Numerical study of natural convection in an eccentric annulus between a square outer cylinder and a circular inner cylinder using DQ method

Abstract

In this paper, natural convective heat transfer in a horizontal eccentric annulus between a square outer cylinder and a heated circular inner cylinder is numerically studied using the differential quadrature (DQ) method. The vorticity-stream function formulation is taken in the governing equation. To take the global circulation flow into consideration, the pressure single-value condition is applied, an explicit formulation is derived and the stream function value on the inner cylinder wall is updated from the values at all the interior points. To apply the DQ method, the coordinate transformation is performed. A super elliptic function is introduced in this paper for approximating the square outer boundary located eccentrically to the inner boundary. As a result, the coordinate transformation from the physical domain to the computational domain is set up by an analytical expression. It is demonstrated in this paper that the DQ method is an efficient approach in computing the weak global circulation in the domain. The present method is validated by comparing its numerical results with available data in the literature and very good agreement has been achieved. A systematic study is conducted for the analysis of flow and thermal fields at different eccentricities and angular positions. © 2001 Elsevier Science Ltd. All rights reserved.