body
International Journal of Heat and Mass Transfer, 2003Co-Authors: Cha'o-kuang ChenAbstract:Abstract The paper is an investigation of turbulent Film Condensation on a half oval body. The high tangential velocity of the vapor flow at the boundary layer is determined from potential flow theory. The Colburn analogy is used to define the local liquid–vapor interfacial shear which occurs when the high velocity vapor flows across the body surface. The paper then presents a discussion of the results obtained for the local dimensionless Film thickness and heat transfer characteristics. Furthermore, the present paper discusses the influence of Froude number, sub-cooling temperature and system pressure on mean Nusselt number.
Liang-cai Zhong - One of the best experts on this subject based on the ideXlab platform.
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extensive study on laminar free Film Condensation from vapor gas mixture
International Journal of Heat and Mass Transfer, 2008Co-Authors: Deyi Shang, Liang-cai ZhongAbstract:Abstract The dimensionless velocity component method was successfully applied in a depth investigation of laminar free Film Condensation from a vapor–gas mixture, and the complete similarity transformation of its system of governing partial differential equations was conducted. The set of dimensionless variables of the transformed mathematical model greatly facilitates the analysis and calculation of the velocity, temperature and concentration fields, and heat and mass transfer of the Film Condensation from the vapor–gas mixture. Meanwhile, three difficult points of analysis related to the reliable analysis and calculation of heat and mass transfer for the Film Condensation from the vapor–gas mixture were overcome. They include: (i) correct determination of the interfacial vapor condensate saturated temperature; (ii) reliable treatment of the concentration-dependent densities of vapor–gas mixture, and (iii) rigorously satisfying the whole set of physical matching conditions at the liquid–vapor interface. Furthermore, the critical bulk vapor mass fraction for Condensation was proposed, and evaluated for the Film Condensation from the water vapor–air mixture, and the useful methods in treatment of temperature-dependent physical properties of liquids and gases were applied. With these elements in place, the reliable results on analysis and calculation of heat and mass transfer of the Film Condensation from the vapor–gas mixture were achieved. The laminar free Film Condensation of water vapor in the presence of air was taken as an example for the numerical calculation. It was confirmed that the presence of the non-condensable gas is a decisive factor in decreasing the heat and mass transfer of the Film Condensation. It was demonstrated that an increase of the bulk gas mass fraction has the following impacts: an expedited decline in the interfacial vapor condensate saturation temperature; an expedited decrease in the condensate liquid Film thickness, the condensate liquid velocity, and the condensate heat and mass transfer. It was found that an increase of the wall temperature will increase the negative effect of the non-condensable gas on heat and mass transfer of the Film Condensation from the vapor–gas mixture.
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Extensive study on laminar free Film Condensation from vapor–gas mixture
International Journal of Heat and Mass Transfer, 2008Co-Authors: Deyi Shang, Liang-cai ZhongAbstract:Abstract The dimensionless velocity component method was successfully applied in a depth investigation of laminar free Film Condensation from a vapor–gas mixture, and the complete similarity transformation of its system of governing partial differential equations was conducted. The set of dimensionless variables of the transformed mathematical model greatly facilitates the analysis and calculation of the velocity, temperature and concentration fields, and heat and mass transfer of the Film Condensation from the vapor–gas mixture. Meanwhile, three difficult points of analysis related to the reliable analysis and calculation of heat and mass transfer for the Film Condensation from the vapor–gas mixture were overcome. They include: (i) correct determination of the interfacial vapor condensate saturated temperature; (ii) reliable treatment of the concentration-dependent densities of vapor–gas mixture, and (iii) rigorously satisfying the whole set of physical matching conditions at the liquid–vapor interface. Furthermore, the critical bulk vapor mass fraction for Condensation was proposed, and evaluated for the Film Condensation from the water vapor–air mixture, and the useful methods in treatment of temperature-dependent physical properties of liquids and gases were applied. With these elements in place, the reliable results on analysis and calculation of heat and mass transfer of the Film Condensation from the vapor–gas mixture were achieved. The laminar free Film Condensation of water vapor in the presence of air was taken as an example for the numerical calculation. It was confirmed that the presence of the non-condensable gas is a decisive factor in decreasing the heat and mass transfer of the Film Condensation. It was demonstrated that an increase of the bulk gas mass fraction has the following impacts: an expedited decline in the interfacial vapor condensate saturation temperature; an expedited decrease in the condensate liquid Film thickness, the condensate liquid velocity, and the condensate heat and mass transfer. It was found that an increase of the wall temperature will increase the negative effect of the non-condensable gas on heat and mass transfer of the Film Condensation from the vapor–gas mixture.
Graham Wilks - One of the best experts on this subject based on the ideXlab platform.
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mixed convection laminar Film Condensation on a semi infinite vertical plate
arXiv: Fluid Dynamics, 2014Co-Authors: Jian Jun Shu, Graham WilksAbstract:A comprehensive study of the problem of laminar Film Condensation with both a gravitational type body force and a moving vapour concurrent and parallel to the surface has been presented here. It demonstrates where both the body force and vapour velocity are significant through a comprehensive numerical solution obtained by a modified Keller box method. Important parameters governing Condensation and heat transfer of pure vapour are determined. A perturbation analysis is applied in the leading edge and downstream regimes. The thin Film approximations for the both regimes are obtained and compared with exact numerical solutions.
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Mixed-convection laminar Film Condensation on a semi-infinite vertical plate
Journal of Fluid Mechanics, 1995Co-Authors: Jian Jun Shu, Graham WilksAbstract:The flow of a uniform stream of pure saturated vapour past a cold, semi-infinite vertical plate is examined. The formulation incorporates the limits of both pure forced-convection and pure body-force-convection laminar Film Condensation. Detailed asymptotic and exact numerical solutions are obtained and comparisons drawn with approximate methods and experimental results reported in the literature.
Ping Cheng - One of the best experts on this subject based on the ideXlab platform.
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lattice boltzmann simulation of steady laminar Film Condensation on a vertical hydrophilic subcooled flat plate
International Journal of Heat and Mass Transfer, 2013Co-Authors: Ping ChengAbstract:Abstract Based on the newly developed phase-change Lattice Boltzmann method (LBM), the problem of steady laminar Film Condensation on a hydrophilic vertical flat plate at a subcooled temperature is simulated in this paper. The effects of inertia force, interface shear stress and convection terms are fully taken into consideration in the LBM simulation. The condensate Film thickness, velocity and temperature distributions, and heat transfer characteristics at steady state conditions are obtained numerically. The simulation results are found in good agreement with the classical analytical solutions. The deviations between the classical solutions and those of LBM simulation become somewhat larger at high Jakob numbers and low Prandtl numbers. The contact angle of the fluid with the surface is found to have very little effects on Film Condensation. It is shown that the LBM can be applied to Condensation problems successfully and accurately for the first time.