Modifying the heat equation for multiple sources

[babagoslow]

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.

 

[Chestermiller]

What you seem to be (cleverly) reinventing is the "Method of Images." This can be used in many potential flow problem involving heat transfer and potential fluid flow (including flow in porous underground geological formations containing arrays of injection or production wells). Try Googling.

Chet