An efficient approach to simulate natural convection in arbitrarily eccentric annuli by vorticity-stream function formulation

The global method of polynomial-based differential quadrature (PDQ) and Fou rier expansion-based differential quadrature (FDQ) is applied in this work to simulate the natural convection in an annulus between two arbitrarily ec centric cylinders. The vorticity-stream function formulation in the curvili near coordinate system is taken as the governing equation, and the pressure single value condition is converted to an explicit formulation to update t he stream function value on the inner cylinder wall. The present approach i s very efficient, which combines the high efficiency and accuracy of the di fferential quadrature (DQ) method with simple implementation of pressure si ngle value condition, When the present approach is applied to the concentri c ease, it was found that the computed stream function on the inner cylinde r is almost zero and the pow field is symmetric, The computed average equiv alent conductivity for the concentric ease also agrees very well with avail able data in the literature, For the eccentric case, it was found that the computed stream function on the inner cylinder is not zero and there is a g lobal circulation, The present result confirms the findings by Guj and Stel la (Numer. Heat Transfer, vol. 27, pp, 89-105, 1995).