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.

NOTE:

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.

NOTE:

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.).

OUTCOME:

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