Finite Analytic Numerical Solution Axisymmetric Navier-Stokes and Energy Equations

[+] Author and Article Information
Ching-Jen Chen, Young Hwan Yoon

Division of Energy Engineering and Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa 52242

J. Heat Transfer 105(3), 639-645 (Aug 01, 1983) (7 pages) doi:10.1115/1.3245633 History: Received February 05, 1982; Online October 20, 2009


Connective heat transfer for steady-state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature, and heat transfer coefficients for flow with Reynolds numbers of 5, 100, 1000, and 2000, and Prandtl numbers of 0.1, 1.0, and 10.0 with uniform grid sizes, are reported for an axisymmetric pipe with a sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic is stable, converges rapidly, and simulates the convection of fluid flow accurately, since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values, thereby minimizing the false numerical diffusion.

Copyright © 1983 by ASME
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