Heat equation with annoying source term

In summary, the speaker is urgently seeking help with a heat equation that includes a cyclic source. They are not sure how to approach it and are looking for suggestions or resources, such as the book "Carslaw and Jaeger."
  • #1
tylerbizoff
1
0
Hello to everyone,

I urgently need to solve the following pde: ∂u/∂t +∂²u/∂x² = So*δ(x-xo)*sin(wo*t)

It's the heat equation with a cyclic source. The lentgh of the cable is L.

I have no clue how to do this with such a source, all i have learned was to do a separation of variables, but it does not seem to work in my case.

Anybody can help or has an interesting link for me?
 
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  • #2
Well, I'm not sure I can help out immediately. However, Carslaw and Jaeger is the standard, comprehensive book on the heat equation, and would be the most likely book to help you out. Check to see if your school's library has it.
 

FAQ: Heat equation with annoying source term

What is the "annoying source term" in the heat equation?

The "annoying source term" in the heat equation refers to a term that is added to the original heat equation to account for any external factors that may affect the temperature. This term can make the heat equation more complicated and difficult to solve.

How does the "annoying source term" impact the heat equation?

The "annoying source term" can impact the heat equation by introducing additional variables that must be considered in the calculation. This can make the equation more difficult to solve and may result in a different solution than the original heat equation without the source term.

Why is the "annoying source term" necessary in the heat equation?

The "annoying source term" is necessary in the heat equation because it allows for the inclusion of external factors that may influence the temperature. This can be important in real-world scenarios, where the temperature may be affected by things like heat sources or changes in the environment.

How is the "annoying source term" determined in the heat equation?

The "annoying source term" is determined through experimental data or theoretical calculations. It may involve measuring the impact of external factors on the temperature or using mathematical models to predict their influence. The specific method of determining the source term may vary depending on the situation.

Can the "annoying source term" be removed from the heat equation?

In some cases, the "annoying source term" can be removed from the heat equation by simplifying the model or making assumptions about external factors. However, this may not always be possible or accurate. It is important to carefully consider the impact of the source term before attempting to remove it from the equation.

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