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.     

Natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and internal heat generation

In this paper the natural convection boundary layer on a horizontal elliptical cylinder with constant heat flux and temperature dependent internal heat generation is investigated. The mathematical problem is reduced to a pair of coupled partial differential equations for the temperature and the stream function, and the resulting nonlinear equations are solved numerically by cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. An increase in the aspect ratio of the elliptical cylinder decreases the average surface temperature of the elliptical cylinder with blunt orientation, while it increases the average surface temperature of the elliptical cylinder with slender orientation. Moreover, an increase in the heat generation parameter for natural convection flow over a horizontal elliptic cylinder with constant heat flux leads to an increase in the average surface temperature of the elliptical cylinder.     

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.     

Thermodynamic optimization of free convection film condensation on a horizontal elliptical tube with variable wall temperature

This study focuses on the thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical tube with variable wall temperature. An entropy generation minimization (EGM), technique is applied as a unique measure to study the thermodynamic losses caused by heat transfer and film-flow friction for the laminar film condensation on a non-isothermal horizontal elliptical tube. The results provide us how the geometric parameter ellipticity and the amplitude of non-isothermal wall temperature variation affect entropy generation during filmwise condensation heat-transfer process. The optimal design can be achieved by analyzing entropy generation in film condensation on a horizontal elliptical tube with further account for the amplitude of non-isothermal wall temperature variation.     

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.     

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.     

Three-dimensional simulation of saturated film boiling on a horizontal cylinder

Three-dimensional simulations of film boiling on a horizontal cylinder have been performed. A finite difference method is used to solve the equations governing the conservation of mass, momentum and energy in vapor and liquid phases. A level set formulation for tracking the liquid–vapor interface is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip condition at the fluid–solid interface. From the numerical simulations, the effects of cylinder diameter and gravity on the interfacial motion and heat transfer in film boiling are quantified. The heat transfer coefficients obtained from numerical analysis are found to compare well with those predicted from empirical correlations reported in the literature.     

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.     

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.     

Mixed convection boundary layer flow past an isothermal horizontal circular cylinder with temperature-dependent viscosity

The problem of steady laminar mixed convection boundary layer flow past an isothermal horizontal circular cylinder placed in a viscous and incompressible fluid of temperature-dependent viscosity is theoretically considered in this paper. The partial differential equations governing the flow and heat transfer are shown to be non-similar. Full numerical solutions of these governing equations are obtained using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for various values of the Prandtl number Pr, the mixed convection parameter λ and the viscosity/temperature parameter θ_r. The obtained results show that the flow and heat transfer characteristics are significantly influenced by these parameters.     

Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid

This work studies the free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar governing equations are then solved by the cubic spline collocation method. The effects of the Brownian motion parameter and thermophoresis parameter on the profiles of the temperature, nanoparticle volume fraction and velocity profiles are presented. The local Nusselt number is presented as a function of the thermophoresis parameter, Brownian parameter, Lewis number and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). Results show that the local Nusselt number is increased as the thermophoresis parameter or the Brownian parameter is decreased. The local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased. Moreover, the local Nusselt number of the elliptical cylinder with slender orientation is higher than those of the elliptical cylinder with blunt orientation over the lower half cylinder.     

Mixed convection boundary layer flow on a horizontal plate in a uniform stream

A mixed convection boundary layer on a horizontal plate for uniform wall temperature/uniform heat flux is investigated using a computer extension of the perturbation series. The first 17 terms for the uniform wall temperature case and the first ten terms for the uniform heat flux case are computed for a Prandtl number σ = 0.72. The direct expansion is transformed by a Euler transform and other techniques. The results for buoyancy aiding or opposing the main flow are presented. The present work predicts the result to two digit accuracy for the entire domain of the streamwise coordinate. For uniform wall temperature, the maximum error is 5.983% for skin friction and 1.072% for heat transfer. For uniform heat flux, the maximum error is 6.9% for skin friction and 1.9% for wall temperature.     

Modified theoretical models of film condensation in horizontal microfin tubes

The previously proposed theoretical models of film condensation in horizontal microfin tubes have been modified to describe the characteristics of condensing two-phase flow more accurately. The stratified flow regime and the annular flow regime were considered. For the stratified flow regime, the previously proposed theoretical model was modified to take account of the curvature of stratified condensate due to the surface tension force. For the annular flow regime, a more accurate expression for the interfacial shear stress was incorporated. Generally, the modified theoretical models predicted a lower circumferential average heat transfer coefficient than the previously proposed ones. Comparison of the theoretical predictions with available experimental data for six tubes and five refrigerants revealed that a good agreement (r.m.s error of less than 21.1%) was obtained for all cases when the higher of the two theoretical predictions were adopted as the calculated value.     

The second-order boundary layer along a circular cylinder in supersonic flow

Tha sacond-ordar laminar boundary layar along a circular cylindar in suparsonic (low with and without surfaca mass transfar is studiad using tha mathod of matchad asymptotic axpansions. Spacifically, tha analysis obtains tha sacond-ordar tarms for tha prassura, tha shaar strass, and tha haat transfar at tha wall dua to transvarsa surfaca curvatura and displacamant. For tha flow naar tha laading adga of tha cylindar numarical rasults ara prasantad.Thara ara thraa sacond-ordar affacts, namaly dua to transvarsa curvatura, dua to displacamant, and dua to intaraction of curvatura and displacamant.For tha solid wall all thraa sacond-ordar affacts incraasa tha shaar strass and this rasult incraasas with incraasing wall tamparatura. In tha casa of haat transfar, tha displacamant affact vanishas, tha intaraction affact is always positiva (incraasing tha haat transfar), and tha transvarsa curvatura affact is positiva for small wall tamparaturas and nagativa for larga wall tamparaturas.Tha affact of mass flow at tha wall is ganarally m tha axpactad diraction; i.a. tha injaction of mass thickans tha boundary layar and incraasas sacond-ordar affacts wharaas wall suction, by axtracting mass from tha boundary layar, raducas tha importanca of displacamant and transvarsa curvatura. An axcaption to tha ganaral rula statad abova occurs at high wall tamparaturas.     

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.     

Natural convection heat transfer from a horizontal isothermal elliptical cylinder with internal heat generation

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature dependent internal heat generation. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear systems of partial differential equations are solved numerically applying cubic spline collocation method. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of heat generation parameters, Prandtl numbers and aspect ratios. Results show that both the heat transfer rate and skin friction of the elliptical cylinder with slender orientation are higher than the elliptical cylinder with blunt orientation. Moreover, an increase in the heat generation parameter for natural convection flow over an isothermal horizontal elliptic cylinder leads to a decrease in the heat transfer rate from the elliptical cylinder and an increase in the skin friction of the elliptical cylinder.     

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.     

Effect of vapour velocity on film condensation of R-113 on horizontal tubes in a crossflow

Film condensation of downward flowing R-113 vapour at near atmospheric pressure on single horizontal tubes was studied experimentally over wide ranges of vapour velocity and condensation temperature difference. The flow of condensate was visualized by injecting a dye tracer. Three flow regimes : smooth surface, two-dimensional waves and three-dimensional waves, were observed. In the last flow regime an abrupt thickening of the condensate film was seen at an angular position about 1.75 rad from the tube top. Turbulent mixing of condensate was observed in the thick film region. The present and earlier heat transfer results for R-113 and R-21 were compared with the laminar two-phase boundary-layer theory. The point at deviation from the theoretical prediction was found to be dependent on a dimensionless number which gave a transition criterion between smooth and wavy condensate surfaces. A correlation equation for the average heat transfer coefficient is proposed, where an equivalent Reynolds number is introduced for the high vapour velocity region.     

Prediction of turbine blade heat transfer and aerodynamics using a new unsteady boundary layer transition model

The effects of periodic unsteady flow on heat transfer and aerodynamic characteristics, particularly on the boundary layer transition along the suction and the pressure surfaces of a typical gas turbine blade, are experimentally and theoretically investigated. Comprehensive aerodynamic and heat transfer experimental data are collected for different unsteady passing frequencies that are typical of gas turbines. To predict the effect of the impinging periodic unsteady flow on the heat transfer and the aerodynamics of turbine blades, a new unsteady boundary layer transition model is developed. The model is based on a universal unsteady intermittency function and utilizes an inductive approach that implements the results of comprehensive experimental and theoretical studies of unsteady wake development and the boundary layer flow. Three distinct quantities are identified as primarily responsible for the transition of an unsteady boundary layer: (1) the universal relative intermittency function, (2) maximum intermittency, and (3) minimum intermittency. The analysis of the experimental results and the comparison with the model prediction confirm the validity of the model and its capability to accurately predict the unsteady boundary layer transition.