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


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 



Radius of inner cylinder


Radius of outer cylinder


Specific heat


Chebyshev polynominals


Hydraulic diameter (=2G)




Fourier function


Annular gap (=bg +)


Heat transfer coefficient


Thermal conductivity


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


Reynolds number (=ρu m D h /μ)


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


Wall temperature


Axial flow velocity


Radial coordinates in computational domain

Greek Letters


Thermal diffusivity (=k/ϱc)


Friction factor


Dynamic viscosity


Density of fluid


Shear stress



Stands for nondimensional parameter

Stands for average value



Stands for concentric case


Refers to inner cylinder


Order of Chebyshev polynomials


Order of Fourier function


Stands for mean or mixed mean value


Refers to outer cylinder


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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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