Solving Boundary Condition for Wave Diffusion Equation in Hollow Cylinder

In summary, the conversation discusses difficulties with boundary conditions in a wave diffusion equation in a hollow cylinder problem. The person seeking help needs good references and provides an equation and boundary value for others to see. There is a discussion about the nomenclature and a potential solution is suggested. However, there is a complication with the boundary condition at r=0.
  • #1
mhmonon
5
0
Hi all,
I am facing difficulties about boundary condition in Hollow Cylinder. its like wave diffusion equation in hollow cylinder. can anyone help me out to solve this problem. I need some good reverences.
Thank you
 
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  • #2
Welcome to PF!

Hi mhmonon! Welcome to PF! :smile:
mhmonon said:
Hi all,
I am facing difficulties about boundary condition in Hollow Cylinder. its like wave diffusion equation in hollow cylinder. can anyone help me out to solve this problem. I need some good reverences.
Thank you

We're all very reverend here. o:)

Show us how far you got, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
You need to be more precise with what you are doing. That will directly influence what the BCs are.
 
  • #4
here I attached the equation with the boundary value.
Please see the attachment.
 

Attachments

  • boundaryvalue.pdf
    11.3 KB · Views: 195
  • #5
I think your nomenclature is a bit different than what I am used to seeing. You are solving a PDE for the velocity potential, correct? Your boundary conditions are on omega which is usually circular frequency. Is that correct?
 
  • #6
actually it is a wave diffusion equation in hollow cylindrical problem.. I think I can solve this problem.
 
  • #7
that is the equation for r, after you have separted variables r and [itex]\theta[/itex]. One "unstated" boundary condition is that the function must be finite at r= 0. That gives you one of your constants immediately.
 
  • #8
hi HallsofIvy,
Thanks for your reply. Yep you are right. But I am facing here another problem. The problem is that I have no condition at r=0; Instead of r=0 I have another condition that is ri(internal radius)=0. So I can not eliminate one. Bye
 

1. What is the wave diffusion equation?

The wave diffusion equation is a partial differential equation that describes the propagation of waves in a medium. It is used to model a variety of physical phenomena, such as heat transfer, sound waves, and electromagnetic waves.

2. How is the wave diffusion equation applied to a hollow cylinder?

In the case of a hollow cylinder, the wave diffusion equation is applied to solve for the behavior of waves traveling along the radial direction, as well as the azimuthal and axial directions. This allows for a more accurate representation of wave propagation in the cylinder.

3. What are boundary conditions in the context of the wave diffusion equation?

Boundary conditions are mathematical constraints that are applied to the wave diffusion equation to account for the behavior of waves at the boundaries of the hollow cylinder. These conditions are necessary to ensure the accuracy of the solution.

4. How do you solve for boundary conditions in the wave diffusion equation?

Solving for boundary conditions involves applying the appropriate constraints to the wave diffusion equation and solving for the unknown variables. This can be done analytically using mathematical techniques, or numerically using computer simulations.

5. What are some practical applications of solving boundary conditions for the wave diffusion equation in a hollow cylinder?

Some practical applications of this problem include predicting the behavior of heat transfer in pipes and cylinders, modeling sound waves in musical instruments, and understanding the propagation of electromagnetic waves in cylindrical antennas.

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