Stationary temperature field inside a house

[ficku1]

Homework Statement

House: a room (see figure) has perfectly isolated walls, except the two windows
where a convective heat exchange takes place (with the same transfer coefficient).
Outside temperature in front of a sun-faced wall-sized panoramic window is T1,
while at the back it is T2.Calculate the stationary temperature field inside the
room. You can also play by adding an additional energy flux through the front
window due to a sunlight at an angle φ.

Homework Equations

The Attempt at a Solution

For this assignment we have to use the diffusion equation

dT/dt=D (d²T)/dx²

If we are calculating stationary temperature the equation is actually Lapace ΔT=0 .

I think it is not the same in the x and y direction because the windows aren't the same size and the sun is only shining in the room on one side. So we separate the variables T=X(x)Y(y) and we get

1/X * (d²X)/dx²=-1/Y * (d²Y)/dy² =C

But i am not sure what the boundary conditions should be?

Thank you for your help.

 

[anathema]

Thank you for your question. The boundary conditions for this problem would depend on the specific dimensions and properties of the room and windows. However, in general, the boundary conditions for this problem would involve the temperature at the walls and windows, as well as the heat transfer coefficient and any additional energy flux from sunlight.

One possible approach to solving this problem would be to use the boundary conditions at the walls and windows to set up a system of equations, and then use numerical methods or analytical techniques to solve for the temperature field inside the room. It may also be helpful to consider any other factors that could affect the temperature, such as air flow or insulation.

I hope this helps. Good luck with your calculations!