Consider steady-state heat conduction in an annulus with periodic boundary condition.

The governing equation and boundary condition of the problem are given by

with and ,

with the following subsidiary conditions:

(symmetry condition),

(symmetry condition),

(temperature at the cylindrical inner wall),

(periodic temperature at the circular outer wall).

The dimensionless temperature can be found using the Chebyshev collocation technique with collocation points in both spatial directions. The discretization yields a system of 441 algebraic equations, where the unknowns are the values of at the nodes. The contour plot of the solution (for and ) is readily obtained for user-set values of parameters and .