How to solve Transient conduction equation with boundary conditions using green's function in matlab to find the temperature?

[Hariesh Krishnan B]

@Alan Weiss Can you help me with this problem?

[Torsten]

Greens's function is a nice theoretical tool, but not much suited for the practical solution of PDEs.

Use the PDE toolbox instead.

Or discretize the equation in space and use ode15s to solve the resulting system of ordinary differential equations with time as the independent variable. Look up "method-of-lines" for more details.

[Hariesh Krishnan B]

@Torsten

Will i be able to use emethod of lines with three variables(t,r,z)? Can you mention any code for reference?

A simple code from your side will be helpful to start with.

[Torsten]

If you have that little background about discretization and solving, maybe you better use the PDE toolbox:

https://de.mathworks.com/help/pde/ug/heat-distribution-in-a-circular-cylindrical-rod.html

[Hariesh Krishnan B]

https://in.mathworks.com/help/pde/ug/axisymmetric-thermal-and-structural-analysis-of-disc-brake.html

Will this be better as to change it as a rectangle in x axis instead of y axis? taking the strip in contact

[Torsten]

You didn't mention that you want to couple thermal with structural analysis.

So you want to solve additional equations to the one you posted ?

[Hariesh Krishnan B]

No I am looking for solving temperature in transient conduction condition. I am not able to comprehend the methids you have suggested. A piece of code from your side will be helpful.

Note: I have attached the research paper for reference.

[Torsten]

So you don't want to use the PDE toolbox ? Since there is no method to comprehend in this case - "simply" applying the software package.

If you want to learn about the method of lines:

Here is a one-dimensional code that solves the heat equation over the radius of a cylinder.

See the answer from me that starts with "For comparison:":

https://de.mathworks.com/matlabcentral/answers/1776920-computing-temperature-of-a-fluid-inside-a-cylinder-using-pdepe?s_tid=srchtitle