Challenges in Solving Poisson's Equation in Polar Coordinates with a Heat Source

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In summary, the conversation discusses solving a heat equation in plane polar coordinates using the separation of variables method. The equation includes a heat source and is subject to certain constraints. The person speaking has attempted to solve it but is struggling to separate the r and theta terms. They are reminded that showing their work is required in order for others to help identify any errors.
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sachi
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I have to solve 1/r*d/dr(r*dT/dr) + 1/(r^2)*(d^2)T/(d theta)^2 = q(r) where all derivatives are partials. N.b this is just poisson's equation in plane polar co-ordinates. A heat source of form q(r) = K/(r^2) where K is a constant i applied to a olis between coaxial cylinders of radius a and b.

I have tried using the separation of variables method, but I can't get the r terms and the theta terms to separate. Thanks very much.
 
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Our policies state that you must show your work. You agreed to that before you posted. Unless you show your work it is impossible for anyone to find your error.
 

FAQ: Challenges in Solving Poisson's Equation in Polar Coordinates with a Heat Source

What is Poisson's equation problem?

Poisson's equation problem is a mathematical equation used to model the behavior of electrical or gravitational fields in a given region. It is a type of partial differential equation that relates the potential of a field to its sources or charges.

What is the formula for Poisson's equation?

The general formula for Poisson's equation is ∇²Φ = ρ, where ∇² is the Laplace operator, Φ is the potential of the field, and ρ is the charge density.

What are some real-world applications of Poisson's equation problem?

Poisson's equation is used in various fields including physics, engineering, and mathematics. It can be applied to model the electric potential in a circuit, the gravitational potential of a planet, and the electrostatic potential in a charged conductor. It is also used in image processing and computer vision for edge detection and image reconstruction.

What are the boundary conditions for Poisson's equation?

The boundary conditions for Poisson's equation depend on the specific problem being solved. In general, they describe the potential at the boundaries of the field and can be either Dirichlet boundary conditions (specifying the potential itself) or Neumann boundary conditions (specifying the normal derivative of the potential).

How is Poisson's equation solved?

Poisson's equation can be solved using various numerical methods, such as finite difference, finite element, or boundary element methods. These methods discretize the equation and solve it iteratively to obtain a numerical solution. Analytical solutions are also available for simpler problems with specific boundary conditions.

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