The discussion revolves around solving a heat equation for a metal bar using the Fourier Cosine Transform (FFCT). The problem involves a bar of length L, initially at a constant temperature, with one end suddenly heated to a different temperature while the other end is insulated. Participants are exploring the implications of boundary conditions and the appropriateness of the chosen method.
Some participants have provided guidance on separating variables and suggested reconsidering the use of the FFCT due to the mixed boundary conditions. Others are questioning whether additional information is needed to proceed with the FFCT method effectively.
There is uncertainty regarding the boundary conditions, specifically the lack of explicit information about the derivative at one end of the bar. The discussion also highlights the difference between the Fourier Cosine Transform and the Laplace Transform solutions, noting that they may lead to different function sets.
But I described to you how to use it. What in that description poses a problem?Aows said:i don't know how to use your approach, we never use it before ...
What you are asking is agains the forum rules. You need to solve the problem yourself based on the hints that you have been given. If there are things you do not understand about those hints, ask about it specifically.Aows said:
Yes, and you have been given help and guidance. That you are refusing to work with that guidance is up to you. Providing full answers is against the forum rules and you should not be expecting people to do so.Aows said:dear Mr. @Orodruin ,
i read the forum rules since the first day that i signed up, and it says that you need to show your attempt so others can help with what you need, and i posted all my attempts.
so that's why am asking for the answer...
I already did.Aows said:Ok, then Mr. @Orodruin , can you tell me what is the first step ?
Orodruin said:You should get rid of the inhomogeneous boundary condition before you attempt the transform. Essentially you can do this by the ansatz ##u(x,t) = v(x,t) + h(x)## where ##h(x)## is the stationary solution for your inhomogeneous boundary conditions. You will then get an ODE for ##v(x,t)## that you can solve using either the eigenfunctions proposed in #13 or by the extension proposed in #19.
So first step: What is the stationary solution?
If you have problems with this, you can also start by solving the problem for ##U_1=0## and deal with this in the end. In that case, do you understand the odd extension around ##x=L##?
I will try my best to follow this step even though this is the first time using it, hopefully we reach to a solution.Orodruin said:I already did.
This has nothing to do with how we offer to help people here. You created this thread over two weeks ago and until now you have shown very little interest in putting in the effort necessary to actually solve the problem. We are volunteers and mostly help people who want to be helped. Stating that you need help immediately because your exam is two days away is likely to have the exact opposite effect as compared to what you are going for. In order to learn this properly, you need to sit down with the material and think about each step. I have already given you several hints that should be sufficient to at least find the stationary solution.Aows said:just put yourself in my shoes, exam is two days away.