Boundary Conditions Question
 

I'm trying to solve an unsteady thermal diffusion problem, where a flat plate at 0 C has one end immersed in 25 C water. The boundary condition at the immersed end (x=0) is given by



where h and λ are known (Presumably T(0,t=0) can be assumed to be 0 C)

Here is where I am lost, I am not sure how to implement this boundary condition in my TDMA matlab code. Would it be reasonable to make the assumption that the temperature at x=0 immediately goes to steady state? Or is there a way to solve the PDE directly?

Any help would be greatly appreciated

you don't need to specify the temperature at immersed end. you need to discretize your boundary equation using one-way differencing for (∂T/∂x) then you have aW, aP, aE, Sc, Sp. (either aW or aE will be zero depending on the boundary location)