The Mathematica code is here: http://demonstrations.wolfram.com/TransientHeatConductionWithNoSteadyState/
Consider the heat conduction problem with Neumann (constant flux) at both boundaries of a solid slab. A constant radiant heat flux is imposed on one surface (derivative = -1) and the other surface is thermally insulated (derivative = 0).
If you increase the flux of the heat at one boundary, the temperature inside the system should raise faster over time. However, with the current code, if you increase the flux from 1 to 100, the system behavior doesn't change at all.
In the code, Quiet[NDSovle...] is used to suppress the error message: "NDSolve::ibcinc: Warning: Boundary and initial conditions are inconsistent. " The simulation might be incorrect due to this error message.
I want to have the ability to change the system behavior by changing the value of the flux at the boundary.
This is a very important question to me and I couldn't figure it out. Any help will be highly appreciated.