Interfacial mass transfer around a vapor bubble during nucleate boiling

Interfacial mass transfer from vapor bubbles affects markedly the heat transfer efficiency of nucleate boiling. The position of the interfacial zone that exhibits zero net mass flux, namely, the zero-flux zone, represents an essential parameter in detailed modeling works on nucleate boiling. Assuming a linear temperature profile in the superheated liquid adjacent to the heating wall, our previous work (Li et al. [10]) demonstrated the zero-flux angle as a function of wall superheat, solid-liquid- vapor contact angle, and bubble growth rate. To make a more realistic framework, we refined in this paper the proposed mass flux model by taking into account the role of thermocapillary flow that is induced by the temperature gradient around the vapor bubble, and that of non-condensable gas presented in the boiling liquid. The Hertz-Kundsen-Schrage equation describes the interfacial mass flux distribution along the vapor bubble surface. Owing to the flattened temperature distribution produced by thermocapillary flow, which significantly reduces the interfacial area to evaporation, the zero-flux zone shifts to the bubble base with most of the cap regime to condense vapor at the interface and to produce the thermal jet. This occurrence also weakens the dependence of bubble growth rate and of the contact angle on the location of zero-flux zone, and yields early occurrence of the non-condensation limit at which the entire bubble surface is subjected to evaporation. Sensitivity analysis demonstrated the significance of process parameters on the evaluation of zero-flux angle using the HKS equation.     

Convection and heat transfer in a spherical vessel,partly filled with liquid,under low-gravity conditions

In [1] the problem of natural and thermocapillary convection in a spherical vessel containing a bubble under low-gravity conditions, i.e., at low Bond numbers (Bo 1), was examined in one of the limiting cases — where the bubble is located in the center of the vessel. The results of [1] and experimental data, however, indicate that when heat is supplied from outside over a long period, the most probable location of the bubble under low-gravity conditions is at the vessel wall. In this paper, which is a continuation of [1], convection and heat transfer in the latter case are investigated. Possible locations of the bubble at the top and bottom of the vessel relative to the resultant of the weak mass forces are discussed. It is shown that natural and thermocapillary convection contribute to the increase in the mean free-surface temperature, which determines the increase in pressure in the closed vessel for a prescribed heat flux. The rates of increase of this temperature are compared in the cases considered here and in [1–4], where there is a fuller bibliography relating to convective heat and mass transfer under low-gravity conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–159, March–April, 1976.     

An investigation on near wall transport characteristics in an adiabatic upward gas–liquid two-phase slug flow

The near-wall transport characteristics, inclusive of mass transfer coefficient and wall shear stress, which have a great effect on gas–liquid two-phase flow induced internal corrosion of low alloy pipelines in vertical upward oil and gas mixing transport, have been both mechanistically and experimentally investigated in this paper. Based on the analyses on the hydrodynamic characteristics of an upward slug unit, the mass transfer in the near wall can be divided into four zones, Taylor bubble nose zone, falling liquid film zone, Taylor bubble wake zone and the remaining liquid slug zone; the wall shear stress can be divided into two zones, the positive wall shear stress zone associated with the falling liquid film and the negative wall shear stress zone associated with the liquid slug. Based on the conventional mass transfer and wall shear stress characteristics formulas of single phase liquid full-pipe turbulent flow, corrected normalized mass transfer coefficient formula and wall shear stress formula are proposed. The calculated results are in good agreement with the experimental data. The shear stress and the mass transfer coefficient in the near wall zone are increased with the increase of superficial gas velocity and decreased with the increase of superficial liquid velocity. The mass transfer coefficients in the falling liquid film zone and the wake zone of leading Taylor bubble are lager than those in the Taylor bubble nose zone and the remaining liquid slug zone, and the wall shear stress associated falling liquid film is larger than that associated the liquid slug. The mass transfer coefficient is within 10⁻³ m/s, and the wall shear stress below 10³ Pa. It can be concluded that the alternate wall shear stress due to upward gas–liquid slug flow is considered to be the major cause of the corrosion production film fatigue cracking.     

Transfer model and kinetic characteristics of $${\rm NH}_{4}^{+}$$ –K+ ion exchange on K-zeolite

Based on the mass transfer theory, a new mass transfer model of ion-exchange process on zeolite under liquid film diffusion control is established, and the kinetic curves and the mass transfer coefficients of –K⁺ ion-exchange under different conditions were systemically determined using the shallow-bed experimental method. The results showed that the –K⁺ ion-exchange rates and transfer coefficients are directly proportional to solution flow rate and temperature, and inversely proportional to solution viscosity and the size of zeolite granules. It also showed that the transfer coefficient is not influenced by the ion concentrations. For a large ranges of operational conditions including temperatures (10 − 75°C), flow rates (0.031 m s⁻¹ −0.26 m s⁻¹), liquid viscosities (1.002 × 10⁻³ N s m⁻² − 4.44 × 10⁻³ N s m⁻²), and zeolite granular sizes (0.2 − 1.45 mm), the average mass transfer coefficients calculated by the model agree with the experimental results very well.     

Upper limit of enhancement of boiling heat transfer in a narrow vertical rectangular channel due to passing bubbles

An experimental study has been made of saturated boiling heat transfer for water and R113 in a narrow vertical rectangular channel (2 mm space, 20 mm wide, and 200 mm long) at atmospheric pressure, in which the vertical heated surface (10 mm long and 20 mm wide) is located on one side at a position of 150 mm from its entrance and bubbles are forcibly passed through it at a designated period from 0.33 to 1.0 sec. The experiment shows that the heat transfer coefficients are increased by the bubble passing through the heated surface for the value of thermal diffusivity,a, times period, T₀, of the passing bubbles above about 6×10^–9 m² (a T ₀>6×10^–9 m²) while fora T ₀< 6×10^–9 m², the heat transfer coefficients become independent of the period and the effectiveness of the enhancement of the heat transfer owing to the passing bubble disappears.

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Die obere Grenze der Verbesserung des Wärmeübergangs beim Sieden in einem vertikalen, rechteckigen Kanal infolge von aufsteigenden Blasen

Zusammenfassung Es wurden Experimente über den Wärmeübergang beim Sättigungssieden mit Wasser und R113 in einem engen, vertikalen, rechteckigen Kanal (2 mm Abstand, 20 mm Breite und 200 mm Länge) bei Umgebungsdruck durchgeführt, wobei die vertikale, beheizte Oberfläche (10 mm lang und 20 mm breit) auf der einen Seite in einem Abstand von 150 mm vom Eintritt angeordnet ist und die Blasen zwangsweise durch den Kanal sich mit einem Periodenabstand von 0,033 bis 1,0 s bewegen. Das Experiment zeigt, daß die Wärmeübergangskoeffizienten durch das Vorbeistreichen der Blasen an der beheizten Oberfläche verbessert werden, wenn das Produkt aus Temperaturleitfähigkeit,a, mal der Periode, T₀, der vorbeistreichenden Blasen größer als 6×10^–9 m² liegt, während unterhalb dieses Wertes der Wärmeübergangskoeffizient unabhängig von der Blasenperiode ist und die Effektivität der Wärmeübergangsverbesserung infolge der Blasenströmung verschwindet.

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Nomenclature a thermal diffusivity of liquid - ¯h time-averaged heat transfer coefficient - q _w heat flux at wall - T ₀ period of passing bubble - T _w(t) temperature of heated surface - T _w amplitude of heated surface temperature Greek symbols thermal conductivity - thickness of liquid film     

Heat conduction in a plane wall subject to periodic temperature changes

Analytical solutions for the heat conduction in a plane wall with periodic temperature variations at the wall surface are presented. Series and asymptotic developments of these solutions are deduced. The results are important for the calculation of the heat transfer in rotary kilns or other rotaring units.

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Die Wärmeleitung in einer ebenen Wand mit periodischen Temperaturänderungen

Zusammenfassung Es werden analytische Lösungen für die Wärmeleitung in einer ebenen Wand mit periodischen Temperaturänderungen an ihrer Oberfläche mitgeteilt. Reihen- und asymptotische Entwicklungen dieser Lösungen werden abgeleitet. Die Ergebnisse sind wichtig für die Berechnung des Wärmetransportes in Drehrohröfen oder ähnlichen Maschinen.

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Nomenclature a ² =/ C m²/s thermal diffusivity, Eq. (1) - C J/kg K specific heat - F K initial temperature of the wall, Eq. (4) - F m² surface of the wall - G Green's function, Eq. (10) - G₁ Green's function, Eq. (12) - h m thickness of the wall - H Heaviside function, Eq. (5) - k constant, Eq. (25) - k _x constant, Eq. (25) - Q J total energy, Eq. (17) - Q ^u J total energy from temperatureU, Eq. (18) - Q ^v J total energy from temperatureV, Eq. (19) - s s^–1 Laplace variable - t s time - t ₁ s heating time, Eq. (5) - t ₂ s period, Eq. (5) - T K temperature of the wall - T _i K surface temperature of the wall - T ₁ K surface temperature of the wall during the heating time - T ₂ K surface temperature of the wall during the cooling time - U K temperature of the wall defined in problem 1 - V, K temperature of the wall defined in problem 2 - x m coordinate - ₀ W/m²K overall heat transfer coefficient, Eq. (31) - ₁₀ W/m² K overall heat transfer coefficient, Eq. (32) - ₂₀ W/m² K overall heat transfer coefficient, Eq. (33) - Dirac Delta function - s^–1/2 parameter, Eq. (6) - W/mK thermal conductivity - kg/m³ specific mass - dimensionless time, Eq. (34) - Riemann Zeta function surfix Laplace transformed variable     

The problem of a gas bubble in plane ideal fluid flow

We study the problem of two-dimensional fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall.Two-dimensional ideal fluid flow past a gas bubble on whose boundary surface-tension forces act (or a gas bubble bounded by an elastic film) has been studied by several authors. Zhukovskii, who first studied jet flows with consideration of the capillary forces, constructed an exact solution of the problem of symmetric flow past a gas bubble in a rectilinear channel [1]. However, Zhukovskii's solution is not the general solution of the problem; in particular, we cannot obtain the flow past an isolated bubble from his solution. Slezkin [2] reduced the problem of symmetric flow of an infinite fluid stream past a bubble to the study of a nonlinear integral equation. The numerical solution of this problem has recently been found by Petrova [3]. McLeod [4] obtained an exact solution under the assumption that the gas pressure p₁ in the bubble equals the flow stagnation pressure p₀. Beyer [5] proved the existence of a solution to the problem of flow of a stream having a given velocity circulation provided p₁p₀.We examine the problem of two-dimensional ideal fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall. The solution depends on the value of the contact angle . The existence of a solution is proved in some range of variation of the parameters, and a technique for finding this solution is given. The situation in which =1/2 is studied in detail.     

Effect of surface permeability on the structure of a separated turbulent flow and heat transfer behind a backward-facing step

The structure and heat transfer in a turbulent separated flow in a suddenly expanding channel with injection (suction) through a porous wall are numerically simulated with the use of two-dimensional averaged Navier–Stokes equations, energy equations, and v ²–f turbulence model. It is shown that enhancement of the intensity of the transverse mass flux on the wall reduces the separation region length in the case of suction and increases the separation region length in the case of injection up to complete boundary layer displacement. The maximum heat transfer coefficient as a function of permeability is accurately described by the asymptotic theory of a turbulent boundary layer.     

Visualization study of evaporation of single n-pentane drops in water

A laser shadowgraph system was constructed to enable successive filming of a drop or a bubble rising or falling in an immiscible liquid confined within a vertical column. The assembly was applied to a study of the evaporation of n-pentane drops in a stagnant medium of water. The liquid/vapor two-phase bubble evolving from each pentane drop was observed together with its wake, the morphology and the dynamics of which are our primary concern in considering the mechanism of the medium-to-bubble heat transfer.List of symbols a minor axis of ellipsoidal two-phase bubble - b major axis of ellipsoidal two-phase bubble - D ₀ diameter of saturated-liquid drop set to vaporize - Re Reynolds number based on instantaneous, volume-equivalent spherical diameter and rise velocity of two-phase bubble and kinematic viscosity of the continuous phase - t time lapse after the start of evaporation - T ^* excess of undisturbed continuous-phase temperature above the temperature at which the sum of the saturated vapor pressures of the dispersed- and the continuous-phase fluids is equal to the pressure at the position where evaporation starts - opening angle of wake-covered region on bubble surface - _w zenith angle at flow-separation ring on bubble surface - mass fraction of vapor in two-phase bubble     

Turbulent heat and mass transfer for Pr ≫ 1 and law of turbulent diffusion damping at a solid wall

The question of determining the law of damping for the turbulent diffusion coefficient at a smooth wall according to data on mass and heat transfer for Pr 1 is discussed. It is proved that the hypothesis that this law is determined by the first member of the Taylor series expansion of , namely, / = yⁿ ₊ is valid in the Pr range from 10³ to 10⁵ only under the assumption that the subsequent terms in the expansion have smaller coefficients. A statistical analysis of electrochemical and other experiments devoted to this problem shows that apparently n = 3, but singularities in the experimental results do not permit making a final conclusion. Requirements on a conclusive experiment are formulated on the basis of the analysis made.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 172–175, March–April, 1977.     

Pressure wave breakdown of a gas film in a liquid-filled slit

In [1–4] the results of investigating the breakdown of gas bubbles by medium-intensity pressure waves are presented and various bubble breakdown mechanisms are proposed. It is shown that breakdown may occur as a result of the formation of a cumulative jet on the boundary of the bubble or as a result of instability due to the relative motion of the bubble in the wave. In [5] experimental data on the pressure wave breakdown of a gas film in a liquid on a solid wall are reported. It is shown that at wave amplitudes p/p₀1 a liquid jet is formed at the edge of the gas film. The jet, traveling along the wall, strips off the film and carries it into the surrounding liquid. Below we investigate the pressure wave behavior of a gas film in a liquid-filled slit.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 175–178, September–October, 1992.     

Effects of Bubbles on the Hydraulic Conductivity of Porous Materials – Theoretical Results

In a porous material, both the pressure drop across a bubble and its speed are nonlinear functions of the fluid velocity. Nonlinear dynamics of bubbles in turn affect the macroscopic hydraulic conductivity, and thus the fluid velocity. We treat a porous medium as a network of tubes and combine critical path analysis with pore-scale results to predict the effects of bubble dynamics on the macroscopic hydraulic conductivity and bubble density. Critical path analysis uses percolation theory to find the dominant (approximately) one-dimensional flow paths. We find that in steady state, along percolating pathways, bubble density decreases with increasing fluid velocity, and bubble density is thus smallest in the smallest (critical) tubes. We find that the hydraulic conductivity increases monotonically with increasing capillary number up to Ca 10^–2, but may decrease for larger capillary numbers due to the relative decrease of bubble density in the critical pores. We also identify processes that can provide a positive feedback between bubble density and fluid flow along the critical paths. The feedback amplifies statistical fluctuations in the density of bubbles, producing fluctuations in the hydraulic conductivity.     

Heat transfer to an isothermal flat plate in turbulent flow of a liquid over a wide range of prandtl and reynolds numbers

The study of heat transfer in turbulent flow over a flat plate is very important, not only because this situation frequently arises in practice, but also in that data for an isothermal flat plate are used to calculate heat transfer in more complex cases. In particular, such data are necessary when one uses the limiting relative laws which allow calculation of the effect of compressibility, pressure gradient, blowing, and other perturbing factors [1]. Most papers dealing with heat transfer for an isothermal flat plate refer to comparatively low Re values, when the velocity distribution in the boundary layer over almost its entire thickness can be described by the universal law of the wall. However, as Re increases there is an increasing layer adjacent to the outer boundary in which the velocity distribution cannot be described by the law of the wall, and therefore the results obtained for low Re are inapplicable. In the present paper coefficients of heat transfer from a turbulent flow to an isothermal flat plate have been obtained by numerical integration of the thermal boundary-layer equations over a wide range of the parameters 3 · 10⁵ Re 2.5·10¹², 10² Pr 10³.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 94–100, July–August, 1976.     

Experimental investigation of mixed convection from an array of discrete heat sources at the bottom of a horizontal channel

Mixed convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally under various operating conditions for air. The lower surface of the channel was equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux, sidewalls and the upper wall are insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR = 10, Reynolds numbers 241 Re_Dh 980, and modified Grashof numbers Gr^* = 9.53 × 10⁵ to 1.53 × 10⁷ . From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers, with emphasis on changes obtained for different discrete heat source locations. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit, especially for low Reynolds numbers.     

Oscillating convection modes in the surroundings of an air bubble under a horizontal heated wall

The development of different oscillatory modes and their transition into a non-periodic state of convection, initiated by the thermal Marangoni-effect in the vicinity of an air bubble under a horizontal, heated wall, was investigated. In the further surroundings of the air bubble a stably stratified thermal field was maintained. The flow phenomena in the vicinity of the bubble were studied using light sheet and shearing interferometer flow visualization techniques. The observed modes are described with regard to their kinematics. The influence of the Marangoni number and of the bubble geometry on the mode selection is discussed. The boundaries of the different modes and of the non-periodic state are indicated.List of symbols a thermal diffusivity - Bo Bond number, Eq. (4) - c phase velocity, Eq. (6) - g acceleration due to gravity - l characteristic length - Mg Marangoni number, Eq. (1) - n wavenumber - Pr Prandtl number ( = v/a) - r radial coordinate - r _B bubble radius - Ra Rayleigh number ( = ga¦T/r¦l ⁴/va) - Re Reynolds number ( = u _mg l/) - t _p oscillation period - T temperature - T _w wall temperature - u _mg characteristical Marangoni velocity, Eq. (2) - z axial coordinate normal to the heated wall - z _B bubble height Greek letters surface tension - kinematic viscosity - dynamic viscosity Dedicated to Professor Dr.-Ing. Julius Siekmann on the occasion of his 65th birthday     

Wärmetransport in der Umgebung einer wachsenden Dampfblase

Zusammenfassung Der Wärmetransport in der Heizwand sowie die Blasenform während des Blasenwachstums werden qualitativ analysiert. Der Entstehungsvorgang der Mikroschicht wird eingehend beschrieben. Es wird gezeigt, daß die im allgemeinen angenommene Verdampfung an der Mikroschicht nicht in allen Fällen zutrifft. Der Wärmetransport in der Nähe der wachsenden Dampfblase wird ausschließlich durch die physikalischen Eigenschaften der Flüssigkeit und der Heizwand bestimmt.

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Heat transfer in the surrounding of a growing vapour bubble

Heat transfer during bubble growth and the shape of the vapour bubble near a heated wall are qualitatively analysed. The development of the temperature field in the wall near the growing bubble and the formation of the microlayer are described. It is shown that the usual microlayer theory does not hold in all cases of bubble growth. Processes of heat transfer during bubble growth and, consequently, boiling phenomena depend essentially on the physical properties of the boiling liquid and of the heating wall.

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Formelzeichen a Temperaturleitfähigkeit - Wärmestrom - Ergiebigkeit der Wärmesenke - r Radius, Kugelkoordinate - r _* Krümmungsradius - t Zeit - T Temperatur - T ₀ konstante Temperatur - Oberflächenspannung - Wärmeleitfähigkeit     

Transients in flow and local heat transfer due to a pressure wave in pipe flow

The effect of a pressure wave on the turbulent flow and heat transfer in a rectangular air flow channel has been experimentally studied for fast transients, occurring due to a sudden increase of the main flow by an injection of air through the wall. A fast response measuring technique using a hot film sensor for the heat flux, a hot wire for the velocities and a pressure transducer have been developed. It was found that in the initial part of the transient the heat transfer change is independent of the Reynolds number. For the second part the change in heat transfer depends on thermal boundary layer thickness and thus on the Reynolds number. Results have been compared with a simple numerical turbulent flow and heat transfer model. The main effect on the flow could be well predicted. For the heat transfer a deviation in the initial part of the transient heat transfer has been found. From the turbulence measurements it has been found that a pressure wave does not influence the absolute value of the local turbulent velocity fluctuations. They could be considered to be frozen.Nomenclature A surface area (m²) - D diameter (m) - h heat transfer coefficient (Wm^–2 K^–1) - p pressure drop (Pa) - P pressure (Pa) - Q heat flow (W) - R tube radius (m) - T bulk temperature (K) - T _s surface temperature (K) - t time (s) - u velocity (m/s) - V voltage (V) - y distance from wall (m) - viscosity (N s m^–2) - kinematic viscosity (m^–2 s^–1) - density (kg m^–3) - _w wall shear stress (N m^–2) - Nu Nusselt number - Re Reynolds number     

Heat transfer of gas-particle flow in a supersonic convergent-divergent nozzle

Summary Heat flux, wall heat transfer coefficients, and wall pressures are determined for high velocity flow of gas-solid mixtures in a converging-diverging nozzle. Flow separation accompanied with oblique shock formation occurs in the diverging section of the nozzle. The shock strength is reduced upon the addition of solid particles. The wall pressure in the convergent section of the nozzle appears unaffected by the presence of solid particles. In the divergent section, however, the wall pressure is slightly lowered. At the maximum ratio of solid to air flow used in the experiments (3.7) increases in the heat transfer rate of up to 20 and 50 percent are obtained in the convergent and separated (divergent) regions of the nozzle, respectively. Slightly larger increases in the wall heat transfer coefficients are also obtained. It is concluded that the wall heat flux and heat transfer coefficients are influenced strongly by the presence of disturbances upstream of the nozzle inlet.Nomenclature W _a air flow rate - W _s solids flow rate - x axial distance from nozzle entrance - L axial length of nozzle - specific heat ratio of fluid - A _e exit cross section of flow - A _* throat cross section of flow - P ₀ inlet pressure - P _s wall separation pressure - P _a ambient exhaust pressure - shock wave angle - shock wave deflection angle - M ₁ Mach number upstream of shock wave - Mach number normal to shock wave - q heat flux - k _f thermal conductivity of fluid - T _wi inside wall temperature - T _wo outside wall temperature - T _ad adiabatic wall temperature - h wall heat transfer coefficient - C nozzle constant - A local cross section of flow - c _p specific heat of fluid - Pr Prandtl number - viscosity of fluid - r _c throat radius of curvature - factor accounting for variation of and Units absolute temperature °R(ankine) °F+459.7 - conductivity 1 BTU (hr ft °F)^–1 4.137×10^–3 cal (s cm °C)^–1 - specific heat 1 BTU (1b °F)^–1 1 cal (g °C)^–1 - absolute pressure 1 psia 0.0680 atm Supported in part by aid provided by the UCLA Space Science Center (Grant NsG 236-62 Libby).Listed for readers not familiar with the units adopted in this paper (editor).     

Understanding the Piche evaporimeter as a simple integrating mass transfer meter

Results are presented of a comparison of measured and calculated evaporation rates of the Piche evaporimeter under indoor and outdoor (within a meteorological screen) conditions. In both cases, application of mass transfer formulae in use for horizontal (turbulent) flow to the evaporating blotting paper of the instrument yield very good results under pure forced convection conditions. For mixed convection regimes, comparisons using either pure free (combined heat and mass transfer) or pure forced convection equations give as expected too low calculated values. Reasons for such differences with measured values are reviewed. Our forced convection results confirm that main stream turbulence is only of influence on mass transfer to a zero incidence flow in combination with pressure gradient (bluff body) effects, which under our conditions appear to be absent around the Piche surfaces. The same results prove absence of any influence of the particular temperature distribution over the blotting paper on the mass transfer. The understanding and importance of these conclusions in relation to the use of the Piche evaporimeter as a simple integrating mass transfer meter under actual farming conditions are discussed. The importance to obtain such mass transfer data is explained in the introduction.Nomenclature A Numerical constant in free convection Sherwood number - Coefficient of thermal expansion (K^–1) - C _{(s, b)} Water vapour concentration average at the evaporating surface (s) and in the bulk air (b) (g m^–3) - D Coefficient of molecular diffusion of water vapour in air (m² s^–1) - d Characteristic dimension of the paper disc in the direction of flow (m) - E _{(c, m)} Evaporation rates of the Piche evaporimeter, calculated (c) and measured (m) (units in text) - e _{(s, b)} Partial water vapour pressure average at the evaporating surface (s) and in the bulk air (b) (mbar) - Gr Grashof number - g Acceleration of gravity (m s^–2) - m Number of measuring periods - n Numerical constant in free convection Sherwood number - Coefficient of kinematic viscosity of air (m² s^–1) - P Atmospheric pressure (mbar) - Re Reynolds number - _{(s, b)} Air density average at the evaporating surface (s) and of the bulk air (b) (g m^–3) - Sh Sherwood number - T _{(s, b)} Temperature average of the evaporating surface (s) and in the bulk air (b) (K) - T _{(vs, vb)} Virtual temperature average at the evaporating surface (s) and in the bulk air (b) (K) - U Wind speed (air movement) average of the bulk air (m s^–1)