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I am trying to solve a system of partial differential equations in Matlab, with both derivatives in time and space domains. I am using the pdepe function for that.

The system is, to be simple, a sort of solar thermal panel, made of three layers: an absorber plate, a fluid layer of running water and a back insulation layer. each of these layers is represented by a differential equation. Of course, many assumptions are implicit in the model, e.g. the model is here considered 1D (no edge effects...), the temperature disuniformity inside each layer is neglected ecc.

I'd like to describe the profile of the water temperature, giving a constant mass flow rate, a constant inlet temperature, variable forcing boundary conditions such as solar radiation, the initial conditions for the three layers etc.

In the first simulation, I just assume that solar radiation is constant and, starting at time t=0, it heats up the absorber while the circulating water removes the heat.

Here my questions:

1 Matlab_pdepe asks me to define boundary conditions also on the "right side" (outlet of the solar panel), which is actually unknown!

2 The results shows that in correspondence of the boundaries, the profile gets unstable. This does not change significantly with the mesh size nor with the integration time span. Please consider that the left boundary condition of the absorber plate is fixed by the heat balance with the water inlet temperature and the ambient temperature, both supposed constant.

Any idea or request for further explanations will be welcome :) :) :)

Thank you in advance

Giulio

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# Solving PDEPE without boundary conditions? heat transfer

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