Regarding the boundary conditions in square cavity problem

Questions
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1

Dear Sir/Madam,
While solving square cavity problem, I’m facing some issues.
After rotation of 30 degrees of the cavity at a center (0,0), how to give the boundary condition for the left wall as hot i.e., theta=1 and for left wall as cold i.e., theta=0 using Dirichlet condition

Screenshot2024-12-07223757.png
Screenshot2024-12-07223757.png791×535 28.5 KB

bc = {{DirichletCondition[\[Theta][x, y] == 1, x <= 0], 
   DirichletCondition[\[Theta][x, y] == 0, x <= 1], 
   DirichletCondition[{u[x, y] == 0, v[x, y] == 0}, True], 
   DirichletCondition[p[x, y] == 0, x <= 0 || y >= 0]}}

I have given like this but I don’t know whether it is assigning correctly or not.

2

find straight-line eq of each edge, then the condition for them would be a x + b == y

3

Thank you for your reply. I defined that and even though I’m not getting it sir

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4

do you have the answer for the case that is not rotated?