We can specify the temperature at the boundaries (on either side
of a slab for example *T*=*T*_{1} at
*x*_{1} and *T*=*T*_{2} at
*x*_{2}). 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, T_{1}=50C)

We can specify a constant *flux* at the boundary (for
example, $\displaystyle{-k\frac{dT}{dx} = C}$ at some position
*x*_{1}). 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.

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)