Heat transfer in non-Newtonian falling liquid film on a horizontal circular cylinder

 This study aims to investigate numerically the laminar flow and heat transfer in a pseudoplastic non-Newtonian falling liquid film on a horizontal cylinder for the constant heat flux and isothermal boundary conditions. The inertia terms are taken into account. An implicit finite difference method is carried out to solve the governing boundary layer equations. The effects of operational parameters on the hydrodynamic and heat transfer characteristics are examined and discussed in detail. The results presented show that the local and average Nusselt numbers varies significantly as a function of the concentration of aqueous carboxymethylcellulose (CMC) solutions and the cylinder diameter. Higher concentration of aqueous CMC solutions generate larger heat transfer coefficients. Finally, a comparison with the experimental and numerical results available in the literature for Newtonian fluids shows clearly that the present analysis is reasonably accurate. Received on 29 March 2001 / Published online: 29 November 2001     

Experimental study of heat transfer and flow characteristics of liquid falling film on a horizontal fluted tube

The aim of the present study is to investigate experimentally the effect of the fluted surface tube on the heat transfer and flow characteristics of liquid falling film. Experiments have indicated that, when a liquid falling film falls on a horizontal fluted surface tube, the transition starts at low Reynolds number than that of the plain tube. The value of the film thickness has been slightly decreased by decreasing the fluted pitch. A reduction of the film thickness was observed at about 9% for tube number 4, which has lower pitch, at Reynolds number of 485. A clear reduction of the dimensionless wavelength, λ*, has occurred at low fluted pitch tube. The use of enhanced surfaces can provide heat transfer coefficients higher values than those obtained from plain tube. Heat transfer enhancement was noticed due to the use of fluted tube surface. An improvement of the Nusselt number reached about 45% for tube 4. However, the low values of the fluted pitch increased the heat transfer enhancement than that of the high values.     

Evaporation of laminar,falling liquid film on a horizontal cylinder

An analytical study of falling film evaporation on a horizontal tube is accomplished for the case of constant heat flux condition imposed at the wall. The process of evaporation from the liquid film interface is conjugated to thermal conduction in the wall of the tube around its periphery. In addition, the flow of the film is considered to be thermally developing throughout its travel around the tube. Influence of various governing parameters on local and average heat transfer coefficient is presented. The theoretical investigation is compared with the available experimental data. The agreement is found to be satisfactory.     

Heat and mass transfer characteristics of a horizontal tube falling film absorber with small diameter tubes

This paper presents experimental results of the heat and mass transfer characteristics of a water–LiBr horizontal tube absorber made of small diameter tubes. The experimental set up includes a tube absorber, a generator, solution distribution system and cooling water system. Three different tube diameters of 15.88, 12.70 and 9.52 mm have been installed inside the absorber to investigate the effect of the tube diameter on the absorber performance. The experimental results show that the heat and mass transfer performance of the absorber increases as the tube diameter decreases. A comparison of the heat and mass transfer coefficients of the present study agree reasonable well with that of the previous studies.     

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.     

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a vertical tube

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a 0.1 m diameter vertical tube is studied experimentally with the purpose of validating a model formulated in an earlier phase of our research. According to this model for a fixed liquid velocity the gas entrainment should be proportional to the waviness of the film (its intermittency) and the wave height and inversely proportional to the film thickness. For Taylor bubble lengths ranging from 1D to 15D these film parameters have been measured with a Laser Induced Fluorescence technique. The gas entrainment has been determined from the net gas flux into the liquid column underneath the Taylor bubble by using data on gas re-coalescence into the rear of the Taylor bubble. These data are available for lengths ranging from 4.5D to 9D. The model results with the measured film characteristics compare well with the observed gas entrainment. The fact that the net gas flux becomes constant for long Taylor bubbles, whereas the wave height still increases, warrants further study.     

Three-dimensional surface characteristics of a falling liquid film

Optical methods are described for examining the three-dimensional character of waves on a falling liquid film. This involved monitoring the motion of the local film surface normal through the use of laser beam refraction. The wavy motion was found to be primarily of a two-dimensional nature only for Re (equal to 4Q/v) less than 1500.

Surface characteristics were examined for Reynolds numbers from 217 to 4030 and for different distances along the direction of flow.     

A simple physical model for steam absorption into a falling film of aqueous lithium bromide solution on a horizontal tube

For one horizontal tube in an absorber the Nusselt solution for film thickness and velocity distribution was applied, assuming steady state in heat transfer and a semi-infinite body’s concentration profile with unsteady state mass transfer. The model was applied to the absorption of steam into aqueous lithium bromide in absorption chillers. The results are compared to published experimental values and show fair agreement.     

Hall effects on hydromagnetic falling liquid film

An investigation is made of flow of an electrically conducting falling liquid film over a smooth vertical surface taking Hall effects into account, the liquid being permeated by a transverse magnetic field. Consideration of Hall current into the flow indicates a similarity between the flow of a rotating liquid and that due to the non-rotating system in presence of Hall currents. Discussion has been made for electrically conducting falling film in presence of cross-flow due to hall effect in non-rotating system.     

Influence of a sureactant on the instability of a falling liquid film

The hydrodynamic instability of a film flow of a weak solution containing a soluble volatile surfactant is investigated. Diffusion of the surfactant in the liquid, its evaporation into the boundary gas medium, and the adsorption and desorption processes in the near-surface layer are taken into account. A system of evolutionary equations is derived and a steady-state solution film flow along a vertical surface and the stability of this flow are investigated for the simultaneous action of body and capillary forces and the Marangoni effect. Hydrodynamic and diffusion instability modes are detected and their properties are investigated for constant and variable surfactant concentration in the adsorbed sublayer. Moscow, Madrid. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 56–67, July–August, 2000. The work was carried out with support from the Russian Foundation for Basic Research (project No. 97-01-00153) and the Spanish Ministry of Higher Education (program DGICYT (Spain), project No. PB 96-599).     

Analyses of pseudo-similarity and boundary layer thickness for non-Newtonian falling film flow

One aim of this paper is to provide an extensive study on pseudo-similarity solutions of thermal boundary layer in falling film flow with non-Newtonian power-law fluids. The related mathematical models and solution approach are systematically presented. Another aim of this work is to further investigate the momentum boundary layer and the thermal boundary layer. Based on a newly defined local Prandtl number, the dependence of the thickness of the momentum boundary layer and thermal boundary layer on the power-law index is discussed. It is found that the momentum boundary layer thickness decreases monotonically with power-law index; while the thermal boundary layer thickness decreases slightly with power-law index and increases significantly with the decrease of the local Prandtl number. This study shows that the adopted pseudo-similarity approach is capable of solving the problem of non-similarity thermal boundary layer in the falling film of a non-Newtonian power-law fluid.     

Displacement of a liquid from a horizontal circular tube by another liquid

We consider the axisymmetric problem of expulsion of one liquid from a horizontal circular pipe by another for the laminar flow regime.Studies of Taylor [1], Cox [2, 3], and others have been devoted to the experimental investigation of the displacement of a liquid from a capillary. Experiments on the displacement of mutually immiscible liquids show that the length of the combined flow region and the amount of displaced liquid remaining in this region are determined primarily by the magnitude of the interphase tension forces at the leading edge of the interface. The equilibrium of these forces and the hydrodynamic differential, established some time after the beginning of displacement, give rise to the rigid bullet-shaped form of the interface leading edge. This portion of the interface, whose stiffness is achieved as a result of the force balance, is termed the head of the interface between the liquids. The radius of the head-the relatively small autonomous portion of the interface-defines the dimensions and deformations of the entire remaining interface.The existence of a rigid autonomous interface head is the basis of the physical displacement model used in this article.     

Entropy generation in gas absorption into a falling liquid film

The study of mass transfer into falling films constitutes a significant aspect for numerous applications in the chemical technology and is considered the subject of many theoretical and experimental researches. Evaluating the second law of thermodynamics is one of the contemporarily used methods to determine the performances of an industrial process and to study various sources of irreversibility. Expressions of the liquid velocity, the gas concentration, the entropy generation rate as well as the main sources of irreversibility in the case of gas absorption (carbon dioxide) into a laminar falling viscous incompressible liquid film (water) without chemical reaction, are analytically derived and graphically presented and discussed.     

Entropy generation in gas absorption into a falling liquid film

The study of mass transfer into falling films constitutes a significant aspect for numerous applications in the chemical technology and is considered the subject of many theoretical and experimental researches. Evaluating the second law of thermodynamics is one of the contemporarily used methods to determine the performances of an industrial process and to study various sources of irreversibility. Expressions of the liquid velocity, the gas concentration, the entropy generation rate as well as the main sources of irreversibility in the case of gas absorption (carbon dioxide) into a laminar falling viscous incompressible liquid film (water) without chemical reaction, are analytically derived and graphically presented and discussed.     

Experimental study on surface wave and film breakdown of falling liquid film flow

In order to evaluate characteristics of the liquid film flow and their influences on heat and mass transfer, measurements of the instantaneous film thickness using a capacitance method and observation of film breakdown are performed. Experimental results are reported in the paper. Experiments are carried out at Re = 250–10000, T _in = 20–50°C and three axial positions of vertically falling liquid films for film thickness measurements. Instantaneous surface waveshapes are given by the interpretation of the test data using the cubic spline method. The correlation of the mean film thickness versus the film Reynolds number is also given by fitting the test data. It is revealed that the surface wave has nonlinear behavior. Observation of film breakdown is performed at Re = 1.40 × 10³–1.75 × 10⁴ and T _in = 85–95°C. From experimental results, the correlation of the film breakdown criterion can be obtained as follows: Bd = 1.567 × 10⁻⁶ Re ^1.183     

Model of a wavy flow in a falling film of a viscous liquid

A new model is developed for describing long-wave perturbations in a falling film of a viscous liquid. The model is based on an integral approach and an expansion of the velocity profile into a series in linearly independent basis functions of a boundary-value problem. A linear analysis of film flow stability is performed, and dispersion dependences are obtained. Results predicted by the new model are demonstrated to be in good agreement with available experimental data on the film flow over a gently sloping surface.     

Wave flow of a liquid film in a horizontal separator

The calculation of the motion of separated moisture in a linear horizontal separator is made on the basis of the analysis of the development of the waves in a flow of a thin layer of liquid along a vertical surface without allowance for the transverse flow of mass [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–176, March–April, 1985.     

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.