Heat conduction within an elliptic annulus heated at either CWT or CHF

Exact and numerical solutions of heat conduction in the annulus between two elliptic long tubes are obtained. The annulus is heated from its inner wall at either constant wall temperature, CWT or constant heat flux, CHF. The elliptic coordinate transformation along with Fourier spectral method are used to deduce the exact and numerical solutions. The heat conduction within the enclosure is mainly influenced by the method of heating, axis ratio of inner tube and major axes ratio of the two tubes. The solutions are obtained for the dimensionless temperature and local heat flux distributions within the annulus and along its walls.