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Effect of wall conduction on natural convection over a vertical slender hollow circular cylinder

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Abstract

An analysis is made of the laminar natural convection of incompressible fluids over a slender, hollow circular cylinder with the inner surface at a constant temperature ofT b . The temperature of the outer surface must be solved from the coupled conduction of the cylinder and the natural convection of the fluid over the cylinder. The objective of this paper is to investigate the effect of conduction on the heat transfer characteristics of the natural convection boundary layer of the fluid. A wall conduction parameter,p, is introduced which is a measure of the heat conductivities of the solid and the fluid and the thickness of the cylindrical shell. The governing differential equations, being non-similar, are solved by a finite-difference method. Numerical results are generated for a series of values ofp's and Prandtl numbers.

The present analysis shows that the overall effect of conduction of the cylinder is to reduce the heat transfer. Any calculation of the heat transfer rate based on the assumption of a constant wall temperature overestimates this quantity. The effect increases for large values ofp.

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Abbreviations

C p :

specific heat

f, g :

similarity variables

\(\bar g\) :

gravitational acceleration

Gr:

Grashof number

k :

heat conductivity

L :

length of cylinder

p :

axial conduction parameter defined in Eq. (19)

Pr:

Prandtl number

q :

heat transfer

r :

coordinate in ther-direction

r i ,r 0 :

inner and outer radii of the hollow cylinder

R :

ratio of adjacent interval in η-direction

Re:

Reynold number

T b :

temperature at the inner surface of the hollow cylinder

T :

temperature of the fluid

T s :

temperature of the cylinder

u c :

reference velocity

v r :

velocity component inr-direction

v z :

velocity component inz-direction

z :

coordinate along the axis

ρ:

density

ν:

kinematic viscosity

α:

thermal diffusivity

β:

bulk modulus

θ:

dimensionless temperature

ψ:

stream function

b :

condition forx ≤ L

∞:

condition at infinity iny-direction

f :

fluid

s :

solid

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Authors and Affiliations

  1. Department of Mechanical Engineering, School of Engineering, University of Michigan, 48128-1491, Dearborn, MI, U.S.A.

    Tsung-Yen Na

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  1. Tsung-Yen Na
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Na, TY. Effect of wall conduction on natural convection over a vertical slender hollow circular cylinder. Appl. Sci. Res. 54, 39–50 (1995). https://doi.org/10.1007/BF01666801

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  • DOI: https://doi.org/10.1007/BF01666801

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