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The flow of heat in a given circle of radius R is given as: $$ \frac{\partial T}{\partial t} = \kappa \nabla ^2 T $$ Where $T(r=R,\theta, t) = T_0 sin^2(2\theta)$ and the starting temperature is $T(r,\theta, t=0) = T_0$

Find the stationary temperature $(T_s = (r,\theta))$ that we expect to get after long times, $t\to \infty$

I'm having difficulties understanding the question. I understand that for stationary solutions, we know the solution is not dependent on time, so does left hand side become 0? If so, what exactly do with the initial starting temperature? $(T_0)$

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    I forget what the transition part is called but when it settles out is call steady state. – 2017-02-13
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    @Paparazzi yep. In terms of the equation, the left-side that's dependent on time is zero, and the starting condition where t=0 is extraneous information not needed to solve for the stationary time. – 2017-02-13

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