Created in COMSOL Multiphysics 6.

Evaporative Cooling of Water

This model is licensed under the COMSOL Software License Agreement 6.3.
All trademarks are the property of their respective owners. See www.comsol.com/trademarks.
Introduction
This tutorial shows how to simulate cooling of water including evaporative cooling. As an
example, a beaker filled with water is used surrounded by an air domain. The airflow
transports the water vapor which causes the liquid to cool down. The approach used here
neglects volume change of the water inside the beaker. This is a reasonable assumption for
problems where the considered time is short compared to the time needed to evaporate a
noticeable amount of water.

Model Definition
The model geometry is shown in Figure 1. The size of the air domain is chosen such that
increasing the domain would have no remarkable effect on the flow field around the
beaker. Symmetry is used to reduce the model size.

Air domain

Beaker filled
with water

Symmetry plane

Figure 1: Model geometry, using symmetry.

The beaker is made of glass and contains hot water at 80°C. The air has an initial
temperature of 20°C and enters the modeling domain with this temperature.

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For modeling evaporative cooling, three effects must be taken into account: turbulent flow
of the air around the beaker, heat transfer in all domains, and transport of water vapor in
the air. This is a real multiphysics problem and this tutorial shows how to set it up.

TURBULENT FLOW
The airflow is modeled with the Turbulent Flow, Low Re k- interface, because the
Reynolds number is about 15,000 and turbulent effects must be considered. In addition,
they must be taken into account in the transport equations correctly. With the Low Re k-
 turbulence model, the turbulence variables are solved in the whole domain down to the
walls and thus provide accurate input values for the transport equations. Using the
assumption that the velocity and pressure field are independent of the air temperature and
moisture content makes it possible to calculate the turbulent flow field in advance and then
use it as input for the heat transfer and species transport equations.

Note that because the mass contribution due to the evaporation is small at the water
surface, a wall (no slip) condition is used on this boundary for the airflow computation.

HEAT TRANSFER
The heat transfer inside the beaker and water is due to conduction only. For the moist air,
convection dominates the heat transfer and the turbulent flow field is required. The
material properties are determined by the moist air theory.

During evaporation, latent heat is released from the water surface which cools down the
water in addition to convective and conductive cooling by the surrounding. This
additional heat flux depends on the amount of evaporated water. The latent heat source
then is

q evap = – L v g evap (1)

The latent heat of vaporization Lvap is given in J/kg. The evaporative flux gevap is
discussed in the next section.

MOISTURE TRANSPORT
To obtain the correct amount of water which is evaporated from the beaker into the air,
the Moisture Transport in Air interface is used. The initial relative humidity is 20%. At the
water surface evaporation occurs. The evaporative flux at the surface is

g evap = K  c sat – c v M v (2)

with the evaporation rate K, the molar mass of water vapor Mv, the vapor concentration
cv and the saturation concentration csat which can be calculated from the correlation

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 p sat
c sat = ----------
- (3)
Rg T

The transport equation again uses the turbulent flow field as input. Turbulence must also
be considered for the diffusion coefficient, by adding the following turbulent diffusivity to
the diffusion tensor:

T
D T = ---------- I (4)
Sc T

where T is the turbulent kinematic viscosity, ScT is the turbulent Schmidt number, and I
the unit matrix.

Results and Discussion

The image below shows the temperature field after 20 min with streamlines indicating the
flow field.

Figure 2: Temperature distribution after 20 min (latent heat of evaporation taken into
account) and streamlines indicating the flow field.

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Due to convection, conduction, and evaporation, the water cools down over time. As
shown in Figure 3 the average temperature after 20 min is about 35°C.

Figure 3: Average water temperature over time (latent heat of evaporation taken into
account).

Figure 4 shows the concentration and relative humidity at the symmetry plane. Close to
the water surface, the relative humidity is about 100% as expected. Behind the beaker the
relative humidity can become even smaller than 20%. Due to the high temperature, air can
absorb a higher amount of water.

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Figure 4: Concentration distribution and contour lines for the relative humidity.

The second and third studies compute heat transfer, with the latent heat effects due to
evaporation neglected or accounted for. Figure 5 shows the comparison between average

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water temperatures, without and with latent heat of evaporation, to see its importance in
the cooling process. A difference of approximately 8.5°C can be observed.

Figure 5: Average water temperature without and with latent heat of evaporation accounted
for.

Application Library path: Heat_Transfer_Module/Phase_Change/

evaporative_cooling

Modeling Instructions
The first step is to compute the turbulent flow field. After that, the resulting velocity field
will be used to compute the transport of heat and moisture. To get an accurate velocity
field for the turbulent transport equations, the Low-Reynolds k- turbulence model is
used here.

From the File menu, choose New.

NEW
In the New window, click Model Wizard.

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MODEL WIZARD
1 In the Model Wizard window, click 3D.
2 In the Select Physics tree, select Fluid Flow > Single-Phase Flow > Turbulent Flow >
Turbulent Flow, Low Re k- (spf).
3 Click Add.
4 Click Study.
5 In the Select Study tree, select Preset Studies for Selected Physics Interfaces >
Stationary with Initialization.
6 Click Done.

GEOMETRY 1
Load the geometry sequence from an existing MPH file.

1 In the Geometry toolbar, click Insert Sequence and choose Insert Sequence.
2 Browse to the model’s Application Libraries folder and double-click the file
evaporative_cooling_geom_sequence.mph.

3 In the Geometry toolbar, click Build All.

4 Click the Wireframe Rendering button in the Graphics toolbar.
5 Click the Zoom Extents button in the Graphics toolbar.
The flow calculation is done for the air domain only. For now, air is the only material
you need.

ADD MATERIAL
1 In the Home toolbar, click Add Material to open the Add Material window.
2 Go to the Add Material window.
3 In the tree, select Built-in > Air.
4 Click the Add to Component button in the window toolbar.
5 In the Home toolbar, click Add Material to close the Add Material window.

TURBULENT FLOW, LOW RE K- (SPF)

1 In the Settings window for Turbulent Flow, Low Re k-, locate the Turbulence section.
2 From the Wall treatment list, choose Low Re.
This makes sure that the flow field is resolved down to the wall everywhere.
3 Locate the Domain Selection section. Click Clear Selection.

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4 Select Domain 1 only.
Create a selection from this domain. It can be used later to create new selections or to
assign physical properties.
5 Click Create Selection.
6 In the Create Selection dialog, type Air in the Selection name text field.
7 Click OK.

Now, define the boundary conditions.

Inlet 1
1 In the Physics toolbar, click Boundaries and choose Inlet.
2 Select Boundary 33 only.
3 In the Settings window for Inlet, locate the Velocity section.
4 In the U0 text field, type 2[m/s].

Open Boundary 1
1 In the Physics toolbar, click Boundaries and choose Open Boundary.
2 Select Boundary 1 only.

Symmetry 1
1 In the Physics toolbar, click Boundaries and choose Symmetry.
2 Select Boundary 2 only.

MESH 1
Customize the mesh, so that it resolves both, the fluid flow and later the transport of heat
and moisture properly. Use the Physics-controlled mesh as starting point.

1 In the Model Builder window, under Component 1 (comp1) click Mesh 1.

2 In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3 From the Element size list, choose Extra coarse.
4 Locate the Sequence Type section. From the list, choose User-controlled mesh.

Size 3
1 In the Model Builder window, under Component 1 (comp1) > Mesh 1 click Size 3.
2 Remove boundaries 9, 12, and 29 from the list.
3 In the Settings window for Size, locate the Element Size section.
4 Click the Predefined button.
5 From the Predefined list, choose Coarse.

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6 Click Build Selected.

Size 4
1 Right-click Component 1 (comp1) > Mesh 1 > Size 3 and choose Duplicate.
2 In the Settings window for Size, locate the Element Size section.
3 From the Predefined list, choose Fine.
4 Locate the Geometric Entity Selection section. Click Clear Selection.
5 Select Boundaries 9, 12, and 29 only.
6 Locate the Element Size section. Click the Custom button.
7 Locate the Element Size Parameters section.
8 Select the Maximum element size checkbox. In the associated text field, type 0.2.
Strong gradients appear near the water surface for velocity, temperature and moisture
content. Make the mesh elements smaller close the surface to improve accuracy.

Free Tetrahedral 1
1 In the Model Builder window, click Free Tetrahedral 1.
2 In the Settings window for Free Tetrahedral, locate the Domain Selection section.
3 From the Selection list, choose All domains.

Boundary Layers 1
1 In the Model Builder window, click Boundary Layers 1.
2 In the Settings window for Boundary Layers, click to expand the Corner Settings section.
3 In the Trim for angles greater than text field, type 350.

Boundary Layer Properties 1

1 In the Model Builder window, expand the Boundary Layers 1 node, then click
Boundary Layer Properties 1.
2 In the Settings window for Boundary Layer Properties, locate the Layers section.
3 In the Number of layers text field, type 4.

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4 In the Model Builder window, right-click Mesh 1 and choose Build All.

STUDY 1
In the Study toolbar, click Compute.

RESULTS
Change the unit of the temperature results to degrees Celsius.

Preferred Units 1
1 In the Results toolbar, click Configurations and choose Preferred Units.
2 In the Settings window for Preferred Units, locate the Units section.
3 Click Add Physical Quantity.
4 In the Physical Quantity dialog, select General > Temperature (K) in the tree.
5 Click OK.
6 In the Settings window for Preferred Units, locate the Units section.
7 In the table, enter the following settings:

Quantity Unit Preferred unit

Temperature K °C

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8 Click Apply.

Velocity (spf)
1 Click the Go to Default View button in the Graphics toolbar.
2 Click the Zoom Extents button in the Graphics toolbar.
The resulting velocity field is shown below:
3 In the Model Builder window, under Results click Velocity (spf).

With this velocity field, the transport equations can be computed. The Heat Transfer in
Moist Air together with the Moisture Transport in Air interface are used to describe the
transport of heat and moist air and the interaction of both processes.

ADD PHYSICS
1 In the Home toolbar, click Add Physics to open the Add Physics window.
2 Go to the Add Physics window.
3 In the tree, select Heat Transfer > Heat and Moisture Transport > Moist Air.
4 Find the Physics interfaces in study subsection. In the table, clear the Solve checkbox for
Study 1.
5 Click the Add to Component 1 button in the window toolbar.
6 In the Home toolbar, click Add Physics to close the Add Physics window.

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GLOBAL DEFINITIONS

Parameters 1
1 In the Settings window for Parameters, locate the Parameters section.
2 In the table, enter the following settings:

Name Expression Value Description

phi0 0.2 0.2 Initial relative humidity
K 100[m/s] 100 m/s Evaporation rate constant

The evaporation rate is chosen so that the solution is not affected if the rate is further
increased. This corresponds to assuming that vapor is in equilibrium with the liquid.

MATERIALS
Add the materials for heat transfer calculations in the cup and water.

ADD MATERIAL
1 In the Materials toolbar, click Add Material to open the Add Material window.
2 Go to the Add Material window.
3 In the tree, select Built-in > Water, liquid.
4 Click the Add to Component button in the window toolbar.

MATERIALS

Water, liquid (mat2)

1 Select Domain 3 only.
2 In the Settings window for Material, locate the Geometric Entity Selection section.
3 Click Create Selection.
4 In the Create Selection dialog, type Water in the Selection name text field.
5 Click OK.

With this selection and the one for the air domain, it is easy to create the selection for the
glass body.

DEFINITIONS

Glass
1 In the Model Builder window, expand the Component 1 (comp1) > Definitions node.
2 Right-click Definitions and choose Selections > Complement.

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3 In the Settings window for Complement, type Glass in the Label text field.
4 Locate the Input Entities section. Under Selections to invert, click Add.
5 In the Add dialog, in the Selections to invert list, choose Air and Water.
6 Click OK.

ADD MATERIAL
1 Go to the Add Material window.
2 In the tree, select Built-in > Glass (quartz).
3 Click the Add to Component button in the window toolbar.
4 In the Home toolbar, click Add Material to close the Add Material window.

MATERIALS

Glass (quartz) (mat3)

1 In the Settings window for Material, locate the Geometric Entity Selection section.
2 From the Selection list, choose Glass.

HEAT TRANSFER IN MOIST AIR (HT)

Add a Fluid node for the water domain. To save computational time, the velocity field
driven by natural convection is not computed. Instead, an increased thermal conductivity
determined by built-in Nusselt number correlations is defined in the next steps to
compensate the missing convective heat flux.

Fluid 1
1 In the Physics toolbar, click Domains and choose Fluid.
2 Select Domain 3 only.

Convectively Enhanced Conductivity 1

1 In the Physics toolbar, click Attributes and choose
Convectively Enhanced Conductivity.
2 In the Settings window for Convectively Enhanced Conductivity, locate the
Convectively Enhanced Conductivity section.
3 From the Nusselt number correlation list, choose Vertical rectangular cavity.
4 In the H text field, type 8[cm].
5 In the L text field, type 3.5[cm].

Then, add a Solid node for the glass domain.

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Solid 1
1 In the Physics toolbar, click Domains and choose Solid.
2 In the Settings window for Solid, locate the Domain Selection section.
3 From the Selection list, choose Glass.

The air enters the domain at room temperature. At the outlet, the heat is transported away
by convection.

Inflow 1
1 In the Physics toolbar, click Boundaries and choose Inflow.
2 Select Boundary 33 only.

Open Boundary 1
1 In the Physics toolbar, click Boundaries and choose Open Boundary.
2 Select Boundary 1 only.

Symmetry 1
1 In the Physics toolbar, click Boundaries and choose Symmetry.
2 Click the Go to YZ View button in the Graphics toolbar.
With this tool, draw a box around all symmetry boundaries, which corresponds to:

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3 Select Boundaries 2, 6, 11, 13, 18, 31, and 32 only.
You should see the following in your Graphics window:

The fluid in the beaker has an initial temperature of 80°C.

Initial Values 2
1 In the Physics toolbar, click Domains and choose Initial Values.
2 Select Domain 3 only.
3 In the Settings window for Initial Values, locate the Domain Selection section.
4 From the Selection list, choose Water.
5 Locate the Initial Values section. In the T text field, type 80[degC].

Set up the Moisture Transport in Air interface.

MOISTURE TRANSPORT IN AIR (MT)

1 In the Model Builder window, under Component 1 (comp1) click
Moisture Transport in Air (mt).
2 In the Settings window for Moisture Transport in Air, locate the Domain Selection section.
3 From the Selection list, choose Air.

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Initial Values 1
1 In the Model Builder window, under Component 1 (comp1) >
Moisture Transport in Air (mt) click Initial Values 1.
2 In the Settings window for Initial Values, locate the Initial Values section.
3 In the w,0 text field, type phi0.

Inflow 1
1 In the Physics toolbar, click Boundaries and choose Inflow.
2 Select Boundary 33 only.
3 In the Settings window for Inflow, locate the Upstream Properties section.
4 In the w,ustr text field, type phi0.

Open Boundary 1
1 In the Physics toolbar, click Boundaries and choose Open Boundary.
2 Select Boundary 1 only.
3 In the Settings window for Open Boundary, locate the Upstream Properties section.
4 In the w,ustr text field, type phi0.

Symmetry 1
1 In the Physics toolbar, click Boundaries and choose Symmetry.
2 Select Boundary 2 only.

Wet Surface 1
1 In the Physics toolbar, click Boundaries and choose Wet Surface.
2 Select Boundary 12 only.
3 In the Settings window for Wet Surface, locate the Wet Surface Settings section.
4 In the K text field, type K.

Now, set up the multiphysics couplings for moisture and heat transport by the airflow.
Start with a fictive model where latent heat source due to evaporation is neglected.

MULTIPHYSICS

Heat and Moisture 1 (ham1)

1 In the Model Builder window, under Component 1 (comp1) > Multiphysics click
Heat and Moisture 1 (ham1).
2 In the Settings window for Heat and Moisture, locate the Latent Heat section.
3 Clear the Include latent heat source on surfaces checkbox.

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Nonisothermal Flow 1 (nitf1)
1 In the Physics toolbar, click Multiphysics Couplings and choose Domain >
Nonisothermal Flow.
2 In the Settings window for Nonisothermal Flow, locate the Material Properties section.
3 Select the Boussinesq approximation checkbox.

Couple the flow and pressure field.

Moisture Flow 1 (mf1)

1 In the Physics toolbar, click Multiphysics Couplings and choose Domain >
Moisture Flow.
To keep Study 1 in its original state, deselect these last two multiphysics coupling
features from the study tables.

STUDY 1

Step 1: Wall Distance Initialization

1 In the Model Builder window, under Study 1 click Step 1: Wall Distance Initialization.
2 In the Settings window for Wall Distance Initialization, locate the
Physics and Variables Selection section.
3 In the Solve for column of the table, under Component 1 (comp1) > Multiphysics, clear
the checkboxes for Nonisothermal Flow 1 (nitf1) and Moisture Flow 1 (mf1).

Step 2: Stationary
1 In the Model Builder window, click Step 2: Stationary.
2 In the Settings window for Stationary, locate the Physics and Variables Selection section.
3 In the Solve for column of the table, under Component 1 (comp1) > Multiphysics, clear
the checkboxes for Nonisothermal Flow 1 (nitf1) and Moisture Flow 1 (mf1).

ADD STUDY
1 In the Home toolbar, click Add Study to open the Add Study window.
2 Go to the Add Study window.
3 Find the Physics interfaces in study subsection. In the table, clear the Solve checkbox for
Turbulent Flow, Low Re k- (spf).
4 Find the Studies subsection. In the Select Study tree, select General Studies >
Time Dependent.
5 Click the Add Study button in the window toolbar.
6 In the Home toolbar, click Add Study to close the Add Study window.

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STUDY 2 : NO LATENT HEAT SOURCE
In the Settings window for Study, type Study 2 : No Latent Heat Source in the Label
text field.

Step 1: Time Dependent

Due to the Wet Surface boundary condition, the time-dependent simulation of heat and
moisture transport is very sensitive to the choice of the time dependent solver settings.
Tune the solver, by restricting the time step size.

1 In the Model Builder window, under Study 2 : No Latent Heat Source click
Step 1: Time Dependent.
2 In the Settings window for Time Dependent, locate the Study Settings section.
3 From the Time unit list, choose min.
4 In the Output times text field, type range(0,20[s],20).
5 Click to expand the Values of Dependent Variables section. Find the
Values of variables not solved for subsection. From the Settings list, choose
User controlled.
6 From the Method list, choose Solution.
7 From the Study list, choose Study 1, Stationary.
Because you do not solve for the flow field again, but want to use the results from the
first study, you have to tell the time-dependent study that the results from the stationary
study should be used.

Solution 3 (sol3)
1 In the Study toolbar, click Show Default Solver.
2 In the Model Builder window, expand the Solution 3 (sol3) node, then click Time-
Dependent Solver 1.
3 In the Settings window for Time-Dependent Solver, click to expand the Time Stepping
section.
4 Select the Initial step checkbox. In the associated text field, type 0.1.
5 From the Maximum step constraint list, choose Constant.
6 In the Maximum step text field, type 1.
7 Right-click Study 2 : No Latent Heat Source > Solver Configurations > Solution 3 (sol3) >
Time-Dependent Solver 1 and choose Fully Coupled.
8 In the Settings window for Fully Coupled, click to expand the Method and Termination
section.

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9 From the Jacobian update list, choose On every iteration.

Step 1: Time Dependent

In the Study toolbar, click Compute.

RESULTS

Transparency 1
1 In the Model Builder window, expand the Results > Temperature (ht) node.
2 Right-click Volume 1 and choose Transparency.
Create a plot showing both the temperature distribution and the streamlines of the flow.

Temperature and Fluid Flow (nitf1) 1

In the Model Builder window, right-click Temperature and Fluid Flow (nitf1) and choose
Duplicate.

Fluid Flow
1 In the Model Builder window, expand the Temperature and Fluid Flow (nitf1) 1 node.
2 Right-click Fluid Flow and choose Delete.

Temperature and Streamlines

1 In the Model Builder window, under Results click Temperature and Fluid Flow (nitf1) 1.
2 In the Settings window for 3D Plot Group, type Temperature and Streamlines in the
Label text field.

Streamline 1
1 In the Temperature and Streamlines toolbar, click Streamline.
2 In the Settings window for Streamline, locate the Data section.
3 From the Dataset list, choose Study 1/Solution 1 (sol1).
4 Locate the Coloring and Style section. Find the Point style subsection. From the Color
list, choose White.
5 Select Boundary 33 only.
6 From the Type list, choose Arrow.
7 Select the Number of arrows checkbox. In the associated text field, type 80.
8 In the Temperature and Streamlines toolbar, click Plot.

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9 Click the Go to Default View button in the Graphics toolbar.
Note that for the Streamline 1 plot, we chose to display the results from the first study
but it is also possible to choose the dataset from Study 2. Indeed, as the flow field is not
solved again, it will not change the plot.
To visualize the moisture distribution, follow the next steps.

Cut Plane 1
1 In the Results toolbar, click Cut Plane.
2 In the Settings window for Cut Plane, locate the Plane Data section.
3 From the Plane list, choose xz-planes.
4 Locate the Data section. From the Dataset list, choose Study 2 : No Latent Heat Source/
Solution 3 (sol3).

Moisture Concentration and Relative Humidity

1 In the Results toolbar, click 2D Plot Group.
2 In the Settings window for 2D Plot Group, type Moisture Concentration and
Relative Humidity in the Label text field.

3 Locate the Plot Settings section. From the View list, choose New view to generate a
dedicated view for this plot.
4 Locate the Data section. From the Dataset list, choose Cut Plane 1.
5 From the Time (min) list, choose 10.

Surface 1
1 In the Moisture Concentration and Relative Humidity toolbar, click Surface.
2 In the Settings window for Surface, click Replace Expression in the upper-right corner of
the Expression section. From the menu, choose Component 1 (comp1) >
Moisture Transport in Air > Moist air properties > mt.cv - Vapor concentration - mol/m³.

Moisture Concentration and Relative Humidity

In the Model Builder window, click Moisture Concentration and Relative Humidity.

Contour 1
1 In the Moisture Concentration and Relative Humidity toolbar, click Contour.
2 In the Settings window for Contour, locate the Expression section.
3 In the Expression text field, type mt.phi.
4 Locate the Levels section. In the Total levels text field, type 7.
5 Locate the Coloring and Style section. From the Contour type list, choose Tube.

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6 Select the Radius scale factor checkbox. In the associated text field, type 0.025.
7 Select the Level labels checkbox.
8 In the Precision text field, type 2.
9 From the Label color list, choose White.
10 In the Moisture Concentration and Relative Humidity toolbar, click Plot.
Use the Zoom Box button in the Graphics window to get a better view of the contour
lines.
The relative humidity decreases quickly with the distance to the surface. Due to the high
temperature behind the beaker, the relative humidity becomes even lower than 20%.
It is interesting to see how the average temperature decreases with time.

Average Water Temperature

1 In the Results toolbar, click More Derived Values and choose Average >
Volume Average.
2 In the Settings window for Volume Average, type Average Water Temperature in the
Label text field.
3 Locate the Data section. From the Dataset list, choose Study 2 : No Latent Heat Source/
Solution 3 (sol3).
4 Select Domain 3 only.
5 Click Replace Expression in the upper-right corner of the Expressions section. From the
menu, choose Component 1 (comp1) > Heat Transfer in Moist Air > Temperature > T -
Temperature - K.
6 Click Evaluate.

TABLE 1
1 Go to the Table 1 window.
2 Click the Table Graph button in the window toolbar.

RESULTS

Average Water Temperature over Time

1 In the Model Builder window, under Results click 1D Plot Group 9.
2 In the Settings window for 1D Plot Group, type Average Water Temperature over
Time in the Label text field.

Finally, compute how much water is evaporated in the air.

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Amount of Evaporated Water
1 In the Results toolbar, click More Derived Values and choose Integration >
Surface Integration.
2 In the Settings window for Surface Integration, type Amount of Evaporated Water in
the Label text field.
3 Locate the Data section. From the Dataset list, choose Study 2 : No Latent Heat Source/
Solution 3 (sol3).
4 Select Boundary 12 only.
5 Locate the Expressions section. In the table, enter the following settings:

Expression Unit Description

2*mt.ntflux kg/s

6 Locate the Data Series Operation section. From the Transformation list, choose Integral.
7 Click next to Evaluate, then choose New Table.

TABLE 2
1 Go to the Table 2 window.
The factor 2 in the expression is based on the use of a symmetry condition. Within
20 minutes, about 12.58 g of water have been evaporated.

MULTIPHYSICS
Repeat the previous steps with a third study that takes latent heat source due to
evaporation into account. A comparison with the results returned by Study 2 will then
highlight and quantify the cooling effects of evaporation.

Heat and Moisture 2 (ham2)

1 In the Physics toolbar, click Multiphysics Couplings and choose Domain >
Heat and Moisture.
2 Select Domain 1 only.
To keep Study 1 and Study 2 in their original states, disable the Heat and Moisture
multiphysics coupling feature in the studies.

STUDY 1

Step 2: Stationary
1 In the Model Builder window, under Study 1 click Step 2: Stationary.
2 In the Settings window for Stationary, locate the Physics and Variables Selection section.

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3 In the Solve for column of the table, under Component 1 (comp1) > Multiphysics, clear
the checkbox for Heat and Moisture 2 (ham2).

STUDY 2 : NO LATENT HEAT SOURCE

Step 1: Time Dependent

1 In the Model Builder window, under Study 2 : No Latent Heat Source click
Step 1: Time Dependent.
2 In the Settings window for Time Dependent, locate the Physics and Variables Selection
section.
3 In the Solve for column of the table, under Component 1 (comp1) > Multiphysics, clear
the checkbox for Heat and Moisture 2 (ham2).

ADD STUDY
1 In the Study toolbar, click Add Study to open the Add Study window.
2 Go to the Add Study window.
3 Find the Physics interfaces in study subsection. In the table, clear the Solve checkbox for
Turbulent Flow, Low Re k- (spf).
4 Find the Studies subsection. In the Select Study tree, select General Studies >
Time Dependent.
5 Click the Add Study button in the window toolbar.
6 In the Study toolbar, click Add Study to close the Add Study window.

STUDY 3 : LATENT HEAT SOURCE

In the Settings window for Study, type Study 3 : Latent Heat Source in the Label text
field.

1 In the Model Builder window, under Study 3 : Latent Heat Source click
Step 1: Time Dependent.
2 In the Settings window for Time Dependent, locate the Study Settings section.
3 From the Time unit list, choose min.
4 In the Output times text field, type range(0,20[s],20).
5 Locate the Physics and Variables Selection section. In the Solve for column of the table,
under Component 1 (comp1) > Multiphysics, clear the checkbox for
Heat and Moisture 1 (ham1).

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6 Locate the Values of Dependent Variables section. Find the
Values of variables not solved for subsection. From the Settings list, choose
User controlled.
7 From the Method list, choose Solution.
8 From the Study list, choose Study 1, Stationary.

Solution 4 (sol4)
1 In the Study toolbar, click Show Default Solver.
2 In the Model Builder window, expand the Solution 4 (sol4) node, then click Time-
Dependent Solver 1.
3 In the Settings window for Time-Dependent Solver, locate the Time Stepping section.
4 Select the Initial step checkbox. In the associated text field, type 0.1.
5 From the Maximum step constraint list, choose Constant.
6 In the Maximum step text field, type 1.
7 Right-click Study 3 : Latent Heat Source > Solver Configurations > Solution 4 (sol4) >
Time-Dependent Solver 1 and choose Fully Coupled.
8 In the Settings window for Fully Coupled, locate the Method and Termination section.
9 From the Jacobian update list, choose On every iteration.

Step 1: Time Dependent

In the Study toolbar, click Compute.

RESULTS

Transparency 1
1 In the Model Builder window, expand the Results > Temperature (ht) 1 node.
2 Right-click Volume 1 and choose Transparency.

Duplicate the temperature plot created for the former study, to get the results shown in
Figure 2. First begin with the Surface 2 dataset.

Temperature and Streamlines 1

1 In the Model Builder window, right-click Temperature and Streamlines and choose
Duplicate.
2 In the Model Builder window, click Temperature and Streamlines 1.
3 In the Settings window for 3D Plot Group, locate the Data section.
4 From the Dataset list, choose Study 3 : Latent Heat Source/Solution 4 (sol4).

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5 Click the Go to Default View button in the Graphics toolbar.

Modify the source dataset of Cut Plane 1 to update the moisture and humidity plot with
the effects of latent heat of evaporation (see Figure 4).

Cut Plane 1
1 In the Model Builder window, under Results > Datasets click Cut Plane 1.
2 In the Settings window for Cut Plane, locate the Data section.
3 From the Dataset list, choose Study 3 : Latent Heat Source/Solution 4 (sol4).

Moisture Concentration and Relative Humidity

1 In the Model Builder window, under Results click
Moisture Concentration and Relative Humidity.
2 In the Moisture Concentration and Relative Humidity toolbar, click Plot.
To visualize the average temperature evolution with the latent heat of evaporation
effects as in Figure 5, follow the steps below.

TABLE 1
1 Go to the Table 1 window.
2 Click the Clear Table button in the window toolbar.

RESULTS

Average Water Temperature 1

1 In the Model Builder window, expand the Results > Tables node.
2 Right-click Average Water Temperature and choose Duplicate.
3 In the Settings window for Volume Average, locate the Data section.
4 From the Dataset list, choose Study 3 : Latent Heat Source/Solution 4 (sol4).
5 Click Evaluate.

TABLE 1
1 Go to the Table 1 window.
2 Click the Table Graph button in the window toolbar.

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RESULTS

Table Graph 1

Now, add the results without the effects of latent heat of evaporation to the graph to get
a comparison of both studies.

Average Water Temperature

1 In the Model Builder window, under Results > Derived Values click
Average Water Temperature.
2 In the Settings window for Volume Average, click Evaluate.

TABLE 1
1 Go to the Table 1 window.
2 Click the Table Graph button in the window toolbar.

RESULTS

Table Graph 1
1 In the Settings window for Table Graph, locate the Coloring and Style section.
2 From the Width list, choose 2.
3 Click to expand the Legends section. Select the Show legends checkbox.

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4 From the Legends list, choose Manual.
5 In the table, enter the following settings:

Legends
Latent heat of evaporation accounted for
Latent heat of evaporation neglected

Average Water Temperature over Time

1 In the Model Builder window, click Average Water Temperature over Time.
2 In the Settings window for 1D Plot Group, locate the Plot Settings section.
3 Select the y-axis label checkbox. In the associated text field, type Temperature (degC).
4 Locate the Legend section. From the Layout list, choose Outside graph axis area.
5 From the Position list, choose Bottom.
6 In the Average Water Temperature over Time toolbar, click Plot.

In this model, latent heat of evaporation accounts for a decrease of about 10°C at the
end of the simulation.

Mass Balance
Finally, follow the instructions below to check the overall mass balance over time.

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1 In the Results toolbar, click Global Evaluation.
2 In the Settings window for Global Evaluation, type Mass Balance in the Label text field.
3 Locate the Data section. From the Dataset list, choose Study 3 : Latent Heat Source/
Solution 4 (sol4).
4 Click Replace Expression in the upper-right corner of the Expressions section. From the
menu, choose Component 1 (comp1) > Moisture Transport in Air > Mass balance >
mt.massBalance - Mass balance - kg/s.
5 Click Add Expression in the upper-right corner of the Expressions section. From the
menu, choose Component 1 (comp1) > Moisture Transport in Air > Mass balance >
mt.dwcInt - Total accumulated moisture rate - kg/s.
6 Click Add Expression in the upper-right corner of the Expressions section. From the
menu, choose Component 1 (comp1) > Moisture Transport in Air > Mass balance >
mt.ntfluxInt - Total net moisture rate - kg/s.
7 Click Add Expression in the upper-right corner of the Expressions section. From the
menu, choose Component 1 (comp1) > Moisture Transport in Air > Mass balance >
mt.GInt - Total mass source - kg/s.
8 Click Add Expression in the upper-right corner of the Expressions section. From the
menu, choose Component 1 (comp1) > Moisture Transport in Air > Mass balance >
Net mass flows, boundary features > mt.ws1.ntfluxInt - Total net moisture rate - kg/s.
9 Click Add Expression in the upper-right corner of the Expressions section. From the
menu, choose Component 1 (comp1) > Moisture Transport in Air > Mass balance >
Net mass flows, boundary features > mt.ifl1.ntfluxInt - Total net moisture rate - kg/s.
10 Locate the Expressions section. In the table, enter the following settings:

Expression Unit Description

mt.ws1.ntfluxInt kg/s Total net moisture rate,
evaporation
mt.ifl1.ntfluxInt+ kg/s Total net moisture rate,
mt.open1.ntfluxInt inlet/outlet

11 Click Evaluate.

TABLE 3
1 Go to the Table 3 window.
2 Click the Table Graph button in the window toolbar.

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RESULTS

Mass Balance
1 In the Model Builder window, under Results click 1D Plot Group 14.
2 In the Settings window for 1D Plot Group, type Mass Balance in the Label text field.
3 Locate the Legend section. From the Layout list, choose Outside graph axis area.
4 From the Position list, choose Bottom.
5 In the Number of rows text field, type 6.

Table Graph 1
1 In the Model Builder window, click Table Graph 1.
2 In the Settings window for Table Graph, locate the Legends section.
3 Select the Show legends checkbox.
4 Locate the Coloring and Style section. From the Width list, choose 2.

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