DBE: Thermal Boundary Conditions

1st kind:

We can specify the temperature at the boundaries (on either side of a slab for example T=T1 at x1 and T=T2 at x2). This is know as the Dirichlet condition or boundary condition of the first kind.


It is critical that we realize that we can only use this condition if we actually know a value for the temperature (for example, T1=50C)

2nd kind:

We can specify a constant flux at the boundary (for example, $\displaystyle{-k\frac{dT}{dx} = C}$ at some position x1). This is know as a Neumann or second kind condition.


Again, we must know the value of the flux, C. The special case where this is equal to zero is the insulated or adiabatic boundary condition.

3rd kind:

Finally, we can combine the two, and specify that the flux is somehow related to the temperature (for example, $\displaystyle{-k\frac{\partial T}{\partial y} = h(T-T_\infty)}$). This is called the Robin or third type. (The special case shown here is the convection condition, but it could also be radiation, etc.).


Identify reasonable boundary conditions in a heat transfer problem (explain when each is most useful)