Convective Heat Transfer with Pseudo-Periodicity

This example simulates convective heat transfer in a channel filled with water. It also demonstrates a technique to reduce memory requirement, by solving the model repeatedly on a pseudo-periodic section of the channel. Each solution corresponds to a different section, and before each solution step the temperature of the outlet boundary from the previous solution is mapped to the inlet boundary.

Model Definition

The geometry represents the inside of a 1 meter long section of a pipe. The length of the entire pipe is 6 meters.

The channel is filled with water that flows at a velocity of 1 mm/sec. To take the fluid flow into account in the heat transfer equation use a laminar velocity profile in the convective term. Such a profile can be represented as a function of the radial position according to

The water in the channel is heated through the walls. Model this heating by applying a 100 W/m2 heat flux to these boundaries.

For the first solution set a constant temperature of 283 K at the inlet boundary. For subsequent solutions, apply the outlet temperature distribution from the previous solution to the inlet boundary.

Implement and compare two methods for temperature evaluation at the outlet boundary:

In the first method you specify a point grid on the boundary. The temperature is then evaluated by interpolation on the specified grid.

In the second method you obtain the temperature at the mesh node points.

Results and Discussion

Figure 1 shows the temperature distribution in the model for each solution, corresponding to the 6 sections of the pipe. These can be placed together to view the temperature distribution in the entire length of the pipe. As the water flows through the pipe it reaches a maximum temperature of 294 K.

Figure 1: Temperature distribution along the pipe, the inlet is of section 1 at the left boundary.

Figure 2 shows the temperature distribution at the bottom of the pipe (edge number 5). The blue line corresponds to the outlet temperature obtained according to the interpolation method. The red line corresponds to the outlet temperature evaluated on the mesh node points. You can notice a slight difference in the solution; the red line is expected to be more accurate, because evaluation of the temperature in the mesh node points is more accurate than the interpolation on the point grid.

Figure 2: Temperature distribution along the bottom line of the pipe. In blue the solution using interpolated outlet temperature values, in red the solution using outlet temperature evaluated at the mesh node points.

Notes About the COMSOL Implementation

This example demonstrates how to map data from one domain to another, and from one solution to another. This involves writing data to file, then using an interpolation function to read the file and apply the data in the model.

The most efficient approach for this simulation is to start by setting up the model in the graphical user interface of the COMSOL Desktop®. You can then save the model *.mph file, which you can easily load into MATLAB®, where you continue to implement the script for solving the problem.

Wrapper functions used by the script:

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to load the model *.mph file.

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to evaluate the outlet temperature at the mesh node points.

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to evaluate the outlet temperature at specified points.

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to display plots.

LiveLink_for_MATLAB/Tutorials/pseudoperiodicity_llmatlab

Modeling Instructions — MATLAB®

In this section you find a detailed explanation of the commands you need to enter at the MATLAB command line in order to run the simulation.

Start .

You now have two possibilities to continue:

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Enter each command, starting at step 2 below, at the MATLAB command line.

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Paste the full model script, included in the section Model M-File, into a text editor, then save the file with a “.m” extension, and finally run this file in MATLAB.

Start by loading the model object containing the base settings of the physics model, to proceed enter the command:

model = mphopen('pseudoperiodicity_llmatlab');

See the section Modeling Instructions — COMSOL Desktop for the modeling instruction of the model .mph file pseudoperiodicity_llmatlab.mph.

Solving with the Interpolated Outlet Temperature

Set-up a for-loop that runs for 6 iterations:

for i = 1:6

The first operation to run in loop is to compute the solution:

model.study('std1').run;

After the computation of the first solution, the model object needs some changes in order to take into account the solution of the previous solution. Use the if statement, as indicated below, to apply these changes only once:

if i==1

Now add an interpolation function feature node named inletTemp to the model object. This reads the file pseudoperiodic_data.txt, which contains the temperature distribution at the outlet boundary. You generate the file under step 13 below. Type the following commands:

Name	Expression	Value	Description
R	10[cm]	0.1 m	Pipe radius
u0	1[cm/s]	0.01 m/s	Maximum velocity
T0	283.15[K]	283.15 K	Inlet temperature
q0	100[W/m^2]	100 W/m²	Inward heat flux

Name	Expression	Unit	Description
r	sqrt(y^2+z^2)	m	Radius parameter