My lecturer told me that analytical solution for a 2d steady state problem is is hard to find. But getting the initial data from the known exact solution is far more easy. can anyone, give me a example how to get the initial data?
To get solution of thermal problem you need to set initial and boundary conditions of the problem, then, using them, you can find coefficients of the general solution of the thermal conduction differential equation (which can be found in handbooks). Also, as I found not long time ago, the 2D steady state thermal problems can be easily solved numerically using Finite Elements calculated by Excel with circular reference calculations. Each cell's temperature is average of its four neighboring cells' temperatures. Excel's settings should allow the circular reference calculations with big enough number of iterations.
I'm not certain what you mean by exact solution - do you have the T(x,y) equation?
Then the boundary condition should be relatively easy to find, you just insert the x and y of your boundaries and find T at the boundaries.
Also it is not certain what you mean by the initial data. Initial conditions occur in unsteady problems and not in steady ones.
Actually, steady-state problems don't contain time, so there is no any certain initial conditions. Any initial conditions eventually will drift into the final steady-state solution of the thermal problem after long enough time - onlly boundary conditions play role here. If I understood the question correctly.
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