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Quick question related to flux and Laplace's equation watch

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    I'm doing a question about a cylinder made of a permeable material placed in a solute of diffusivity k. Lets say the concentration of the solute at a point inside the cylinder is P(r,theta) and the normal component of the flux is given by Fcos2(theta) where F is a constant. I need to find the steady state distribution of solute within the cylinder.

    I kinda know what to do but before I can do that I need to relate the normal component of the flux to grad(P) and then find P from this. How would I go about doing this?

    Currently I have the expression -k*grad(P).n=Fcos2(theta) but I'm confused as to how to proceed from here.
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    Ok I think I've got it, grad(P) in plane polars involves derivatives of P in the r and theta directions, obviously P will depend on theta but won't depend on r, so it seems that grad(P) is only related to dP/d(theta) in which case we can integrate up to find and expression for P. Is this correct?
 
 
 

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