Semi-analytic solution of the two-dimensional turbulent energy equation in round tubes using an analytic velocity profile and its experimental validation |
| |
Authors: | A Campo C Cortés |
| |
Institution: | (1) College of Engineering Idaho State University Pocatello, ID 83209, USA, US;(2) Dpto. de Ingenieríia Mecánica Universidad de Zaragoza Zaragoza 50015, Spain, ES |
| |
Abstract: | A semi-analytic solution of the temperature development of single-phase, turbulent viscous flows inside smooth round tubes
is performed. The special feature of the theoretical analysis revolves around two single universal functions of analytic form
for the accurate characterization of the turbulent diffusivity of momentum and the turbulent velocity profile in the entire
cross-section of a round tube. Using this valuable information that emanates from the analytic solution of the one-dimensional
momentum balance equation, the two-dimensional energy balance equation was reformulated into an adjoint system of ordinary
differential equations of first–order with constant coefficients. Each equation in the system of differential equations governs
the axial variation of the average temperature of a finite volume of fluid of annular shape. Exploiting the linearity of the
system of differential equations, an analytic solution of it was obtained via the matrix eigenvalue method with LAPACK, a
library of Fortran 77 subroutines for numerical linear algebra. Reliable series have been determined for the axial variation
of the two thermal quantities of importance: (a) the time-mean bulk temperature and (b) the local Nusselt number. The semi-analytic
nature of the local Nusselt number distribution is advantageous because it may be viewed as an analytic-based correlation
equation. Prediction of the local Nusselt numbers for turbulent air flows compare satisfactorily with the comprehensive correlation
equations and the abundant experimental data that are accessible from the literature. The air flows are regulated by a wide
spectrum of turbulent Reynolds numbers.
Received on 4 June 2001
RID="★"
ID="★" Current address Mechanical Engineering Dept. The University of Vermont Burlington, VT 05405, USA |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|