If I have a hot wire, the distribution of its temperature with respect to radius (from the center of the wire) and time follows the heat/diffusion equation.
However, now consider two wires, or even an array of many such wires. Say we can ignore the z coordinate and treat them as a point source in cylindrical polar coordinates. How would one modify the heat equation to account for all of them?
One way that I have thought about in this direction is considering symmetry. Due to the symmetry between two heated wires, there must be a zero temperature gradient in the geometrical centre between the two wires. But then you would have the problem of extending this to the case of N arbitrary heat sources.
However, now consider two wires, or even an array of many such wires. Say we can ignore the z coordinate and treat them as a point source in cylindrical polar coordinates. How would one modify the heat equation to account for all of them?
One way that I have thought about in this direction is considering symmetry. Due to the symmetry between two heated wires, there must be a zero temperature gradient in the geometrical centre between the two wires. But then you would have the problem of extending this to the case of N arbitrary heat sources.