A novel finite volume method for cylindrical heat conduction problems

A new finite volume method for cylindrical heat conduction problems based on Lnr-type diffusion equation is proposed in this paper with detailed derivation. On the basis of coordinate transformation, the diffusion term in the r direction of the heat conduction equation in a cylindrical coordinate is transformed into the Lnr-type diffusion term. Considering the influence of different boundary conditions, source terms and ratios of the internal to external radius, four typical categories of cases are calculated by the newly proposed method based on Lnr-type diffusion equation, the method based on local analytical solution and traditional central difference finite volume method respectively. The comparison of calculation results indicates that the new finite volume method is more accurate than the conventional one, since when the governing equation is discretized, the new method transforms λr∂T∂r into λ∂T∂lnr and treats this term as a whole to guarantee the conservativeness of diffusion flux. Numerical results also show that the total calculating time and required computation grid number of the new method are significantly less than the other two methods for achieving the same level of accuracy.