PDE Toolbox Heat Transfer

I am totally new to the Matlab pde toolbox. How can I set the values required in the problem in the interface? Step by step screenshots will be very helpful. Thank you!

[Torsten]

Note, you must learn to use this tool on your own as this won't be discussed in class.

There is a documentation and several examples on how to set up heat transfer problems using the pde toolbox. Start reading.

[Haige]

I am currently stuck here on specifying pde coefficients. I don't know where to add the ".*" expression.

[Haige]

Also, where is the document?

[Torsten]

I guess it's

100*sin(2*pi*x).*sin(2*pi*y) - (0.01/0.01)*(exp(u(1)*0.01-1))

instead of your expression.

https://www.mathworks.com/help/pdf_doc/pde/pde.pdf

https://uk.mathworks.com/help/pde/index.html?s_tid=CRUX_lftnav

[Haige]

It is still not working.

[Torsten]

I think you can only specify constant expressions for f in the GUI.

Take a look at page 2-89 / 2-90 of the pdf document I included to see how to write a function depending on x, y and u to accomplish what you want.

Answer 1

[Yash]

Hi Haige,

I understand that you are facing issues while using the MATLAB PDE Toolbox. To gain a better understanding of how this toolbox operates, I recommend consulting the documentation available below:

• PDE Toolbox User's Guide: https://www.mathworks.com/help/pdf_doc/pde/pde.pdf
• PDE Toolbox Functions and Features: https://www.mathworks.com/help/pde/index.html?s_tid=CRUX_lftnav

Regarding the first error message you mentioned, it indicates that the dimensions of "sin(2*pi*x)" and "sin(2*pi*y)" are incompatible for direct multiplication, likely because they are both row vectors. To perform element-wise multiplication, you should use the ".*" operator. The corrected expression would be:

100*sin(2*pi*x).*sin(2*pi*y) - (0.01/0.01)*(exp(u*0.01-1))

The second error that you have received is because of "u(1)". The index exceeds the number of elements in "u".

For defining a function that depends on "x", "y", and "u", you can refer to the documentation on specifying coefficients with the "SpecifyCoefficients" function, available at: https://www.mathworks.com/help/pde/ug/f-coefficient-for-specifycoefficients.html

Hope this helps!