Buoyancy-affected laminar film condensation

The flow and heat transfer in a laminar condensate flim on an isothermal vertical plate is modelled mathematically. The strict Boussinesq approximation is adopted to account for buoyancy due to local temperature variations within the film. A similarity transformation reduces the governing boundary-layer type equations to a coupled set of ordinary differential equations and the resulting three-parameter twopoint boundary value problem is solved numerically for Prandtl numbers,Pr, ranging from 0.001 to 1000 and Jakob numbers,Ja, between 0.0001 and 1.5. The principal effects of the favourable buoyancy are to reduce the thickness of the condensate film and increase the film velocity at the smooth liquid-vapour interface, whereas the friction and heat transfer at the plate are enhanced. In accordance with the classical Nusselt theory, it is found that the temperature varies nearly linearly across the film. The computed similarity profiles for velocity reveal, however, substantial departures from the parabolic distribution assumed in the simplified Nusselt analysis.     

Influence of the aspect ratio on boiling flows in rectangular mini-channels

This article presents experiments conducted with two single rectangular mini-channels of same hydraulic diameter (1.4 mm) and different aspect ratios for conditions of horizontal boiling flow. The Forane® 365 HX used was subcooled (ΔT_sub = 15 °C) for all the boiling curves presented in the paper. Local heat transfer coefficients were measured for heat flux ranging from 25 to 62 kW m⁻² and mass flux from 200 kg m⁻² s⁻¹ to 400 kg m⁻² s⁻¹. The boiling flows were observed with two different cameras (depending on the flow velocity) through a visualization window. The flow patterns in the two channels were compared for similar conditions. The results show that the boiling heat transfer coefficient and the pressure drop values are different for the two single mini-channels. For low heat flux condition, the channel with lowest aspect ratio (H/W = 0.143) has a higher heat transfer coefficient. On the other hand, for high heat flux condition, the opposite situation occurs, namely the heat transfer coefficient becomes higher for the channel with highest aspect ratio (H/W = 0.43). This is probably due to the earlier onset of dryout in the channel with lowest aspect ratio. For the two cases of heating, the pressure drop for the two-phase flow remains lower for the channel with lowest aspect ratio. These results show that the aspect ratio plays a substantial role for boiling flows in rectangular channels. As for single-phase flows, the heat transfer characteristics are significantly influenced (even though the hydraulic diameter remains the same) by this parameter.     

Mixed convection film condensation from downward flowing vapors onto a sphere with uniform wall heat flux

A model is developed for the study of mixed convection film condensation from downward flowing vapors onto a sphere with uniform wall heat flux. The model combined natural convection dominated and forced convection dominated film condensation, including effects of pressure gradient and interfacial vapor shear drag has been investigated and solved numerically. The separation angle of the condensate film layer, φ _s is also obtained for various pressure gradient parameters, P ^* and their corresponding dimensionless Grashof?'s parameters, Gr ^*. Besides, the effect of P ^* on the dimensionless mean heat transfer, will remain almost uniform with increasing P ^* until for various corresponding available values of Gr ^*. Meanwhile, the dimensionless mean heat transfer, is increasing significantly with Gr ^* for its corresponding available values of P ^*. For pure natural-convection film condensation, is obtained.     

Binary diffusion and heat transfer in laminar mixed convection channel flows with uniform wall heat flux: extremely thin film thickness

A detailed numerical study has been performed to investigate the combined heat and mass transfer in laminar mixed convection channel flows with uniform wall heat flux. In an initial effort the liquid film on the channel wall is assumed to be extremely thin in thickness. Major dimensionless groups governing the present problem areGr _T,Gr _Mx,Pr,Sc, φ andRe. Results are specifically presented for an air-water system under various conditions. The effects of wall heating flux, the Reynolds number and the relative humidity of the moist air in the ambient on the momentum, heat and mass transfer in the flow are investigated in great detail.     

Chebyshev finite difference approach to modeling the thermoviscosity effect in a power-law liquid film on an unsteady stretching surface

The effect of thermoviscosity (temperature-dependent viscosity) on the heat transfer in a power-law liquid film over an unsteady stretching sheet is investigated. Similarity analysis is used to transform the governing equations for mass, momentum and energy into a system of ordinary differential equations, which contain a thermoviscosity parameter θ_r, unsteadiness parameter S, generalized Prandtl number Pr and power-law index n. The film thickness, the temperature distributions, the local heat transfer rate, and the local skin-friction coefficient were obtained using the Chebyshev finite difference method (ChFD). The results show that thermoviscosity significantly increases the film thickness and the local heat transfer rate while decreasing the local skin-friction coefficient as θ_r → 1. It is found that liquids with a higher power-law index will have a larger film thickness and a higher free-surface temperature, which indicate a lower local heat transfer rate, ?θ′(0).     

Comment on “Correlation of entrainment for annular flow in horizontal pipes”, by Pan,L., Hanratty,T.J., Int. J. Multiphase flow, 28(3), (2002), pp. 385–408

The above referenced paper, published in International Journal of Multiphase Flow (Pan and Hanratty, 2002), proposed an entrainment fraction correlation for annular flow in horizontal pipes. The entrainment fraction in annular flow is defined as the ratio of the mass flow rate of the liquid droplets in the gas to the total mass flow of liquid, F_E = W_LE/W_L. The proposed correlation was verified with experimental data for liquids with viscosities close to that of water. The proposed entrainment fraction correlation includes another correlation for the critical film flow rate, W_F,cr to estimate a maximum entrainment fraction F_E,max. It is shown that the critical film flow rate correlation can result in negative maximum entrainment fraction values, for low liquid flow rates.     

Prediction of film boiling heat transfer coefficients for binary mixtures

Film boiling of binary liquid mixtures may be significantly different from that of single-component liquids due to the mass diffusion effect. A theoretical analysis is performed to outline the effects of mass diffusion phenomena on film boiling heat transfer process from a horizontal cylinder heating surface to the binary liquid mixtures of ethylene oxide/water and ethanol/benzene over whole range of compositions. These two binary systems are chosen for illustrating the strong and weak mass diffusion effects, respectively, on film boiling. Furthermore, a simple correlation for predicting heat transfer coefficient is proposed to demonstrate the idea that the dimensionless F factor can satisfactorily account for the mass diffusion effect on film boiling heat transfer of binary mixtures.     

Experimental studies on heat and mass transfer performance of a coiled tube absorber for R134a-DMAC based absorption cooling system

Absorber is an important component in vapor absorption refrigeration system and its performance has greater influence in overall efficiency of absorption machines. Falling film heat and mass transfer in an absorber is greatly influenced by fluid properties, geometry of heat exchanger and its operating parameters. This paper presents on the results of experimental studies on the heat and mass transfer characteristics of a coiled tube falling film absorber, using 1,1,1,2-Tetrafluroethane(R-134a) and N-N Dimethyl Acetamide (DMAC) as working fluids. The effects of film Reynolds number, inlet solution temperature and cooling water temperature on absorber heat load, over all heat transfer coefficient and mass of refrigerant absorbed are presented and discussed. Normalized solution and coolant temperature profiles and refrigerant mass absorbed along the height of absorber are also observed from the experimental results. The optimum over all heat transfer coefficient for R-134a–DMAC solution found to be 726 W/m²K for a film Reynolds number of 350. The R-134a vapour absorption rate is maximum in the normalized coil height of 0.6 to 1.     

Transient Film Condensation on a Vertical Plate Imbedded in Porous Medium

The present paper introduces a mathematical model that simulates the transient film condensation on a vertical plate imbedded in a porous medium. In this model, the Brinkman-extended Darcy model is adopted and the local macroscopic inertial term is included. Analytical solutions are presented that describe the transient behavior of the condensate film thickness, condensate mass flow rate and heat transfer coefficient. The current results show the effect of the permeability of the porous material on several issues including the velocity profiles, the film thickness and the time required to reach steady state conditions.     

The effect of vapour super-heating on hydrocarbon refrigerant condensation inside a brazed plate heat exchanger

This paper investigates the effect of vapour super-heating on hydrocarbon refrigerant 600a (Isobutane), 290 (Propane) and 1270 (Propylene) condensation inside a brazed plate heat exchanger.Vapour super-heating increases heat transfer coefficient with respect to saturated vapour, whereas no effect was observed on pressure drop.The super-heated vapour condensation data shows the same trend vs. refrigerant mass flux as the saturated vapour condensation data, but with higher absolute values. A transition point between gravity controlled and forced convection condensation has been found for a refrigerant mass flux around 15-18 kg m⁻² s⁻¹ depending on refrigerant type. The super-heated vapour heat transfer coefficients are from 5% to 10% higher than those of saturated vapour under the same refrigerant mass flux.The experimental heat transfer coefficients have been compared against Webb (1998) model for forced convection condensation of super-heated vapour: the mean absolute percentage deviation between the experimental and calculated data is ±18.3%.HC-1270 shows super-heated vapour heat transfer coefficient 5% higher than HC-600a and 10-15% higher than HC-290 together with total pressure drops 20-25% lower than HC-290 and 50-66% lower than HC-600a under the same mass flux.     

FEM application in phase change exchangers

Application of FEM in the analysis of condenser and vaporizer has been illustrated taking into account property variation with temperature. Accurate shell side pressure drop in a condenser has been determined by the present method taking into account the gradual reduction in vapour flow due to condensation from inlet to outlet. As the present method analyses the exchanger in small elements, analysis of an evaporator working under the conditions of partial vapour blanketing is also possible.

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Anwendung der Finite Elemente Methode bei Wärmetauschern mit Phasenwechsel

Zusammenfassung Die Verwendung der Finite Elemente Methode zur Berechnung von Kondensator und Verdampfer unter Berücksichtigung von temperaturabhängigen Stoffwerten ist hier dargestellt worden. Mit dem dargestellten Verfahren ist der genaue Druckverlust im Rohrraum eines Kondensators bestimmt worden, wobei die schrittweise Verminderung der Dampfströmung aufgrund der Kondensation von Ein-zu Auslaß mit berücksichtigt wurde. Mit der gegenwärtigen Methode, die einen Wärmeaustausch mittels kleiner Elemente berechnet, ist ebenso eine Auslegung eines Verdampfers mit einer partiellen Dampfabdeckung möglich.

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Nomenclature A heat transfer area in an elment upto any section, m² - A _c elemental heat transfer area, m² - B weightage - C UA/2 - D _e characteristic dimension, m - D _s shell diameter, cm - F _t temperature correction factor - f friction factor, m²/cm² - G mass velocity, kg/m² sec - G W/LN ^2/3 - g acceleration of gravity, m/sec² - h condensing coefficient, W/m²°C - h ₀ boiling coefficient, W/m²°C - k ₁ thermal conductivity of condensate atT _f , W/m°C - L length of tubes in the element, m - l distance of the fluid stream traverses in the element, m - LMTD log mean temperature difference, °C - N ₁,N ₂ shape functions - N _t number of tubes effective for condensation - P pressure drop, N/cm² - P _shell shell side vapour pressure drop, N/cm² - P _tube tube side stream pressure drop, N/cm² - q heat flux in the element, W/m² - S specific gravity of vapour - T _c tube side stream temperature, °C - T _c2 tube side stream exit temperature, °C - T _f (T _w +T _s )/2 - T _s saturation temperature, °C - T _w mean wall temperature in an element, °C - T ₁,T ₂ temperatures at nodes 1 and 2, °C - U overall heat transfer coefficient, W/m²°C - W ₁ tube side fluid thermal capacity rate, W/°C - W ₂ vapour mass flow rate, kg/hr - W mass of vapour condensed in any element, kg/sec - _f viscosity of condensate atT _f , N sec/m² - _f density of condensate atT _f , kg/m³     

Free- and forced-convection film condensation from a horizontal elliptic tube with a vertical plate and horizontal tube as special cases

A simple mathematical model is developed for the study of the mixed-convection film condensation with downward flowing vapors onto a horizontal elliptic tube. Analytical analysis for both the local condensate film thickness and heat transfer characteristics under simultaneous effects of interfacial vapor shear and pressure gradient has been performed by adopting a unified geometry parameter, eccentricity e. The present results for two limit cases, e = 0 (circular tube) and e = 1.0 (vertical plate) are in an excellent agreement with the earlier works. For very slow vapor flow, the present result for dimensionless mean heat transfer coefficient reduces to the same form as in the earlier works, , whose value is 0.728 for e = 0 and 0.943 for e = 1.0. As for very fast vapor flow, the dimensionless mean heat transfer coefficient, increase with increasing eccentricity under the effects of pressure gradient caused by potential flow and surface tension.     

Numerical study of condensing a small concentration of vapour inside a vertical tube

The purpose of this study is to analyse the combined heat and mass transfer of liquid film condensation from a small steam–air mixtures flowing downward along a vertical tube. Both liquid and gas stream are approached by two coupled laminar boundary layer. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. The effects of a wide range of changes of three independent variables (inlet pressure, inlet Reynolds number and wall temperature) on the concentration at exit tube, local Nusselt and Sherwood numbers, film thickness, accumulated condensate rate and temperature are carefully examined. The numerical results indicate that in the case of condensing a small concentration of vapours from a mixture, the resistance to heat and mass transfer by non-condensable gas becomes very intense. The comparisons of average Nusselt number and local condensate heat transfer coefficient with the literature results are in good agreement.     

Heat transfer and thermal performance characteristics of heat exchanger tube fitted with perforated twisted-tapes

Twisted tape insert was applied as a swirling flow generator for the passive heat transfer enhancement in the present work. The influences of the perforated twisted tapes (PTs) on the heat transfer, pressure loss and thermal performance characteristics were investigated experimentally. The experiments were performed under uniform wall heat flux condition by using PTs with y/W?=?3, 4 and 5, d/W?=?0.11, 0.14 and 0.17 and s/W?=?0.4, 0.6 and 0.8 where y is a twist length, d is a perforation hole diameter, s is a spacing between holes (pitch) and W is a tape width. The experimental results reveal that Nusselt number increased with decreasing s/W and y/W and increasing d/W. For the present range, the maximum heat transfer was obtained by utilizing the tape with s/W?=?0.4, d/W?=?0.17 and y/W?=?3, which is higher than those obtained from the plain tube with and without typical twisted tape by around 27.4 and 86.7%, respectively. In addition, the empirical correlations for Nusselt number, friction factor and thermal performance are also proposed in the present paper.     

Analysis of viscous dissipation effect on thermal entrance heat transfer in laminar pipe flows with convective boundary conditions

Consideration is given to the influence of viscous dissipation on the thermal entrance region laminar pipe flow heat transfer with convective boundary condition. The Eigenfunction series expansion technique is employed to solve the governing energy equation. The results for axial distributions of dimensionless bulk and wall temperatures, local Nusselt number as well as modified local Nusselt number are presented graphically forNu ₀ =0.1, 2, and 100. The complicated variations of conventional local Nusselt number is due to the inappropriate definition of conventional heat transfer coefficient in this problem. A modified local heat transfer coefficient, based on the difference of bulk fluid temperature and wall temperature, is introduced. Its value can clearly indicate the extent and the direction of heat exchange between the fluid in the pipe and the ambient. The effects of outside Nusselt number are also investigated. Significant viscous dissipation effects have been observed for large Br.     

Heat and mass transfer characteristics of simulated high moisture flue gases

The heat transfer process occurring in a condensing heat exchanger where noncondensible gases are dominant in volume is different from the condensation heat transfer of the water vapor containing small amount of noncondensible gases. In the process the mass transfer due to the vapor condensation contributes an important part to the total heat transfer. In this paper, the Colburn-Hougen method is introduced to analyze the heat and mass transfer process when the water vapor entrained in a gas stream condenses into water on the tube wall. The major influential factors of the convective-condensation heat transfer coefficient are found as follows: the partial pressure of the vapor p _v , the temperature of the outer tube wall T _w , the mixture temperature T _g , Re and Pr. A new dimensionless number Ch, which is defined as condensation factor, has been proposed by dimensional analysis. In order to determine the relevant constants and investigate the convection-condensation heat and mass transfer characteristics of the condensing heat exchanger of a gas fired condensing boiler, a single row plain tube heat exchanger is designed, and experiments have been conducted with vapor-air mixture used to simulate flue gases. The experimental results show that the convection-condensation heat transfer coefficient is 1.52 times higher than that of the forced convection without condensation. Based on the experimental data, the normalized formula for convention-condensation heat transfer coefficient is obtained. A heat transfer area m² - Ch condensation factor - c _p specific heat at constant pressure, J/(kg·K) - G mass flux Kg/(m²·s) - h heat transfer coefficient W/(m²·K) - J J-factor - Nu Nusselt number - pa pressure - Pr Prandtl number - Q heat transfer rate - q heat flux W/m² - r latent heat, kJ/kg - Re Reynolds number - Sc Schmidt number - T temperature, C or K - heat conductivity m W/(m·K) - density, kg·m³ - g gas - h moistened hot air - i interface - v vapor - w water     

Finite difference analysis of mass transfer effects on flow past an impulsively started infinite vertical plate in dissipative fluid and constant heat flux

A finite-difference solution to the flow past an impulsively started infinite vertical plate is derived by assuming 1) presence of species concentration like water vapour, CO₂ etc. and 2) constant heat flux at the plate. The velocity and the temperature profiles, the skin-friction and the rate of heat transfer are shown graphically. The effects of the modified Grashof number,Gm, the Eckert numberE, the Schmidt numberSc on the flow of air are discussed.     

The effect of suction or injection on the boundary layer flows induced by continuous surfaces stretched with prescribed skin friction

The boundary layer flow and heat transfer on a stretched surface moving with prescribed skin friction is studied for permeable surface. Three major cases are studied for isothermal surface (n=0) stretched corresponding to different dimensional skin friction boundary conditions namely; skin friction at the surface scales as (x ^?1/2) at m=0, constant skin friction at m=1/3 and skin friction scales as (x) at m=1. The constants m and n are the indices of the power law velocity and temperature exponent respectively. Similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as Prandtl number Pr, suction/injection parameter f _w , m and n are studied. The results show that for isothermal surface increasing m enhances the dimensionless heat transfer coefficient for fixed f _w at the suction case and the reverse is true at the injection case. Furthermore, for fixed m, as f _w increases the dimensionless heat transfer coefficient increases. Large enhancements are observed in the heat transfer coefficient as the temperature boundary condition along the surface changes from uniform to linear where the dimensional skin friction is of order (x) at m=1. This enhancement decreases as the suction increases.     

Diffusion-Thermo and Radiation Effects on Unsteady MHD Flow Through Porous Medium Past an Impulsively Started Infinite Vertical Plate with Variable Temperature and Mass Diffusion

The objective of this study is to investigate diffusion-thermo (Dufour effect) and radiation effects on unsteady MHD free convection flow past an impulsively started infinite vertical plate with variable temperature and uniform mass diffusion in the presence of transverse applied magnetic field through porous medium. At time t > 0, the plate is given an impulsive motion with constant velocity u ₀ in the vertical upward direction against to the gravitational field. At the same time, the plate temperature is raised linearly with time t and the level of concentration near the plate is raised to ${{C}_{\rm w}^{\prime}}$ . A magnetic field of uniform strength B ₀ is applied normal to the direction to the flow. The dimensionless governing equations are solved in closed form by Laplace transform technique. The effect of flow parameters on velocity, temperature, concentration, the rate of heat transfer and the rate of mass transfer are shown through graphs.     

Turbulent film condensation on a horizontal elliptical tube

An investigation has been made of turbulent film condensation on a horizontal elliptical tube. The present study is based on Colburn analogy [1] and potential flow theory to determine the high tangential velocity of vapor flow at the boundary layer and to define the local interfacial shear owing to high velocity vapor flow across the tube surface. The condensate film flow and local/or mean heat transfer characteristics from a horizontal elliptical tube with variable ellipticities, e, under the influence of Froude number, sub-cooling parameter and system pressure have been performed. The present result for dimensionless mean heat transfer coefficient reduces to the same result obtained by Sarma et al.s [2] e=0 (circular tube). Compared with laminar model by Yang and Hsu [3], the present turbulent model shows in better agreement with Michaels experimental data [4] (for e=0). The dependence of mean Nusselt coefficient on the effect of n (power of Reynolds) [1] is also discussed.