Experimental and Numerical Investigation of Natural ...

1-

Experimental and Numerical Investigation of Natural Convection Heat Transfer from a Plane Wall to a Thermally Stratified Environment: Constant Heat Flux Naseem Ali1,2 Ihsan Y. Hussain2 1

Portland State University 2 Baghdad University

The effect of linear thermal stratification in stable stationary ambient fluid on free convective flow

of a viscous incompressible fluid along a plane wall is numerically and experimentally investigated in the present work. The governing equations of continuity, momentum and energy are solved numerically using finite difference method with Alternating Direct Implicit scheme. The velocity, temperature distributions and the Nusselt number are discussed numerically for various values of physical parameters and presented through graphs. Experiments are carried out in an apparatus, consisting of a square Perspex aquarium and heated plate. Temperature measurements are conducted using 12 channel temperature recorders. The temperature profiles and Nusselt number for stratified and unstratified media are compared with corresponding numerical solution and good agreement is obtained. The results show that the thickness of the thermal boundary layer is approximately independent of downstream coordinates. Keywords: Natural convection, Thermal stratification, Linear, Constant Heat Flux

Introduction Convective heat transfer in thermally stratified ambient fluid occurs in many industrial applications and is an important aspect in the study of heat transfer. If stratification occurs, the fluid temperature is function of distance and convection in such environment exists in lakes, oceans, nuclear reactors. The problem had been investigated by many researcher analytically and numerically, see for example (Cheesewright 1967), (Yang et al 1972), (Jaluria and Himasekhar 1983), (Kulkarni et al 1987), (Angirasa and Srinivasan 1992), (Pantokratoras 2003), (Saha and Hossain 2004), (Ahmed 2005), (Ishak et al 2008), (Deka and Neog 2009), (Singh et al 2010). Experimental works also had been reported; see (Tanny and Cohen 1998).Theoretical and experimental work had been investigate by (Chen and Eichhorn 1976). The present work investigates the problem numerically with wide

range of stratification parameter for different kinds of fluids (air, water, and oil), different Grashof number and different inclination angle. To support the numerical solution the problem was investigated experimentally also.

Formulation of the Problem Consider the two dimensional thermal boundary layer flow of natural convection heat transfer of an incompressible fluid along a plane wall immersed in a stable thermally stratified fluid. Figure 1 shows the coordinates system and the flow configuration. Using Boussinesq approximations, the following continuity, momentum and energy equations in nondimensional form for laminar flow adjacent to a plane wall are obtained;

-2-

(1)

X

(2) Heated Wall

L

(3)

φ

gy=gsin φ

φ gx=-gcos φ

g

(4) where (Angirasa and Srinivasan 1992);

,

,

Y

,

,

Figure1. Physical Model

,

Thermal Boundary Layer Thickness ,

,

,

The thickness of the thermal boundary layer was defined as the distance at which, (Tanny and Cohen 1998);

(10)

, The

initial

condition

can

be

written

in

nondimensional form as follows: U = 0, V = 0, Ө = 0

for all X, Y

(5)

In the present work the new definition of the thickness of thermal boundary layer will be the distance at which the temperature profile equal to half wall temperature profile.

The boundary conditions in nondimensional form are:

U = 0, V = 0,

Numerical Solution at Y = 0 for all X (6)

U = 0, V = 0, Ө = 0

at Y

∞ for all X (7)

U = 0, V = 0, Ө = 0

(11)

at Y

∞ for X = 0

(8) The local rate of heat transfer in term of the local Nusselt number at the plate is given by, (9)

Finite Difference Method is considered as efficient technique to solve the thermal problems; therefore it has been used in the present study. The Momentum and Energy equations are solved by Alternating Direction Implicit scheme (ADI). Numerical results were first obtained to check for grid dependency. The results showed that no considerable difference in the results of suggested grid size after (51x51) and showed that no considerable different in the results of suggested transverse distance after (0.5). Therefore in the present study the grid size of (51x51) and transverse distance of (0.5) was used. The

-3convergence of the solution to the steady state result for large time was obtained with a convergence criterion of (1 * 10 -4). This criterion was chosen after varying it over a wide range so that the steady state results were essentially independent of the chosen value. The mathematical model was solved by computer program which was written by the Visual basic language to solve the momentum and energy equations and to calculate Nusselt number. The Tridiagonal system of equation was used to solve the matrix of dependent variables.

thermocouples. The thermocouples were separated by a uniform vertical distance of a (30 mm). The temperature profiles across the boundary layer were measured by horizontal rake of six Alumel-Chromel (type K) thermocouples. The horizontal distance between the thermocouple was chosen to cover up the change in temperature profile, first five thermocouples with interval distance of (5 mm) and the sixth thermocouple with interval distance of (10 mm). The digital thermometer type (12 Channels Temperature Recorder with SD Card Data Logger) was used.

Experimental Work

Numerical Results

The experimental work was conducted in the Heat Transfer Lab. in the Mechanical Engineering department at Baghdad University. It consists of Perspex glass aquarium, which consists of two boxes assembled together, see figure 2. The exterior box was assembled with interior dimensions of (600 * 600 * 600 mm). The interior box was gathered with exterior dimensions of (500 * 500 * 500 mm). The Perspex glass sheets that used for the boxes are with (10 mm thickness). Thermal insulator, with (50 mm thickness), was used to fill space between the two boxes, and also the outer surfaces of the exterior box. The heated plate assembly was made of rectangular Aluminum box with overall dimensions of (200 * 100 * 50 mm) over which the surrounding air at a predetermined temperature could circulate. One side of the aluminum box was insulated by thermal insulator. The other side of the aluminum box served as the heating surface unit. The heater coil that used with a (2 mm) diameter and made from nickel-chrome wire (R). Ceramic beads with diameter (3 mm) electrically isolate this coil. The cooling system and heater coil were used in test rig to perform the gradient heating of the ambient fluid. The cooling system was consisting of cooling pipes, electrical water pump, water tank and water cooler. The water was used as working fluid in cooling system. The cooling pipes were covered up by commercial Aluminum plate, with (1 mm thickness).The ambient stratification in the aquarium was measured continuously by fixed vertical rake of six Alumel-Chromel (type K)

Theoretical investigation are done for three working fluids, air (Pr = 0.7), water (Pr = 6) and oil (Pr = 6400), three Grashof numbers (1*104, 1*105 and 1*106) and three angle (-30, 0 and 30) for wide range of thermal stratification (S = 0, 0.5, 1, 1.5, 2, 3, 4). Figures 3 through 5 show that the temperature profile for the different values of the stratification level at mid high wall plane (X = 0.5). The temperature profile does not affect strongly with increasing the stratification parameter. The constant heat flux boundary condition has been marginalized the effect of stratification. A comparative study of figures 3 through 5 indicates that the effect of stratification parameter is marginalized with the increase in Prandtl number, as the separateness among the temperature profile reduces. Figure 6 shows that the temperature profile decreases with the increase in Prandtl number. In addition, the reversal of temperature was found to be stronger at high Prandtl numbers and weaker at low numbers. It can be suitably remarked that the increase in Grashof number does not practically vary the effect of stratification factor on temperature profiles. Figure 7 shows that with increase in Grashof number the fluid temperature deceases. This must happen because buoyancy force assists the flow by increasing fluid velocity and hence the heat is convected readily thereby reducing fluid temperature. Figure 8 illustrates the influence of the inclination angle (φ) on temperature profile for stratified media (S = 2), where observed that in addition to the influence of thermal stratification the temperature profile will be less effected by the inclination angle of the

-4wall, this is considerably noted for high levels of thermal stratification, therefore the orientation marginalized the effect of the stratification parameter. Figures 9 and 10 show that the velocity profile does not effected strongly with increasing the stratification parameter and the figure 11 shows that the velocity profile decreases with increasing stratification parameter. The limit effect of stratification on velocity profile is a result to the difference between the wall temperature and ambient temperature does not effected strongly by increasing the stratification parameter because the increasing in ambient temperature corresponding to the increasing on the wall temperature. A comparative study of figures 9 to 11 indicates that the effect of stratification parameter is marginalized with the increase in Prandtl number, as the separateness among the velocity profile reduces. Figure 12 shows that the velocity profile decreases with the increase in Prandtl number. At high Prandtl numbers there is a small reversal of flow while for low Prandtl numbers the flow reversal is much stronger. It can be suitably remarked that the increase in Grashof number does not practically vary the effect of stratification factor on velocity profiles. Figure 13 shows that with increase in Grashof number the fluid velocity increases. This is because the buoyancy force assists the flow by increasing fluid velocity. Figure 14 shows that the velocity profile decreases with increasing the Grashof number. This phenomenon is clear at high Prandtl number which lowers fluid velocity. Figure 15 illustrates the influence of the inclination angle (φ) on velocity profile for stratified level (S = 2), where observed that in addition to the influence of thermal stratification the velocity profile will be less effected by the inclination angle of the wall, this is considerably noted for high levels of thermal stratification, therefore the orientation marginalized the effect of the stratification parameter. Figure 16 shows that marginalized effect of stratification parameter on the local Nusselt number because the temperature profile does not affected strongly with increasing the stratification parameter. Figure 17 shows that As the Prandtl number increases the Nusselt number first deceases, then increases. The fluids which have small Prandtl number, Nusselt number decreases with increasing the Grashof number.

The reverse behavior is for fluids which have large Prandtl number where the Nusselt number increases with increasing Grashof number as shown in figure 18.The Nusselt number has the same behavior in stratified and unstratified environment. Figure 19 presents local Nusselt number with downstream coordinates for different angles. Consider an inclined hot plate that makes an angle (φ = 30) from vertical wall plane. In the case of inclined plate, the force that drives the motion is reduced; therefore the convection currents to be weaker and the rate of heat transfer to be lower relative to the vertical plane case. In the case (φ = -30), the rate of heat transfer increases relative to the vertical orientation. In

the stratified media, the Nusselt number has the same behavior of the unstratified media. Figures 20 show that thickness of thermal boundary layer is independent on the downstream coordinates which approximately equal to (2 mm).

Experimental Results Experimental investigation were done for air as working fluid, with wide range of heat flux (250, 1000, 1500, 2000 and 2500 W/m2) and of inclination angle (-30, -15, 0, 15 and 30). The fluid temperature profile has been tested with the transverse coordinates at different downstream coordinates for different heat fluxes. The temperature profiles have been measured for stratified and unstratified fluid. Figures 21through 24 show that the effect of thermal stratification has been marginalized due to heat flux; therefore the thermal stratification does not have clear effect on temperature profile. This state has been proved for all studied range value of heat fluxes. The figure 25 reveals the marginalized effect to inclination angle in stratified media; therefore the temperature profile does affected strongly by change the orientation. This state has been proved for all studied range of heat flux and inclination angle. To examine the effect of the ambient stratification on the heat transfer, the local Nusselt numbers have been measured for stratified and unstratified media. The figures 26 and 27 represent comparison between stratified and unstratified media cases for local Nusselt number. The figures reveal that the local Nusselt number

-5increases with downstream coordinates in stratified and unstratified environment, and the heat transfer rate does not affected by thermal stratification therefore the local Nusselt number has been approximately held in stratified and unstratified media. This is a logic result because the local Nusselt number depends on temperature profile which does not affected by the thermal stratification as mention above. Also fluid temperature profile has been tested with the computational domain normal to the wall for different values of downstream coordinates to find the thickness of the thermal boundary layer. Figure 28 shows that the thermal boundary layer is approximately independent on the downstream coordinate. The thickness of the thermal boundary layer was approximately (2.75 mm).

Verification Figure 29 shows the comparison between the experimental and theoretical temperature profile results for (q"=250 W/m2 and φ=0). The figure reveals that the experimental temperature profile follows the same behavior as the present theoretical results but is approximately with means difference of 7.75 %. Figure 30 shows that the comparison between the experimental and theoretical local Nusselt number results for (q"=250 W/m2 and φ=0). Figure reveals that the experimental local Nusselt number follows the same behavior as the present theoretical results but is approximately with mean difference of 20 %. The difference between the experimental and numerical results is due to inaccurate temperature measurement at the wall and at very small distances from it because of to the flowblocking phenomenon occurring as result of horizontal rake and the deviations between the theoretical and experimental results may be due to the variation of Prandtl number in the ambient stratified fluid (Tanny and Cohen 1998), and the thermal stratification is not perfectly linear in experimental investigation. Also a comparison

is made with the results achieved by previous studies. The effect of Prandlt number on temperature Profile (figure 6) agrees with results of Singh et al (2010) shown in figure

31. Thermal boundary layer thickness (figure 20) agree with Tanny and Cohen (1998) (experimental study) shown in figure 32. Conclusions 1. For constant heat flux, Stratification parameter has the marginalized effect on the temperature, velocity profiles and local Nusselt number. 2. The effect of stratification parameter is marginalized with the increase in Prandtl number. 3. Thermal boundary layer was approximately independent on downstream coordinates. 4. The reversal of temperature is strong at high Prandtl numbers and weaker at low numbers and the reversal of flow velocity is strong at low Prandtl numbers and weaker at high numbers. 5. The increase in Grashof number does not practically vary the effect of stratification on temperature and velocity profiles. 6. As Prandtl number increases the Nusselt number first decrease, then increase

Nomenclature Gr

Grashof number

g

gravitational Acceleration

L

characteristic length of the plane wall

Nu

Nusselt number

Pr

Prandtl number

S

thermal stratification parameter

T

temperature

t

time

t*

non-dimensional time

u

velocity in x-direction

uc

characteristic velocity

U

non-dimensional velocity in Xdirection

-6v

velocity in y-direction kinematic viscosity

V

non-dimensional velocity in Ydirection

X

non-dimensional downstream coordinate

x

downstream coordinate

Y

non-dimensional horizontal space coordinate

y

horizontal space coordinate

ρ

density

φ

angle of inclination

Ө

non-dimensional temperature

Superscript ∞

location away from the wall outside the boundary layer

∞, 0 location away from the wall at x = 0

Greek letters

∞, x location away from the wall at any x w

α

thermal diffusivity

β

volumetric coefficient of thermal expansion

Figure 2: Test Rig

wall

-7-

Figure 3: Temperature Profile for Pr=0.7

Figure 5: Temperature Profile for Pr=6400

Figure 4: Temperature Profile for Pr=6

Figure 6: Temperature profile for Gr=1E6

-8-

Figure 7: Temperature Profile for Pr=6400 and S=4

Figure 9: Velocity Profile for Pr=0.7

Figure 8: Temperature Profile for Pr=6 and S=2

Figure 10: Velocity Profile for Pr=6

-9-

Figure 11: Velocity Profile for Pr=6400

Figure 13: Velocity Profile for Pr=6 and S=4

Figure 12: Velocity Profile for Gr=1E6


- 10 -


Figure 16: Local Nusselt Number for Pr=6400

Figure 17: Local Nusselt Number for Gr=1E5

Figure 18: Local Nusselt Number for Pr=6400 and S=4

- 11 -

Figure 19: Local Nusselt Number for Pr=6 and S=2

Figure 21: Temperature Profile for X=0.25

Figure 20: Thermal Boundary Layer Thickness for S=2


- 12 -


Figure 24: Temperature Profile for q"=2500 w/m2 and X=0.75

Figure 25: Temperature Profile for q"=2500 w/m2 and X=0.5

Figure 26: Local Nusselt Number for q"=1500 w/m2

- 13 -

Figure 27: Local Nusselt Number for q"=250 w/m2

Figure 29: Experimental and Numerical Temperature Profile

Figure 28: Thermal Boundary Layer Thickness for Experimental Results

Figure 30: Experimental and Numerical Local Nusselt Number

- 14 -

Figure 31: Effect of Prandtl Number (Singh et al 2010)

Figure 32: Thermal Boundary Layer Thickness (Tanny and Cohen 1998)

References Ahmed, T.E. (2005) "Transient natural convection heat transfer from a plane wall to a thermally stratified media" MSc. Thesis, University of Technology, Baghdad. Angirasa, D. and Srinivasan, J. (1992) "Natural convection heat transfer from an isothermal vertical surface to a stable thermal stratified fluid" Journal of Heat Transfer Vol.114/917 Cheesewright, R. (1967) "Natural convection from a plane vertical surface in non-isothermal surroundings" Int. J. Heat and Mass Trans. Volume 10, Issue 12, Pages 1847-1859. Chen, C.C and Eichhorn, R. (1976) "Natural convection from a vertical surface to a thermally stratified fluid" ASME Journal of Heat Transfer Vol.98, PP.446-451. Deka, Rudra Kt and Neog, Bhaben Ch. (2009)" Unsteady natural convection flow past an accelerated vertical plate in a thermally stratified fluid" Theoret. Appl. Mech., Vol.36, No.4, PP. 261-274, Belgrade. Isak, Anuar, Nazar, Roslinda and Pop, Ioan. (2008) "Mixed convection boundary layer flow adjacent to a vertical surface embedded in a

stratified medium" Int. J. Heat and Mass Trans.vol. 51, PP. 3693-3695. Jaluria, Y. (1980) "Natural convection heat and mass transfer" Pergamon Press. Jaluria, Y. and Himasekhar, K. (1983) "buoyancy-induced two-dimensional vertical flows in a thermally stratified environment" Computers & Fluids Vol. 11, Issue 1, Page 3949. Kulkarni, A. K., Jacobs, H. R. and Hwang, J. J. (1987) " Similarity solution for natural convection flow over an isothermal vertical wall immersed in thermally stratified medium " Int. J. Heat and Mass Transfer Volume 30, Issue 4, PP 691-698 Pantokratoras, A. (2003) "A note on the Nusselt number adjacent to a vertical isothermal plate immersed in thermally stratified water at low temperatures" Int. J. Heat and Fluid Flow Vol. 32, Issue 2, Pages 278-281.

- 15 Saha, S.C, Hossain, M.A. (2004) " Natural convection flow with combined buoyancy effects due to thermal and mass diffusion in a thermally stratified media " Nonlinear Analysis: Modeling and Control, Vol. 9, No. 1, PP. 89–102. Singh, Gurminder, Sharma, P.R and Chamkha, A.J. (2010) "Effect of thermally stratified ambient fluid on MHD convective flow along a moving non-isothermal vertical plate" international of Physical Science Vol.5 (3), PP.208-215.

Tanny, J. and Cohen, J. (1998) "The mean temperature field of a buoyancy induced boundary layer adjacent to a vertical plate immersed in a stratified medium" Int. J. Heat and Mass Transfer Volume 41, Issue 14, PP. 21252130. Yang, K.T, Novotny, J.L and Cheng, Y.S. (1972) "Laminar free convection from a non-isothermal plate immersed in a temperature stratified medium” Int. j. Heat and Mass Transfer, Vol. 15, PP. 1097–1109.

APPEENDICES: A1: Data Analysis To analyze the heat transfer process from plane wall in a thermally stratified environment simplified steps were used as following,

difference between the wall and the ambient fluid over the entire plate in the stratified case was made equal to the constant temperature difference in the unstratified experiment (Tanny and Cohen 1998). The calculated properties are used to calculate the following relations;

1. The total input power supplied to the wall can be calculated as; (A.1) 2. Calculate the film temperature by using the following relation; (A.10) (A.2) 3. Calculate the Stratification parameter ;

5. Calculate the heat losses from heated plated by using the following relations;

(A.3) (A.4)

(A.11)

(A.5) (A.6)

(A.12)

(A.7) 4. All the air physical properties ρ, μ, υ, and k were evaluated at the average mean film temperature. The average temperature

(A.13) Where, Emissivity of the Aluminum Surface (commercial sheet) = 0.09

- 16 F21 = View Factor = 1 Tin = Temperature of the Inner Aluminum Wall Surface. Tout = Temperature of the Outer surface of the thermal insulator. = The Thickness of the Thermal Insulator = 40 mm

(A.15) Where, The Surface Area of the Aluminum Plate = 0.02 m2 8. Calculate the local heat transfer coefficient by using the following relation;

Stefan – Boltzmann constant = W / m2.K4 The heat losses by conduction which was found experimentally equal to 3 % of the input power. 6. Calculate the heat transfer by convection only by the following relation;

(A.16) 9. Calculate the local Nusselt number by using the following relation;

(A.14) 7. Calculate the convective heat flux by using the following relation;

(A.17)

Sample of Calculation To describe the procedure of data analysis, one of experimental tests has been chosen to analyze. The measuring data of the test were,

Data Analysis:

- 17 -

A2. Error Analysis The accuracy of obtaining experimental results depends upon two factors. The accuracy of measurements and the design details of test rig. The deviations in accuracy are resulted form; 1. The uniformities in heat flux on the wall surface. 2. The alignment of fixing thermocouple in the aquarium. 3. The straightening of heated plate in vertical position and inclined position. 4. Heat lost by conduction from side walls. 5. Linearity of the stratification Parameter. There is no doubt that, the maximum portion of errors in calculations referred essentially to the errors in the measured quantities. Hence, to calculate the error in the obtained results, the procedure of Kline and McClintock (Holman J.P 1979), is used in this field. Let the result R be a function of n independent variables (v1, v2… vn) (A.18) For small variations in the variables, this relation can be expressed in linear form as (A.19) Hence,

the

uncertainty

intervals

(w)

in

the

result

can

be

given (A.20)

as

- 18 Eq.

(A.20)

is

greatly

simplified

upon

dividing

by

Eq.

(A.18)

to

nondimensionalize (A.21)

Hence, the experimental errors that may happen in the used variables are given in table (A.1) which is taken from measuring devices as follows; Table (A.1): Uncertainties of Measuring Tools. INDEPENDENT VARIABLES (V)

UNCERTAINTY INTERVAL (W)

Temperature

± 0.1 oC

Voltage of the heater

± 0.01 Volt

Current of the heater

± 0.001 Amp

Characteristics length

± 0.0001 m

(A.22) Qradiation is very small, so it can be neglected.

(A.23)

(A.24) The Nusselt number is a functional of several variables, each subject to an uncertainty.

Where; = Tin - Tout = Tw - T∞, x

(A.25)

(A.26)

- 19 -

(A.27)

(A.28)

(A.29)

(A.30)

Therefore the uncertainty intervals (w) in the result can be given as follows;

(A.31) Sample of Calculation

ERROR ANALYSIS

- 20 -

- 21 A3. Experimental Temperature Readings:

X4 UNST 36.1 32.1 30.3 30 29.5 29.4 28 28.3 28.6 29 29.2 29.5

X4 UNST 49.8 40.6 35.9 34.5 33.6 31.1 29.8 29.8 29.9 29.9 29.8 29.8

X4 UNST 58.6 40.7 35.6 33.7 32.1 31.9 31

X4 ST 36.4 32.2 30.6 30.1 29.7 29.6 28 28.3 28.6 29 29.2 29.5

X4 ST 50.6 39.3 35.9 34.6 33.7 33.4 29.4 29.8 30.1 30.3 30.6 30.8

X4 ST 59.7 41.5 36.2 34.6 33.2 32.7 29.8

X3 UNST 35.8 31.7 30.2 29.9 29.3 29.3 28 28.3 28.6 29 29.2 29.5

q"=250 W/m2 , φ = 0 X2 X2 X3 ST UNST ST 36.1 35.5 35.7 32 31.2 31.5 30.4 30 30 30.1 29.7 29.7 29.5 29.2 29.2 29.5 29.2 29.2 28 28 28 28.3 28.3 28.3 28.6 28.6 28.6 29 29 29 29.2 29.2 29.2 29.5 29.5 29.5

X1 UNST 35.1 30.8 29.6 29.4 29.1 29.1 28.2 28.3 28.3 28.3 28.2 28.2

X1 ST 35.3 30.7 29.5 29.2 29.2 29.2 28 28.3 28.6 29 29.2 29.5

X3 UNST 4.4 39.7 35.4 33.4 32.6 32.4 29.8 29.8 29.9 29.9 29.8 29.8

q"=1000 W/m2, φ = 0 X2 X2 X3 ST UNST ST 49.5 47.2 48.3 38 38.2 36.3 34.7 34.2 33.3 33.5 32.6 32.3 32.6 31.8 31.5 32.2 31.5 31.2 29.4 29.8 29.4 29.8 29.8 29.8 30.1 29.9 30.1 30.3 29.9 30.3 30.6 29.8 30.6 30.8 29.8 30.8

X1 UNST 46.3 35.9 33 32.1 31.6 315 29.8 29.8 29.9 29.9 29.8 29.8

X1 ST 47.2 34.4 31.9 31.6 31.1 31 29.4 29.8 30.1 30.3 30.6 30.8

X1 UNST 54 35.7 32.5 31.7 31.2 30.8 31

X1 ST 55.2 36.8 33.5 32.7 32.1 31.9 29.8

X3 UNST 57.2 40.1 35.1 33.4 32.2 31.5 31

q"=1500 W/m2, φ = 0 X3 X2 ST UNST X2 ST 58.2 55.4 56.6 41.4 36.7 37.8 36.2 33.4 34.3 34.4 32.6 33.7 33 31.9 32.9 32.5 31.6 32.6 29.8 31 29.8

TEMP T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12


TEMP T1 T2 T3 T4 T5 T6 T7

- 22 31.1 31.2 31.1 31.1 31.1

X4 UNST 71.1 45.3 37.4 35.8 34.4 33.1 31.5 31.6 31.7 31.5 31.5 31.5

X4 UNST 72.4 50.1 41.6 36.4 35.4 34 30.4 30.5 30.5 30.6 30.6 30.6

X4 UNST 35.6 32.5 31.4 31.1 30.7

30.2 30.4 30.6 31 31.3

X4 ST 72.3 46.2 38.5 36.8 35.1 34.4 30.8 31 31.3 31.6 32 32.4

X4 ST 74.4 48.5 39.5 36.5 35.4 33.8 30.2 30.5 30.9 31.2 31.3 31.7

X4 ST 35.8 32.7 31.8 31.4 31.1

31.1 31.2 31.1 31.1 31.1

30.2 30.4 30.6 31 31.3

31.1 31.2 31.1 31.1 31.1

30.2 30.4 30.6 31 31.3

31.1 31.2 31.1 31.1 31.1

30.2 30.4 30.6 31 31.3

X3 UNST 68.4 43.5 36.6 35.5 33.7 33.2 31.5 31.6 31.7 31.5 31.5 31.5

q"=2000 W/m2, φ = 0 X2 X3 ST UNST X2 ST 69.8 67.1 68 44.5 41.9 42.5 37.6 35.5 36.1 36.3 33.9 34.9 34.7 33 34 34.1 32.6 33.6 30.8 31.5 30.8 31 31.6 31 31.3 31.7 31.3 31.6 31.5 31.6 32 31.5 32 32.4 31.5 32.4

X1 UNST 65.2 40.8 34.5 33.5 32.2 32.1 31.5 31.6 31.7 31.5 31.5 31.5

X1 ST 66.3 41.2 35.7 34.7 33.6 33.2 30.8 31 31.3 31.6 32 32.4

X3 UNST 70.55 46.9 38.2 35.7 34 33.7 30.4 30.5 30.5 30.6 30.6 30.6

q"=2500 W/m2, φ = 0 X3 X2 ST UNST X2 ST 72.2 69.3 70 45.5 41.2 42 37.6 35.3 35.7 36 34.5 34.8 34.4 33.3 33.5 33.7 32.9 33.2 30.2 30.4 30.2 30.5 30.5 30.5 30.9 30.5 30.9 31.2 30.6 31.2 31.3 30.6 31.3 31.7 30.6 31.7

X1 UNST 67 36.7 33.7 33.4 32.5 32.1 30.4 30.5 30.5 30.6 30.6 30.6

X1 ST 68 37.7 34.4 34 33 32.7 30.2 30.5 30.9 31.2 31.3 31.7

X3 UNST 35.1 32.2 31.1 30.9 30.5

q"=250 W/m2 , φ = -15 O X3 X2 X2 ST UNST ST 35.3 34.7 34.8 32.2 31.7 31.9 31.2 30.7 31 30.8 30.5 30.9 30.7 30.1 30.5

X1 UNST 34.2 31.1 30.1 29.8 29.3

X1 ST 34.4 31.4 30.5 30.4 30.1

T8 T9 T10 T11 T12



TEMP T1 T2 T3 T4 T5

- 23 30.6 28.5 28.5 28.6 28.6 28.6 28.5

X4 UNST 34.6 32.7 31.6 31.1 30.7 30.5 29.2 29.3 29.2 29.2 29.3 29.3

X4 UNST 36.8 34.1 33.1 32.5 32 31.9 29.5 29.4 29.6 29.5 29.5 29.6

X4 UNST 37.9 34.8

31.1 28.2 28.5 28.8 29.2 29.4 29.6

X4 ST 34.9 32.8 31.9 31.2 30.7 30.6 28.5 28.8 29.1 29.3 29.5 29.8

X4 ST 37 34.2 32.9 32.1 31.9 31.8 28.7 29 29.2 29.5 29.9 30.1

X4 ST 38.3 35.2

30.5 28.5 28.5 28.6 28.6 28.6 28.5

30.7 28.2 28.5 28.8 29.2 29.4 29.6

30.1 28.5 28.5 28.6 28.6 28.6 28.5

30.5 28.2 28.5 28.8 29.2 29.4 29.6

29.3 28.5 28.5 28.6 28.6 28.6 28.5

30.1 28.2 28.5 28.8 29.2 29.4 29.6

X3 UNST 34.2 32.1 31.5 31 30.5 30.5 29.2 29.3 29.2 29.2 29.3 29.3

q"=250 W/m2 , φ = -30 O X3 X2 ST UNST X2 ST 34.5 33.9 34 32.5 31.9 32.1 31.7 31.2 31.4 31 30.9 30.5 30.4 30.4 29.9 30.2 30.3 29.8 28.5 29.2 28.5 28.8 29.3 28.8 29.1 29.2 29.1 29.3 29.2 29.3 29.5 29.3 29.5 29.8 29.3 29.8

X1 UNST 33.4 31.2 30.5 30.1 29.8 29.8 29.2 29.3 29.2 29.2 29.3 29.3

X1 ST 33.6 31.5 30.1 29.9 29.5 29.4 28.5 28.8 29.1 29.3 29.5 29.8

X3 UNST 36.6 33.6 32.5 32.1 31.7 31.6 29.5 29.4 29.6 29.5 29.5 29.6

q"=250 W/m2, φ = 15 O X3 X2 ST UNST X2 ST 36.7 36.2 36.4 33.8 33.5 33.5 32.7 32.4 32.3 32 32 31.9 31.5 31.5 31.4 31.5 31.4 31.3 28.7 29.5 28.7 29 29.4 29 29.2 29.6 29.2 29.5 29.5 29.5 29.9 29.5 29.9 30.1 29.6 30.1

X1 UNST 35.8 32.9 31.8 31.4 30.1 30 29.5 29.4 29.6 29.5 29.5 29.6

X1 ST 36 33 32.1 31.6 31.2 31 28.7 29 29.2 29.5 29.9 30.1

X3 UNST 37.5 34.6

q"=250 W/m2 , φ = 30 O X3 X2 ST UNST X2 ST 37.8 37.2 37.4 34.7 34.3 34.4

X1 UNST 36.8 33.8

X1 ST 37 34.1

T6 T7 T8 T9 T10 T11 T12



TEMP T1 T2

- 24 33.3 32.6 32.4 32.1 30.5 30.5 30.5 30.5 30.6 30.6

X4 UNST 71.3 47 38 35.7 34.5 34 31.3 31.4 31.3 31.4 31.4 31.4

X4 UNST 69.8 49 40.9 37.6 36.6 35.9 31.6 31.7 31.7 31.7 31.7 31.8

X4 UNST 75.5

33.9 33.6 33.1 33 29.3 29.6 30 30.2 30.5 30.9

X4 ST 72.4 48 39.3 37.3 35.8 35.4 30.6 30.9 31.2 31.6 31.8 32.2

X4 ST 70.1 52 42.7 40.1 36.9 36.1 30.8 31.2 31.5 31.9 32.2 32.5

X4 ST 76.5

32.9 32.3 32 31.8 30.5 30.5 30.5 30.5 30.6 30.6

33.4 33 32.7 32.6 29.3 29.6 30 30.2 30.5 30.9

32.6 32 31.7 31.5 30.5 30.5 30.5 30.5 30.6 30.6

33.3 32.9 32.3 32.2 29.3 29.6 30 30.2 30.5 30.9

31.9 31.5 31.2 31 30.5 30.5 30.5 30.5 30.6 30.6

32.9 32.6 32.1 32 29.3 29.6 30 30.2 30.5 30.9

X3 UNST 69.5 45.8 37.7 35.6 34.4 33.9 31.3 31.4 31.3 31.4 31.4 31.4

q"=2500 W/m2 , φ = -15 O X3 X2 ST UNST X2 ST 70.3 67.2 68.4 46.8 43.9 44.2 39.1 36.5 38 37 35.4 36.5 35.6 34.8 35.7 35.2 34.6 35.1 30.6 31.3 30.6 30.9 31.4 30.9 31.2 31.3 31.2 31.6 31.4 31.6 31.8 31.4 31.8 32.2 31.4 32.2

X1 UNST 65 40.3 35.8 35.3 34.4 34.2 31.3 31.4 31.3 31.4 31.4 31.4

X1 ST 66.5 40.7 36.1 35.8 34.9 34.5 30.6 30.9 31.2 31.6 31.8 32.2

X3 UNST 67.7 47 39.8 37.3 36 35.5 31.6 31.7 31.7 31.7 31.7 31.8

q"=2500 W/m2 , φ = -30 O X2 X3 ST UNST X2 ST 68.1 65.5 66.4 50.1 45.1 48.8 40.4 38.2 39.6 38.5 36.3 37.1 36 35 35.5 35.7 34.4 35.3 30.8 31.6 30.8 31.2 31.7 31.2 31.5 31.7 31.5 31.9 31.7 31.9 32.2 31.7 32.2 32.5 31.8 32.5

X1 UNST 63.5 42.9 35.5 34.7 33.9 33.7 31.6 31.7 31.7 31.7 31.7 31.8

X1 ST 64.1 45.2 37.1 35.8 35 34.7 30.8 31.2 31.5 31.9 32.2 32.5

X3 UNST 73.6

q"=2500 W/m2 , φ = 15 O X3 X2 ST UNST X2 ST 74.7 71.7 72.6

X1 UNST 69.6

X1 ST 70.6

T3 T4 T5 T6 T7 T8 T9 T10 T11 T12



TEMP T1

- 25 50.1 42.6 39.6 35 34 31.8 31.7 31.7 31.8 31.8 31.8

X4 UNST 77.4 49.2 44.7 40.5 37 35 32.4 32.4 32.5 32.6 32.5 32.6

52.7 44.6 41 36 34.5 30.7 31 31.3 31.7 32.1 32.3

X4 ST 78.6 50 45.2 41.9 38 36.1 31.7 32.2 32.4 32.7 32.9 33.2

47.8 40 37.8 34.7 33.8 31.8 31.7 31.7 31.8 31.8 31.8

X3 UNST 75.2 47.3 41.8 38.2 36.2 34.6 32.4 32.4 32.5 32.6 32.5 32.6

50.6 40.2 38 35 34 30.7 31 31.3 31.7 32.1 32.3

45.6 38.1 35.8 33.8 33 31.8 31.7 31.7 31.8 31.8 31.8

48.2 38.4 36 34 32.5 30.7 31 31.3 31.7 32.1 32.3

q"=2500 W/m2 , φ = 30 O X3 X2 ST UNST X2 ST 76.7 73.3 74.3 48.8 44.7 45.5 42.1 38.8 39.1 39.9 36.2 37.5 37.4 34.3 35.9 35.7 34.1 35.2 31.7 32.4 31.7 32.2 32.4 32.2 32.4 32.5 32.4 32.7 32.6 32.7 32.9 32.5 32.9 33.2 32.6 33.2

44.2 35.8 33.5 32.5 32 31.8 31.7 31.7 31.8 31.8 31.8

X1 UNST 71.5 43.6 37.1 35.2 34.4 33.6 32.4 32.4 32.5 32.6 32.5 32.6

46.5 36.1 34 33 32.5 30.7 31 31.3 31.7 32.1 32.3

X1 ST 72.1 44.7 38 36.1 34.6 34.1 31.7 32.2 32.4 32.7 32.9 33.2

T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12
