1. Heat and Mass Transfer Laboratory
Micro-channel flow boiling correlations and 3-zone model plus comparison to recent published results
Anthony Servonet
Stefano Nebuloni
Bruno Agostini - supervisor
I present to you Stephano Nebuloni, and I’m Anthony Servonet, and we’ll speak about the “microchannel flow boiling correlations and 3-zones model”. On this project, we also compared these model to recent published results.
08 February 2007
Heat and Mass Transfer Laboratory

2. Contents of the presentation
introduction to micro-channel features
heat transfer prediction models
Kandlikar and Balasubramanian (2004)
Zhang at al. (2004)
3 zone model – Thome-Dupont-Jacobi (2004)
comparison with experimental data
conclusions
On this presentation, I’ll make a short introduction to the difference between macro and micro-channel, Stephano will speak about the three different model we studied, and to finish, I’ll present you the experimental data we treated on this project.
Heat and Mass Transfer Laboratory

3. Heat and Mass Transfer Laboratory
General considerations on micro-scale flow boiling trends (from experiments)
h is not dependent on mass velocity
h is not dependent on vapor quality (x>0.1)
h is dependent on heat flux
h is dependent on saturation temperature
On micro-scale flow boiling, some trends can be noticed, and they are generally respect, but not every time. So we can say the heat transfer coefficient h isn’t really depends on mass velocity, as you can see on this graph (2) where the mass velocity is fourth bigger in this case than in this, and h don’t really increase. Generally, h isn’t also dependant on vapour quality, when it’s bigger than 0.1, as you can on this graph (1). But can also see on the same graph that Tsat has a big influence on h. So, if Temperature increase only 5 or 10°, h really increase. And to finish, we can say h depend also on the heat flux.
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4. Macro to micro-scale transition
Kandlikar and Grande : 3 mm
Mehandal et al. : micro-channels (1 – 100 μm)
meso-channels (100 μm – 1mm)
macro-channels (1 – 6 mm)
conventional (Dh > 6 mm)
Kew and Cornwell :
It’s difficult to know where is the boundary between macro and micro scale because it depends of few parameters. But some physical effect can be observe:
In two-phase micro-scale flows, the liquid phase is laminar for almost all the test conditions, which is quite rare in macro-scale studies.
In addition, it is expected in small diameter tubes that the effect of surface tension may become more pronounced while the influence of gravity may become less important and consequently stratified flows are rarely observed.
Bubbly flow is also seldom observed due to the fact that its lifespan is very short as bubbles coalesce or grow to the channel size very quickly.
Thus, the correlations developed for macro-scale may not extrapolate well to the micro-scale.
So, some authors established diameter to make the transition between macro and micro scale. Kandlikar said the transition between mini channel and conventional is at 3mm. Mehandal et alii proposed different transition, as micro, meso, macro and conventional channels
And to finish, Kew and Cornwell proposed a diameter who depends of the fluids property, and the observation of the effect between gravity and surface tension
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5. Kandlikar and Balasubramanian model (1/2)
this model is an extension of their macro-scale correlation to tube diameter <3mm, eliminating the dependency on Froude number
it is based on Reynolds number ReLO (all liquid), taking into account the laminar or turbulent flow condition
Heat transfer coefficient can be calculated in the following way:
if 100<ReLO <1600 :
if ReLO <100 :
FFL represents the nucleation characteristic of the liquid on a given surface
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6. Kandlikar and Balasubramanian model (2/2)
The model predicts that nucleate boiling becomes dominant for low Reynolds numbers
convective boiling contribution becomes dominant to high vapor quality
The model has been implemented in a MATLAB code (Excel compatible)
Heat and Mass Transfer Laboratory

7. Zhang – modified Chen model (1/3)
this model (2004) is a modification of the macro-scale flow boiling correlation proposed by Chen (1966) where the correlation proposed by Foster and Zuber for nucleate boiling heat transfer is used
Chen model was developed to determine flow boiling heat transfer coefficients when both liquid and vapor phases were both in turbulent flows (Rek>2300)
S: suppression factor
F: Reynolds number factor
C is a function of flow conditions (Re)
Martinelli parameter
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8. Zhang – modified Chen model (2/3)
friction factors for circular channels
for 1000<Rek<2000 an interpolation is used
single phase heat transfer correlations are modified to take into account laminar flow conditions and channels orientation w.r.t. gravity
Solving for the wall temperature allows to obtain the heat transfer coefficient
The model has been implemented in a MATLAB code with a bisection method solver
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9. Zhang – modified Chen model (3/3)
A clear transition zone is identifiable in correspondence of sharp variation of heat transfer coefficient (subordinated to Reynolds number range)
At high vapor quality (x1-) the heat transfer coefficient diverges, due to the big contribution of convective boiling component
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10. 3-Zone model - Thome-Jacobi-Dupont (2004) (1/6)
A three zone flow boiling model of the evaporation of elongated bubbles in micro-channels
the sequential passages of a liquid slug, an evaporating bubble and a vapor slug are assumed as a qualitative description of the flow pattern
local heat transfer coefficient is then obtained by a time average (over the period of the passage of the triple):
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11. 3-Zone model - Thome-Jacobi-Dupont (2004) (2/6)
Major hypothesis:
liquid film remains attached to the wall (shear stresses are assumed negligible) and is assumed very small compared to channel radius
homogeneous flow (vapor and liquid velocities are the same)
heat flux is uniform and constant in time
neither liquid or the vapor phases are superheated
Bubble departure frequency:
bubbles are assumed to grow until r= R where the fluid reaches saturation temperature (x=0)
from bubble departures frequency f =1/ it is possible to evaluate the length of the liquid slug and the residence time of vapor and liquid
mass and volume conservation B V L
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12. 3-Zone model - Thome-Jacobi-Dupont (2004) (3/6)
Residence time:
(homogeneous flow)
Local heat transfer coefficient: liquid slug and dry zone
The flow is assumed to be hydrodynamically and thermally developing
if Re 2300:
London and Shah correlation
if Re> 2300:
Gnielinski correlation
Asymptotic method (Churchill and Usagi)
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13. 3-Zone model - Thome-Jacobi-Dupont (2004) (4/6)
Thin film evaporation model
Energy balance across the liquid layer gives the following evolution with time
of the layer:
mean heat transfer coefficient
Since h tends to infinity if end tends to zero
(and the choice of end is quite complicate)
Liquid film thickness
The prediction of initial liquid film thickness is based on the work done by done
by Moriyama and Inoue (a correlation including a further constant C0)
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14. 3-Zone model - Thome-Jacobi-Dupont (2004) (5/6)
The constant C0. the bubble departure frequency and the end constitute the 3
parameter of the model that can be optimized on a specific database
periodic heat transfer coefficient
(vapor quality 8%)
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15. 3-Zone model - Thome-Jacobi-Dupont (2004) (6/6)
The two models (basic version – logarithm – and modified version) have been
provided for the project development
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16. Threshold diameter criteria
Transitional diameter depends on the refrigerant properties
In this project, we chose the criteria of Kew and Cornewell to make the transition between macro and micro scale. Contrary to the fixed value of Kandlikar and Grande, according to the Kew and Cornwell criterion the macro-to-micro-scale transitional diameter may vary
from a value as high as 5 mm for water at low reduced pressure to values smaller than 1 mm for CO2 at reduced pressures higher than 0.8.
So in this graph, we can see we chose all the data place under this line.
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17. Heat and Mass Transfer Laboratory
Sources
Analysed 890 data in database of 2767 values (32%)
Fluids : CO2, R11, R22, R134a, R141b, R410A, Water.
diameter between et 2.87 [mm],
mass velocity between 23 and 6673 [kg/m2s],
saturation temperature between -18 and 105 [°C],
heat flux between 4.4 and 938 [kW/m2],
vapour qualities between 0 to 1,
heat transfer coefficient measured between 0.2 and 286 [kW/m2K]
Here we have all the experimental data we used during this project. Mainly we took data in a database established by Ribatski, but we acquired somme data in four different scientist article.
We analysed near 32% of 2767 data we have, on 7 different refrigerants :…
The parameters vary between: 0.236mm and 2.87 for the diameter, … etc
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18. Description of project
For the four article we had to analyse to have more data, we proceeded on this way :
We digitalized the page which had an interest in the article,
We transformed the graph on a bitmap image,
We used the program WinDIG to analysed the graph and to obtain the coordinate of all the point we can see,
WinDIG export à text files with the coordinates,
And finally we had this data in our Excel files with the other data.
For some data, we had to find all the important parameters by different process, such as the equation of energy conservation to obtain the heat flux or the mass velocity.
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19. Previous database (collected by Ribatski G.)
In interval ± 30% :
Kandlikar =6.2 %
Zhang = 11.4 %
TZM = 28.4 %
MAPE (Mean Absolute Percentage Error) :
Kandlikar =74 %
Zhang = 116 %
TZM = 83 %
I the database collected by Ribatski, we analysed more than 700 data and we applied the 3 different models, and as we can see, the 3 zones model (in red) is better than the two other model (kandlikar in blue and Zhang in yellow). But strangely, the Mean Absolute Percentage Error is bigger in TZM than in Kandlikar model. We think is because some point are very far of the reality in the TZM.
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20. Heat and Mass Transfer Laboratory
New database (Kew and Cornewell, Steinke, Lee and Mudawar, Qu and Mudawar)
In interval ± 30% :
Kandlikar =12.6 %
Zhang = 43.7 %
TZM = 32.9 %
MAPE :
Kandlikar =75 %
Zhang = 87%
TZM = 49 %
In the set of new data we had to analyse, the model of Zhang is a little bit better than the three zone model, but we can also see that it has à MAPE bigger. And we can see the Zhang model make a curve, whereas the TZM is very straight and if we adapt some parameter, it can be better.
Heat and Mass Transfer Laboratory

21. Heat and Mass Transfer Laboratory
Conclusions
A new set of experimental data of flow boiling heat
transfer coefficient has been acquired and compared with
three different models :
Kandlikar model is simple to be implemented, but the prediction error is quite significant
Zhang model predicts the heat transfer coefficient with a higher accuracy but with higher dispersion and it predicts trends which are not resulting from experiments
Three zones model is the most promising one, approaching the problem from the physics of the phenomena and therefore producing better results.
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