I have been trying to calculate heat function value by the equations given in the equations.png file. The geometry is a rectangular cavity with isothermal sidewalls and the top and bottom walls are insulated. No-slip condition is applied at all the walls. For equation-based modeling I am using the Poisson equation form to calculate the heat function but unable to determine the boundary conditions corresponding to the heat function. Can you please show me the derivation of the boundary conditions based on the equations given in the image file?

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