How about you calculate the temperature on the adjacent nodes and then take their average on the common node?

X

|

O-Y

1. Identify the corner point while reading the grid.

2. then apply BC on all X points and Y points to get their temperature Tx(ij) and Ty(ij).

3. T_o = (Tx(corner)+Ty(corner))/2

This is very commonly done in finite difference, you can use this approach.

"I read somewhere that if Temperature and heat flux is specified on a node then only specified temperature should be considered, but I don't know if I should ignore convective heat transfer when temperature is specified."

I don't think so... why would you prefer one physics over the other? If in our previous grid, T and dT/dx are prescribed, you use "Robin BC", a mix between Neumann and Dirichlet BC. You can get its solution method in any finite difference CFD book like Patankar or K. Muralidhar and T. Sundararajan, Computational Fluid Flow, and Heat Transfer.

Hope this helps

At a boundary surface you can either specify the temperature or heat flux, not both, as the one determines the other. So if you have nodes on the the boundary line which separates these two regions, then, I think you can specify one of these two conditions alternately on every consecutive node.

Regards

Dr Kumar Eswaran

Professor