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KSME Journal

, Volume 10, Issue 1, pp 94–104 | Cite as

Application of spectral collocation method to conduction and laminar forced heat convection in eccentric annuli

  • Woo Gun Sim
  • Jong Min Kim
Article

Abstract

Numerical approach based on the spectral collocation method has been utilized for analyzing heat convection and conduction in eccentric annuli. An eccentric instead of concentric annular duct is sometimes used as a fluid-flow and heat-transfer device especially in nuclear power plants. The hydrodynamically and thermally fully developed laminar flow with uniform heat flux through the inner and outer walls has been analyzed. Also, the conductive heat transfer problem, with uniform rate of internal heat generation in long hollow cylinder, has been solved. The governing equation for the present analysis is Poisson’s equation with constant nonhomogeneous term. Considering temperature and velocity distributions in eccentric annuli, Nusselt numbers and wall shear stresses are presented for various range of eccentricities. The spectral collocation method used in this study is verified by comparing the numerical solutions from the existing analytical solution and it is clear that this method is appropriate for assessing a more complicated heat transfer problem.

Key Words

Spectral Collocation Method Uniform Heat Flux Viscous Shear Stress Friction Factor Mixed Mean Temperature Nusselt Number 

Nomenclature

a

Radius of inner cylinder

b

Radius of outer cylinder

c

Specific heat

C3(Z)

Chebyshev polynominals

Dh

Hydraulic diameter (=2G)

e

Eccentricity

Fk(θ)

Fourier function

G

Annular gap (=bg +)

h

Heat transfer coefficient

k

Thermal conductivity

Nu

Nusselt number (=hD h/k)

\(\dot q\)

Heat generated per unit volume

\(\dot q'\)

Heat energy transferred through unit length per unit time

\(\dot q''\)

Heat flux

Re

Reynolds number (=ρu m D h /μ)

t+

Dimensionless temperature (=(t w−t)/(tw−tm))

tw

Wall temperature

u

Axial flow velocity

Z

Radial coordinates in computational domain

Greek Letters

α

Thermal diffusivity (=k/ϱc)

λ

Friction factor

μ

Dynamic viscosity

ϱ

Density of fluid

τ

Shear stress

Superscripts

+

Stands for nondimensional parameter

Stands for average value

Subscripts

c

Stands for concentric case

i

Refers to inner cylinder

j

Order of Chebyshev polynomials

k

Order of Fourier function

m

Stands for mean or mixed mean value

o

Refers to outer cylinder

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References

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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 1996

Authors and Affiliations

  • Woo Gun Sim
    • 1
  • Jong Min Kim
    • 1
  1. 1.Korea Atomic Energy Research InstituteKorea

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