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I am operating via finite differences.

Say for example, I have this pipe that contains a fluid. I have the boundary condition at x = x

k is the effective thermal conductivity of the fluid, T is the temperature of the fluid at any point x, h

I know how to 'plug in' such boundary conditions in finite difference formulations. My question is which value of T do I use? Is it T at x = x

I keep on seeing that T here is supposed to be the bulk temperature. The problem is since I'm doing this by finite difference, the temperature of the fluid is not constant along the spatial dimension. In this case, which point to use exactly? Is it the point at the fluid beside the wall point?

Or is it that at the 'wall point', there are 'two operating temperatures' - the 'wall temperature' and the 'bulk fluid temperature' at the wall?

Any help is appreciated. Thank you!

Say for example, I have this pipe that contains a fluid. I have the boundary condition at x = x

_{1}:k is the effective thermal conductivity of the fluid, T is the temperature of the fluid at any point x, h

_{w}is the wall heat transfer coefficient, and T_{w}is the temperature at the wall.I know how to 'plug in' such boundary conditions in finite difference formulations. My question is which value of T do I use? Is it T at x = x

_{1}? But isn't that T_{w}already, since x_{1}is the wall?I keep on seeing that T here is supposed to be the bulk temperature. The problem is since I'm doing this by finite difference, the temperature of the fluid is not constant along the spatial dimension. In this case, which point to use exactly? Is it the point at the fluid beside the wall point?

Or is it that at the 'wall point', there are 'two operating temperatures' - the 'wall temperature' and the 'bulk fluid temperature' at the wall?

Any help is appreciated. Thank you!

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