Finite analytic numerical solution axisymmetric Navier-Stokes and energy equations

Journal Article · Mon Aug 01 04:00:00 EDT 1983 · J. Heat Transfer; (United States)

DOI:https://doi.org/10.1115/1.3245633· OSTI ID:5511233

Chen, C; Yoon, Y H

Convective 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.

• Research Organization: Division of Energy Engineering and Iowa Institute of Hydraulic Research, The University of Iowa, Iowa City, Iowa 52242
• DOE Contract Number: AC02-79ER10515
• OSTI ID: 5511233
• Journal Information: J. Heat Transfer; (United States), Journal Name: J. Heat Transfer; (United States) Vol. 105:3; ISSN JHTRA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400 -- Engineering-- Heat Transfer & Fluid Flow
640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
CONTRACTION
CONVECTION
DIFFERENTIAL EQUATIONS
ENERGY TRANSFER
EQUATIONS
EXPANSION
FLUID FLOW
HEAT TRANSFER
LAMINAR FLOW
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PIPES
REYNOLDS NUMBER
STEADY-STATE CONDITIONS
TEMPERATURE DISTRIBUTION