THE INFLUENCE OF AIR VELOCITY AND TRANSPORT PROPERTIES ON THE SURFACE MASS TRANSFER

COEFFICIENT IN A RECTANGULAR TUNNEL – THEORY AND EXPERIMENTS

Goce Taleva*, Arild Gustavsena , and Erling Næssb

aDepartment of Civil and Transport Engineering, Norwegian University of Science and

Technology (NTNU), Høgskoleringen 7, NO-7491 Trondheim, Norway bDepartment of Energy and Process Engineering, Norwegian University of Science and

Technology, Kolbjørn Hejes vei 1B NO-7034 Trondheim, Norway

Abstract

This paper explores the role of transport properties of moist air as well as the air

velocity on the convective surface mass transfer coefficients at different axial positions in

a rectangular cross-section wind tunnel. Experimental work has been performed to

determine the local mass transfer coefficients using three equal horizontal water cups,

placed inline after one another in the tunnel. Each of the three samples holders had a

square shape with length and width equal to 60 mm and was mounted in line with the

bottom surface of the wind tunnel, so that the air stream passed over the water surface.

The experiments were carried out for a bulk air temperature of 20°C and for relative

humidities of 30%, 50% and 70%, and with air velocities between 0, 1 and 5 m/s. The

experimental data showed that the mass transfer coefficients were functions of air

velocity and relative humidity as well as the position of the sample relative to the inlet of

the tunnel. The experimental results were compared to convective mass transfer

correlations from the literature.

* Corresponding author: E-mail: Goce.Talev@ntnu.no, Phone: + 47 73594704.

1

Introduction

The rapid development in modeling development in hygrothemal building

performance requires knowledge of the surface mass transfer coefficients of building

materials. Convective surface mass transfer coefficient describes the moisture transport

resistance between the surface wall and environmental flowing air. To be able to fully

understand the surface mass transfer coefficient it is important to carefully investigate the

effect of the velocity boundary layer as well as temperature and concentration boundary

layers on mass transfer.

The convective surface mass transfer coefficient becomes an important parameter

for indoor environment, since the indoor environment strongly depends on moisture

interaction between the room air and surrounding construction and room furniture. In

addition the influence of the ventilation is important.

Several studies of the surface mass transfer coefficient between the water surface

and air flow have been published. Several of those are experimental investigations that

have studied the convective mass transfer coefficients for water evaporation as a function

of air velocity, e.g. Carrier (1921), Hinchley and Himus (1924), Luire and Michailoff

(1936), Leven (1942), Wadsö (1993), and Iskra and Simonson (2006). Few studies have,

however, been performed on typical building materials. Jacobsen and Aarseth (1997)

used a wind tunnel to investigate permeable materials such as gas concrete, yellow tile

etc. Derome (2004) has investigated the SMTC of the wood specimens with moisture

content of 12%.

Knowledge of the influence of air velocity across a moist surface in combination

with the effects of concentration and thermal boundary layers on the moisture transfer

rate is essential in order to describe and predict the moisture interactions between the

construction and the environmental air. Therefore, the experiments in this paper focus on

determination of the local surface mass transfer coefficients as functions of the air flow

velocity, the relative humidity of the air, and including the unheated and no evaporated

starting length. A wind tunnel with a cross-sectional flow area of 0, 1 x 0, 6 m was used

in the experiments. The experimental results were compared to predictions using

2

theoretical and semi-empirical literature correlations for water evaporation from a

surface.

Theory

The evaporation rate from a surface strongly depends on the air velocity and the

thermal and concentration boundary conditions across the surface. A velocity boundary

layer will develop when air flows over the surface in which the velocity of the air

decreases to zero at the surface.

The thermal boundary layer results from a difference between the surface and free

stream temperatures, while the concentration boundary layer originates from a difference

between the free stream and surface concentration (c∞ ≠ c o) (Incropera and deWitt,

2002).

Figure 1. Development of the velocity, thermal, and concentration boundary layers

(figure from Incropera and deWitt, 2002)

Velocity Boundary Layer

There are basically two different forms of boundary layer flow: laminar and

turbulent. In laminar boundary flow, the transport of species (moisture), temperature and

momentum across the boundary layers are controlled by molecular diffusion. In turbulent

flow, the transport of species, temperature and momentum is greatly enhanced by local

transverse velocity fluctuations (turbulence) in the boundary layer, see Figure 2. The fluid

3

motion in the turbulent velocity boundary layer is very irregular due to the velocity

fluctuations. Due to these velocity fluctuations the turbulent boundary layer thickness

becomes larger than for laminar flow. Velocity fluctuations start to develop in the

transition region, where the fluid viscosity is incapable of damping the instabilities

occurring in the flow. In classical fluid mechanics, the turbulent boundary layer can be

described as composed of three different regions: The laminar sublayer is characterized

by dominated diffusion transport and a linear velocity profile. In the intermediate zone or

buffer layer, turbulent mixing is gradually becoming more pronounced with increasing

distance from the surface. In the outer fully turbulent zone the mixing due to transverse

velocity fluctuations is dominant. The velocity boundary layer strongly influenced by the

transport properties of the working fluid (air), i.e. the dynamic viscosityμ , as well as the

velocity, the axial position and the fluid density ρ . These dependences are described by

the local Reynolds number,

Rexu x u xρμ ν⋅ ⋅ ⋅

= = (1)

where x is the axial position from the leading edge of the surface. The Reynolds number

is a ratio of inertia to viscous forces, and thus the stability of a laminar flow is associated

with the value of Reynolds number. Stable laminar flow is described with low values of

the Reynolds number. For external flows, representative for the flow that will be found

around and within most buildings, laminar flow is found for Reynolds numbers less than

approximately 3×105 (Incropera and deWitt, 2002). Turbulent flow is typical for

Reynolds numbers larger than about 5×105. For the intermediate Reynolds number range,

the flow will be in transition between laminar and turbulent. (For flow in channels and

pipes the channel hydraulic diameter is frequently used as length scale, and the

corresponding Re-numbers are laminar flow for Re < 2 300 and turbulent flow for Re >

10 000 (Incropera and deWitt, 2002)).

4

Figure 2. Development of laminar, turbulent, and transition velocity boundary layers

(figure from Mijakovski, 2003).

Thermal Boundary Layer

In the real building physics cases, there will be heat transfer between the wall

surface and the moist air flowing along the surface. The thin layer above the surface in

which temperature changes from the surface temperature to to the air free-stream

temperature t∞ is called the thermal boundary layer. The Nusselt number represents a

dimensionless effective thermal conductance across the boundary layer and provides a

means for the calculation of the surface-to-air convective heat flux. The local Nusselt is

defined as

·xx

h xNuλ

= (2)

where x is the axial position from the leading edge of the geometry. The Nusselt number

is in general a function of the surface geometry, the Reynolds number, the Prandtl

number and the position, i.e.

)Pr,,(Re xfNu xx = (3)

For laminar external flow over the flat plate the local Nusselt number, according to

Incropera and DeWitt (2002) can be expressed by 130,332· Re·PrNu = (4)

For turbulent external flow over the flat plate the local Nusselt number according to

Incropera and DeWitt (2002) can be expressed by 4 150,0296·Re ·PrxNu = 3 (5)

5

Kays and Crawford (1993), presented a slightly different correlation for turbulent

external gas flow over a flat plate: 0,8 0,60,0287·Re ·PrxNu = (6)

The difference between Equations (5) and (6) are mainly the Pr-number dependency,

however, since Pr is close to unity for gases (Pr≈0, 7 for air), this discrepancy has little

influence on the resulting heat transfer coefficient.

Concentration Boundary Layer

The water vapor concentration (co) at the body interface is determined by

thermodynamic equilibrium condition at the surface. In the free stream the concentration

of the working fluid (air) is c∞. Then the region in which the concentration changes from

c∞ to co is called concentration boundary layer. The concentration boundary layer has

many of the same features as the temperature boundary layer, and in practice the mass

transfer coefficient may be determined from heat transfer by analogy. In practice, this

means that the same correlations/models may be used to describe both heat and mass

transfer. The Sherwood number describes the dimensionless mass transfer coefficient,

and is given by:

xx

AB

xShDβ ⋅

= (7)

By heat and mass transfer analogy, if the dimensionless heat transfer coefficient (Nu) is

described by equation 3 then the dimensionless mass transfer coefficient (Sh) may be

described by

),,(Re xScfSh xx = (8)

where f is the same function for both processes –equation (3) and (8).

Hence, for laminar external flow over the flat plate the local Sherwood number can, by

analogy to equation 4 are express by:

31

PrRe332,0 ⋅⋅= xxSh (9)

The ratio of velocity boundary thickness (δ) and concentration boundary thickness (δc)

can be written:

6

31

~ Sccδδ (10)

and the ratio of the thermal to concentration boundary layer thicknesses is given by 13

~Pr

t

c

Scδδ

⎛ ⎞⎜ ⎟⎝ ⎠

(11)

For turbulent external flow over the flat plate the local Sherwood number can be

determined by analogy to turbulent heat transfer (equation (5)): 4 150,0296 RexSh Sc= ⋅ ⋅ 3x (12)

or equation 6: 0,8 0,60,0287 Re Prx xSh = ⋅ ⋅ (13)

Surface Mass Transfer Coefficients along an Unheated Flat Plate with a No

Evaporation Starting Length

A number of approximate procedures have been proposed for determining mass

transport through laminar and turbulent boundary layers with an unheated and no

evaporation starting length upstream the water pool. The appropriate energy equations

can be used for solving laminar as well as turbulent boundary layers on a flat plate for a

case where evaporation starts at point ξ=x on the plate, rather than at where the

velocity boundary layer starts. It is assumed that velocity boundary layer is thicker than

thermal boundary layer.

0=x

An analysis of the laminar fluid flow over the flat plate that considers

conservation of momentum and energy, including an unheated starting length, results in

the following equation for the Nusselt number Nux as a function of position x (Kays and

Crawford, 1993) 13

13 34

0,332 Pr Re

1

xxNu

xξ

⋅ ⋅=

⎡ ⎤⎛ ⎞⎢ ⎥− ⎜ ⎟⎢ ⎥⎝ ⎠

⎣ ⎦

(14)

7

Figure 3. Boundary layer development on a flat plate with unheated and no evaporation

starting length (figure from Kays and Crawford, 1993)

For turbulent external flow the corresponding solution is (Kays and Crawford, 1993) 1

0,9 90,8 0,60,0287 Re Pr 1x xNu

xξ

−⎡ ⎤⎛ ⎞= ⋅ ⋅ ⋅ −⎢ ⎥⎜ ⎟

⎝ ⎠⎢ ⎥⎣ ⎦ (15)

By analogy to heat transfer, the corresponding correlations for the local

dimensionless mass transfer coefficients (Shx) can be expressed as equation (16) for

laminar flow and equation (17) for turbulent flow. 13

13 34

0,332 Re

1

xx

ScSh

xξ

⋅ ⋅=

⎡ ⎤⎛ ⎞⎢ ⎥− ⎜ ⎟⎢ ⎥⎝ ⎠

⎣ ⎦

(16)

Similar, a local dimensionless Sherwood number including an unheated as well as no

evaporated starting length can be presented for turbulent external flow 1

0,9 90,8 0,60,0287 Re 1x xSh Sc

xξ

−⎡ ⎤⎛ ⎞= ⋅ ⋅ ⋅ −⎢ ⎥⎜ ⎟

⎝ ⎠⎢ ⎥⎣ ⎦ (17)

From Equations (16) and (17) the local surface mass transfer coefficient for laminar and

turbulent flow can be determined

8

13

13 34

0,332 Re

1

x ABx

Sc Dx

x

β

ξ

⋅ ⋅=

⎡ ⎤⎛ ⎞⎢ ⎥− ⎜ ⎟⎢ ⎥⎝ ⎠

⎣ ⎦

⋅ (18)

10,9 9

0,8 0,60,0287 Re 1 ABx x

DScx xξβ

−⎡ ⎤⎛ ⎞= ⋅ ⋅ ⋅ − ⋅⎢ ⎥⎜ ⎟

⎝ ⎠⎢ ⎥⎣ ⎦ (19)

In the figures presented in the experimental part, equations (18) and (19) will be noted as

“Theoretical model 1” while “Theoretical model 2” is given by equation (20), a purely

empirical correlation from Blocken et al. (2006)

)6,54(107,7 9 +⋅⋅= − uxβ (20)

Experimental Procedure

The wind tunnel is constructed from plywood with a rectangular internal cross

section of length L = 1 m, width W = 0,6 m and height H = 0,1 m. Moisture transport

between the free water surface and the surrounding air flowing across the surface by

convection from the water surface. Three were no internal heat sources in the water bath.

Parallel wind direction at varying velocity and relative humidity, at a free-stream air

temperature of 20°C was provided by a fan blowing through honey combs of length in

the flow direction of L1 = 30 mm and a cross section length of d = 3 mm across the

honeycomb cells. The honeycomb flow straightness was included to ensure unidirectional

flow in the wind tunnel. Air velocities were varied in the range between 0, 1 and 5 m/s.

Three equal samples holders, named Cup 1, 2 and 3, are placed in the wind tunnel

on a parallel line to the flow. A window was situated along the full width of the tunnel

above the specimens for visual inspection during the test. Each sample holder had a

quadratic shape with side lengths of 60 mm and was mounted in fluctuation with the wind

tunnel floor, see Figure 4. The sample holders were manufactured from plastic and were

easily removable and adjustable from below the tunnel floor for mounting. The water

supply to the sample holders was arranged to keep the water surface flush with the wind

tunnel floor. The water supplies were also equipped with water gages in order to measure

the water loss/evaporation rate (see Figure 5).

9

The temperature of the water sample surface was measured to be a few degrees

lower than the temperature in the free air stream, close to the wet bulb temperature. This

is as expected, since there was no internal heat source in the liquid pools, and heat had to

be removed from the flowing air in order to evaporate the water.

Figure 4. Bottom surface of the wind tunnel, seen from above.

Figure 5. Water supplies of the sample holders. The numbers in the figure is in

centimeters (cm). The space between the cups is 6 cm.

Results and Discussion

About three hundred experiments were carried out; ninety-seven were successful

in providing a water surface flush with the tunnel floor. In the other experiments concave

or convex water surfaces were observed, and which produced erroneous results. Thus,

these results are not included (but may be analyzed later to see the influence of this

10

effect). By measuring evaporation rate from the “water cup” the convective mass transfer

coefficient from the water surface was found.

Surface Mass Transfer Coefficient as a Function of Airflow Velocity and

Distance from the Tunnel Opening for Varying Air Relative Humidity

A series of experiments was performed to determine the resistance of the moisture

transport between the free water surface and moist air as a function of air velocity,

distance from the tunnel opening and the relative humidity (RH). All the experiments

were carried out for a moist air temperature of 20 °C. The results are shown in Figures 6

to 14. Figures 6, 7 and 8 displays results where RH of 30%, Figures 9, 10 and 11 shows

the results for RH equal to 50%, and Figures 12, 13 and 14 displays results where the

relative humidity is 70%. Figures 6, 9 and 12 are for cup number 1 which is a distance of

0,37 m from the wind tunnel entrance, Figures 7, 10 and 13 are for cup number 2 which is

0,49 m from the tunnel entrance, and the last figures (8, 11 and 14) are of the last cup in

the tunnel which is 0,61 m from the opening. Each figure shows the surface mass transfer

coefficient on the vertical axis in units kg/ (Pa× ·s × ·m2). The horizontal axis shows the

airflow velocity at the tunnel entrance. Further, each diagram includes results from 5

measurements, noted Measurement 1 to 5, and the average of these measurements (noted

“Average Measurement”). In addition the figures include results from applying Equations

(18), (19) and (20), which are noted “Theory 1 Laminar”, “Theory 1 Turbulent”, and

“Theory 2”, respectively. Notice that “Theory 2” is intended for airflow velocity lower

than 5m/s.

First the results in the figures show that there is some spread in the experimental

data. This is mainly attributed by the fact that there was very difficult to maintain a

perfectly flat water surface. The measurements showed that a convex surface had a higher

mass transfer coefficient than a flat surface. A concave water surface has a lower mass

transfer coefficient than a flat water surface (this can not be expressed by the correlations

presented in this paper). The water supply system was also quite difficult to control. Still,

the measured results show the same trend. Questions could also be raised about whether

the measured results represent an ideal external flow or not. For a position of 37 cm (for

cup 1) and 61 cm (for cup3) from the tunnel entrance the velocity boundary layer

11

thickness will be about 4 cm and 5 cm (calculated with an equation from White, 1999),

respectively, at a velocity of 0,1 m/s. At a free stream velocity of 1 m/s the boundary

layer thickness will be about 1, 2 cm for cup 1 and 1,5 cm for cup 3. Generally, a large

Reynolds number represents a thinner boundary layer (at a fixed position, x), while a

small Reynolds number represents in a thicker boundary layer. Thus, data for low

velocities may therefore not be representative for a real external flow. (Later, experiments

will be carried out in a modified wind tunnel to ensure the results are for external flow,

for all velocities.

The figures show that the surface mass transfer coefficient was a function of the

airflow velocity (u ), local position (x), and the relative humidity (RH). This can be seen

both by looking at the individual figures and by comparing the results from figure to

figure. All figures show that the surface moisture transfer coefficient increased with the

air velocity. This is because an increased velocity reduced the boundary layer thickness.

By comparing results from figures 6 (results for cup 1 and relative humidity of 30%) and

12 (cup 1 and RH of 70 %) the measurements show that an increase in the RH resulted in

a decrease in the surface mass transfer coefficients. If we compare the measured results in

Figure 6 (cup 1, 37 cm from tunnel entrance, and RH equal to 30%) with the results in

Figure 8 (cup 3, 61 cm from tunnel entrance, and RH equal to 30%), we find that an

increased distance from the tunnel entrance resulted in a reduction of the surface moisture

transfer coefficient. Similar trends can be seen for the other relative humidities.

Generally, there is quite poor agreement between the measured and the theoretical

results. Lack of resemblance between the measured data and theoretical equations may be

because the theoretical equations not are taking into account all the processes taking place

(e.g. thermal radiation, ‘blowing’ effects (non-zero transverse velocity at interface), etc.).

Further analysis is required in order to explain the observed discrepancies.

12

Figure 6 Surface mass transfer coefficient as a function of air velocity at T=20°C;

RH=30% for the first cup.

Figure 7 Surface mass transfer coefficient as a function of air velocity at T=20°C;

RH=30% for the second cup.

13

Figure 8. Surface mass transfer coefficient as a function of air velocity at T=20°C;

RH=30% for the third cup.

Figure 9. Surface mass transfer coefficient as a function of air velocity at T=20°C;

RH=50% for the first cup.

14

Figure 10 Surface mass transfer coefficient as a function of air velocity at T=20°C;

RH=50% for the second cup.

Figure 11. Surface mass transfer coefficient as a function of air velocity at

T=20°C; RH=50% for the third cup.

15

Figure 12 Surface mass transfer coefficients as a function of air velocity at

T=20°C; RH=70% for the first cup.

Figure 13 Surface mass transfer coefficient as a function of air velocity at T=20°C;

RH=70% for the second cup.

16

Figure 14 Surface mass transfer coefficient as a function of air velocity at T=20°C;

RH=70% for the third cup.

Especially, importance should be paid to the variation of the relative humidity of

the moist air. The experimental results in this study and the results in the experimental

study of Iskra and Simonson (2006) show that the surface mass transfer coefficient

decreases when RH increases. Calculation of the surface moisture transport coefficient by

theoretical model one, including the transport properties of the moist air, shows

increasing values of the surface coefficients by increasing the relative humidity of the

moist air (thus the opposite as the experiments). The change in the surface moisture

transport coefficient in theoretical model 1 is mainly because of changing viscosity and

density (the other properties of moist air do not influence Re, which is the main

parameter for determining mass transfer surface coefficient according to equations (18)

and (19)). Increasing the relative humidity leads to a decrease in the transport properties

of moist air like thermal conductivityλ , dynamic viscosityμ , density ρ , etc., see

Table 1. A decrease in the viscosity again leads to an increase in the Reynolds number,

which again reduces the boundary layer thickness. This leads to a higher value for the

surface mass transfer coefficient. This is the reason for the theoretical results shown in

17

the figure. However, these theoretical results have a trend that is opposite from what we

find in the experiments.

On the other side, an increased thermal conductivity would lead to a higher

transport coefficient (surface heat and mass transfer coefficients). Because of the fact the

thermal conductivity of the moist air decreases by increasing the relative humidity of the

moist air, a lower value of the surface mass transfer coefficients should be expected.

Thus, the theoretical models should be examined in more details in later studies to

investigate how they can be adjusted or expanded to find models that also can be used for

moist air.

The second theoretical model is strictly depend on air velocity but does not take

into account the changes of Relative humidity and the local position. Increasing the air

velocity leads to increasing surface mass transfer coefficient (theoretical model 2)

Table 1. Fundamental physical properties of air at temperature 20°C as a function of

relative humidity. ρ λ Cpa ν (10 ) 6

µ (10 ) 6

⎟⎟

⎠

⎞⎜⎜⎝

⎛s

m2

)(mKW

)( 3mkg

RH (%)

sPa *

)(kgK

J

Cpv

)(kgK

J

Cp

)(kgmixairK

J

0

0,0256 1,203 18,150 15,087 1005,034 1870,445 1005,0334

10

0,0257 1,202 17,960 14,942 1005,034 1870,445 1006,297

20

0,0256 1,201 17,590 14,646 1005,034 1870,445 1007,543

30

0,0251 1,200 17,050 14,208 1005,034 1870,445 1008,798

40

0,0245 1,199 16,350 13,636 1005,034 1870,445 1010,045

50

0,0236 1,198 15,510 12,947 1005,034 1870,445 1011,325

60

0,0226 1,197 14,530 12,139 1005,034 1870,445 1012,580

70

0,0214 1,196 13,440 11,237 1005,034 1870,445 1013,887

80

0,0201 1,195 12,250 10,251 1005,034 1870,445 1015,151

90

0,0187 1,194 10,950 9,171 1005,034 1870,445 1016,475

100

0,0172 1,193 9,750 8,022 1005,034 1870,445 1017,150

18

Comparison with previous results

Figure 15 compares the results in this study with the results of Time (1998) and

Wadsø (1993). The results from this study is reported as an average value. The two set of

data from Time at al. (1998) to differentiate between measurements at 1,5 and 5 m/s (two

data points are included because two results are reported). The results from Wadsø (1993)

is given only for 5 m/s. The graph shows that the experimental our results compare quite

good to the experimental results of Wadsø (1993) and Time et al (1998).

Figure 15. Comparison of the average value of the convective surface mass transfer

coefficient determined in this paper with Wadsø (1993) and Time el at. (1998).

Conclusions and Further Work

Based on the experiments the following conclusions can be drawn:

• Increasing velocity decreases the boundary layer thickness which again increases

the surface mass transfer coefficient (SMTC), β.

19

• Increasing the position from the entrance increases the boundary layer thickness

which again decreases the SMTC.

• Increasing the relative humidity (RH) decreases the SMTC.

The theoretical models presented agrees with the experimental results with regard

to increasing mass transfer coefficient as the velocity increases and a decreasing mass

transfer coefficient as the position increases, although the results are shifted relative to

each other. The theoretical model, however, disagree with the experiments with regard to

the effect of the relative humidity. The experimental results predict a lower surface mass

transfer coefficient when the relative humidity increases, whereas the theory predicts the

opposite.

The theory and experimental results will be studied in more detail in order to find

a better relationship between the surface mass transfer coefficient and the relative

humidity.

Nomenclature

oc Moisture concentration at the surface 3mkg

∞c Moisture concentration at the free stream 3mkg

pc Specific heat capacity kgK

J

d Cross section of the honey comb m

ABD Mass diffusivity m2/s

H Internal height of wind tunnel m

xh Local heat transfer coefficient Km

W2

i Enthalpy of a mixture 2

2

sm

lvh Enthalpy of liquid vapor phase kgJ

L Internal length of wind tunnel m

L1 Honey combs length m

20

Nu Dimensionless Nusselt number -

Pr Dimensionless Prandtl number -

∞p Partial water vapor pressure of free air stream Pa

op Partial water vapor pressure at the surface Pa

Re Dimensionless Reynolds number -

Sc Dimensionless Schmidt number αν -

Sh Dimensionless Sherwood number ABDν -

St Stanton number PrRe

NuSt = -

Stm Stanton number Sc

ShStRe

= -

ot Temperature of the free air steam C o

∞t Temperature of the free air steam C o

W Width of the mind tunnel m

α Thermal diffusivity s

m2

cβ Mass transfer coefficient with c as potential s

m

xβ Mass transfer coefficient with as potential psPam

kg2

Δ Thickness of a thermal boundary layer m

δ Thickness of a velocity boundary layer m

cδ Thickness of a concentration boundary layer m

ϕ Relative humidity in air %

λ Thermal conductivity mKW

μ Dynamic viscosity Pa*s

ν Cinematic viscosity of air s

m2

21

ξ Distance from the beginning of the flat plate m

ρ Density 3mkg

u Air velocity in y direction sm

v Air velocity in y direction sm

v Vapor content of air 3mkg

x Distance m

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