# NUMERICAL ANALYSIS OF LAMINAR FLOW AND HEAT TRANSFER AROUND IN-LINE ELLIPTIC TUBE BANKS

**Sang-Kyu Park**

Department of Machanical Engineering, Chonbuk National University, Chonju 560-756, KOREA

**Terukazu Ota**

Department of Machine Intelligence and Systems Engineering, Tohoku University, 01 Aoba, Aramaki, Aoba-ku, Sendai, 980-8579, Japan

## Abstract

Numerical analyses were made on a two-dimensional laminar flow and heat transfer around in-line elliptic tube banks with the finite difference method for solving Navier-Stokes and energy equations. A boundary-fitted coordinate system was employed and the finite difference equations were solved with the Tschebyscheff SOR method. Treated in the present paper is an elliptic tube of axis ratio 1:2 and its long axis is in line with the oncoming flow direction. Numerical calculations were made on the pitch to axis length ratio (1.2−1.5)×(l.2−1.5), at the Reynolds numbers 60-200, and the Prandtl numbers 0.7, 1.0 and 7 under the condition of uniform heat flux.

Details of the flow and heat transfer characteristics are clarified for the fully developed flow state. It is found that effects of the longitudinal and transversal pitches upon the local Nusselt number are relatively large on the upstream surface. An increase of the longitudinal pitch results in no essential change of the mean Nusselt number. As to the transversal pitch, however, its decrease accompanies a decrease of the mean Nusselt number.

Furthermore, detailed analyses were conducted on the mean Nusselt numbers and the pressure loss coefficients obtained numerically, and their correlation equations are proposed with the method of least squares, which are able to estimate the mean Nusselt number and the pressure loss coefficient for any longitudinal and transversal pitches.