  We consider the finite temperature Casimir force acting on two parallel
plates in a closed cylinder with the same cross section of arbitrary shape in
the presence of extra dimensions. Dirichlet boundary conditions are imposed on
one plate and fractional Neumann conditions with order between zero (Dirichlet)
and one (Neumann) are imposed on the other plate. Formulas for the Casimir
force show that it is always attractive for Dirichlet boundary conditions, and
is always repulsive when the fractional order is larger than 1/2. For some
fractional orders less than 1/2, the Casimir force can be either attractive or
repulsive depending on the size of the internal manifold and temperature.
