Second law based optimization of free convection film-wise condensation on a horizontal tube

This study uses the entropy generation minimization (EGM) method to optimize a saturated vapor flowing slowly onto and condensed on an isothermal horizontal tube. The result shows that the optimal group Rayleigh parameter exists over the parametric range investigated for horizontal tube at which the entropy generated at a minimum rate. The minimum entropy generation number in condensation heat transfer for optimal diameter, D_OPT of tube is expressed in terms of the group Brinkman parameter (Br/ψ). The result provides an immediate estimate of the relative increase in irreversibility associated with using a tube of diameter D ≠ D_OPT.     

Entropy generation minimization of free convection film condensation on an elliptical cylinder

This paper aims to perform thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical cylinder. This analysis provides us how the geometric parameter-ellipticity affects entropy generation during film-wise condensation heat transfer process. The results observe that local condensate film thickness decreases with an increase in ellipticity of a cylinder. From the first law point of view, the local heat transfer coefficient enhances as ellipticity increases. Meanwhile, from the second law point of view, entropy generation increases with increasing the value of ellipticity. We derive an expression for entropy generation, which accounts for the combined action of the specified irreversibilities. The result demonstrates that thermal irreversibility dominates over film flow friction irreversibility. Finally, an expression of minimizing entropy generation in laminar film condensation heat transfer is obtained.     

Effects of eddy diffusivity in film condensation on a horizontal tube

It is an investigation into turbulent film condensation on a horizontal tube. In order to forecast the results more exactly, a new theory model of local film shear stress (τ / τ_w) is presented in the paper. In the study, four models of different eddy diffusivity are considered. The numerical calculation is obtained by using Visual C⁺⁺. The result shows that among the four models, the difference between the higher value and the lower value of the mean Nusselt number is about 10.1%. Besides, the results developed in the current study are compared with those generated by previous theoretical results. The result shows that the present paper considering film local shear has a higher mean Nusselt number than the previous ones that exclude the film local shear.     

Simplified approach of turbulent film condensation on an inclined elliptical tube

The present theoretical study investigates turbulent film condensation on an inclined elliptical tube. Adopting the assumption of an isothermal wall surface, the energy equation, forced balance equations and thermal balance equations are derived to describe the phenomena of the condensate film. Results are obtained for the heat transfer coefficient over a wide range of vapor velocities, i.e. low condensation parameter to high condensation parameter. The optimal inclination angle of the tube in different length–radius ratios and eccentricity can be obtained in the present results. This study also discusses the influence of the degree of eccentricity of the elliptical tube on the heat transfer coefficient. Finally, a comparison is provided between the results of the present study and those reported in a previous theoretical study. It is found that a good agreement exists between the two sets of results.     

Laminar film condensation on an elliptical tube embedded in porous media

Laminar film condensation of saturated vapor flowing over an isothermal elliptical tube embedded in a porous medium is analyzed for conditions of free and forced convection. The flow field in the porous medium is described by the Darcy–Brinkman–Forchheimer model. The effect of vapor shear on condensation is determined by simultaneous solution of the two phase vapor boundary layer and condensate film momentum equations. The numerical results, which are presented in the form of local film thickness and local Nusselt number, show a dependence of these physical parameters on practical dimensionless parameters such as Reynolds number, Darcy number, Bond number and eccentricity.     

Prediction of onset of boundary layer transition in film condensation on a horizontal elliptical cylinder

This article is devoted to a numerical study of prediction of the onset of the boundary layer transition in film condensation of pure saturated vapor on a horizontal elliptical tube, under the simultaneous effects of gravity, shear stress, and the imposed pressure gradients, caused by the vapor flow and curvature, on the condensate film. The inertia and convection terms are retained in the analysis. The hypothesis of Shekriladze and Gomelauri is used at the liquid-vapor interface. Outside the boundary layer, the vapor phase velocity is obtained from potential flow. Temperature, velocity distribution, and dimensionless apparent turbulent stress of the fully developed flow are carried out using the implicit Keller method. The effects of pressure gradients characterized by Froude number, ellipticity, and Bond number on the transition position have been evaluated. The transition criterion has been given in terms of the critical film Reynolds number ( {bf Re}_{bGamma} ) C .     

水平翅片管外混合气体对流冷凝传热的理论研究

以Nusselt理论为基础,结合修正的膜理论,对含湿混合气体横掠水平翅片管外时的翅片表面对流冷凝传热机理进行研究。建议了分区处理方法,建立了翅片侧壁和光管上的液膜流动和传热模型。得到了管壁温度、烟气进口温度和雷诺数对总凝结液量的影响,以及翅片侧壁液膜的厚度分布。     

Unsteady mixed convection flow over a vertical stretching sheet in a parallel free stream with variable wall temperature

The objective of the paper is to investigate the numerical study of an unsteady two-dimensional mixed convection flow along a vertical semi-infinite power-law stretching sheet in a parallel free stream with a power-law wall temperature distribution of the form T_W(x) = T_∞ + Ax^2m?1. The unsteadiness is caused by the free stream velocity as well as by the stretching sheet velocity. The governing non-linear partial differential equations in the velocity and temperature fields are written in non-dimensional form using suitable transformations. The resulting final set of coupled non-linear partial differential equations is solved using an implicit finite difference scheme in combination with a quasi-linearization technique. The effects of various governing parameters on the velocity and temperature profiles are discussed in the present numerical study. In addition, the numerical results for the local skin friction coefficient and local Nusselt number are also presented. The numerically computed results are compared with previously reported work and are found to be in excellent agreement.     

Turbulent film condensation in the presence of non-condensable gases over a horizontal tube

A numerical model is presented for studying turbulent film condensation in the presence of non-condensable gases over a horizontal tube. Inertia, pressure gradient are included in this analysis, and the influence of turbulence in the proposed two-phase model is considered. The numerical results demonstrate that a very small bulk concentration of non-condensable gas reduces the heat transfer coefficient and film thickness considerably. The local heat flux and film thickness increase as tube surface temperature decreases at any bulk concentration of non-condensable gas. Moreover, inlet velocity increases as film thickness decreases and heat flux increases, a numerical result in agreement with that obtained by Nusselt. Numerical results indicate that average dimensionless heat transfer coefficients are in good agreement with theoretical and experimental data.     

Turbulent film condensation on a horizontal circular cylinder

A theoretical analysis is made on the turbulent film condensation. The analysis, unlike other existing analyses, retains the advection terms in the governing equations, and introduces a new parameter associated with the flow acceleration so as to characterize the inertia effects on the heat transfer process. The analysis is quite general, and can, in fact, be employed for any geometrical configurations. As a practical application of the analysis, the calculations are performed on the turbulent film developed over the horizontal circular cylinder, and the results are examined in details. The discussion further extends to a possible means for predicting the flow transition from laminar to turbulent.     

Effects of uniform suction and surface tension on laminar filmwise condensation on a horizontal elliptical tube in a porous medium

This study performs a theoretical investigation into the problem of steady filmwise condensation flow over the external surface of a horizontal elliptical tube embedded in a porous medium with suction at the tube surface. The combined effects of the surface tension force and the gravitational force in driving the flow of the liquid film within the porous medium are modeled using Darcy's law. An effective suction function, f, is introduced to model the effect of the suction force at the wall on the thickness of the condensate film. The theoretical results presented in this study show that the heat transfer performance can be enhanced by applying a suction effect at the wall. Furthermore, it is shown that the surface tension force has a negligible effect on the mean Nusselt number.     

Laminar film condensation on a finite-size horizontal wavy plate

A theoretical analysis of two-dimensional, steady laminar film condensation on a finite-size horizontal wavy plate is studied for the case in which a cold plate faces upwards. The present study considers that the wavy characteristic length, amplitude and the depth of boundary layer at the plate edge is equal to a minimum depth. The dimensionless heat transfer coefficients and the dimensionless film thickness along the surface are found to be functions of five parameters: dimensionless wave length and amplitude, Pr, Ja and Ra.     

Mixed laminar convection in a horizontal tube with natural convection around its boundaries

The laminar flow and heat transfer within a horizontal tube surrounded by a liquid medium are studied both experimentally and numerically. Emphasis is given to flow regimes where a buoyant effect on the forced flow is exhibited inside the tube. The outer surface of the tube is also subjected to natural convection resulting from the temperature difference between the wall and the surrounding fluid. Detailed analyses are performed for a number of cases with various fluids, inlet temperatures and fluid flows. It is found that the variable wall temperature has a marked effect on the secondary flow patterns within the tube as well as on the heat transfer.     

椭圆横管外降膜流动和换热特性分析

本研究基于VOF算法编写用户UDF(自定义函数),采用FLUENT软件建立了椭圆横管外降膜流动和换热的计算模型。根据CFD(计算流体力学)模型计算和分析了在不同长短轴比下管外降膜速度分布、压力分布、液膜内温度分布和管外换热分布的变化规律。研究结果表明:长短轴比的变化影响了管外液膜速度分布、压力分布和膜内温度分布;相比圆管,椭圆管的管外膜内液体流速更快。壁面压力沿周向逐渐减少并在X=0.9附近快速回升;随长短轴比e的增加,周向压力最小值位置逐渐向后推移。局部Nu数分布与压力分布在趋势上存在一致性。当e=1.65附近时,椭圆的换热性能最优;最后,通过对管形的研究分析,提出横管的传热分区模型。     

A Numerical Analysis of the Forced Convection Condensation of Saturated Vapor Flowing Axially Outside a Horizontal Tube

ＡＮｕｍｅｒｉｃａｌＡｎａｌｙｓｉｓｏｆｔｈｅＦｏｒｃｅｄＣｏｎｖｅｃｔｉｏｎＣｏｎｄｅｎｓａｔｉｏｎｏｆＳａｔｕｒａｔｅｄＶａｐｏｒＦｌｏｗｉｎｇＡｘｉａｌｌｙＯｕｔｓｉｄｅａＨｏｒｉｚｏｎｔａｌＴｕｂｅ￥ＷｅｉｚｈｏｎｇＬｉ，ＷｅｉｃｈｅｎｇＷａ...     

Multi-Prandtl correlating equations for free convection heat transfer from a horizontal tube of elliptic cross-section

Steady laminar free convection from a horizontal elliptic cylinder set in unbounded space is studied numerically under the assumption of uniform surface temperature. A specifically developed computer-code based on the SIMPLE-C algorithm is used for the solution of the mass, momentum and energy transfer governing equations. Simulations are performed for ratios between the minor and major axes of the elliptic cross-section of the cylinder in the range between 0.05 and 0.98, inclination angles of the major axis of the elliptic cross-section with respect to gravity in the range between 0° and 90°, Rayleigh numbers based on the major axis of the elliptic cross-section in the range between 10 and 10⁷, and Prandtl numbers in the range between 0.7 and 700. It is found that the heat transfer rate increases with increasing the Rayleigh and Prandtl numbers, while decreases with increasing the orientation angle of the cross-section of the cylinder, i.e., passing from the slender to the blunt configuration. In addition, a noteworthy fact is that in most cases the amount of heat exchanged at the cylinder surface has a peak at an optimum axis ratio which is practically independent of the Prandtl number, while may either increase or decrease with increasing the Rayleigh number depending on whether the orientation angle of the tube is above or below a critical value of approximately 67.5°. Dimensionless correlating equations are proposed both for the optimum axis ratio for maximum heat transfer and for the heat transfer rate from the cylinder surface to the undisturbed surrounding fluid reservoir.     

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by (K. Hooman, K., A.A. Ranjbar-Kani, A perturbation based analysis to investigate forced convection in a porous saturated tube, Journal of Computational and Applied Mathematics 162 (2) (2004) 411–419.). Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.     

Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature

Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one-, two- and three-undulations.The results obtained show that the angle of inclination affects the flow and heat transfer rate in the cavity. With increase in amplitude, the average Nusselt number on the wavy wall is appreciably high at low Rayleigh number. Increasing the number of undulations beyond two is not beneficial. The trend of local Nusselt number is wavy.