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If we define Theta as T_MC * D * nu, The problem can be summarized like this. Poisson's equation, boundary element, And what we need is (round Theta/ roune n) at boundary.

To solve this problem, boundary element method, BEM is convenient. It is obtained by descritizing the boundary integration. If you perform a partial integration of this Poisson's equation, it becomes like this.

X_B is a point on the boundary. Here, Theta with asterisk (*) is called "fundamental solution" of this Poisson's equation, and the Gamma means boundary integration, and Omega means volume integration.

Here, the last term with volume integration becomes just a sum of fundamental solution with the thermalization point and the boundary point of the interest.

If you split the boundary to node elements, and approximate the function to simple form on each node, this integral equation can be discretized to simultaneous equations. It is a standard BEM approach. And by substituting the boundary condition, Theta is ZERO, flux at the boundary can be obtained.