Heat Transfer in an Annulus with Variable Circumferential Heat Flux
hf. 1. Hear Mass Transfer. Vol. 7, pp. 1187-I 194.
Pergamon Press 1964.
Printed in Great Britain
HEAT TRANSFER IN AN ANNULUS WITH VARIABLE CIRCUMFERENTIAL HEAT FLUX?
W. A. SUTHERLAND:
and W. M. KAYS§
(Received 10 March 1964)
Abstract-An analysis of heat transfer in a concentric circular tube annulus with an arbitrarily prescribed heat flux around the periphery of either wall, or both walls, is presented. Solutions have been obtained for the hydrodynamically and thermally fully developed condition for constant heat rate per unit of tube length, for both the laminar and turbulent flow regimes. With these results, the ensuing temperature variation around either wall may be predicted. Contrary to what might be expected, the waI1 temperature variation is very substantial in turbulent as well as laminar flow. An example shows the importance of this effect.
NOMENCLATURE a, b, A, B,
&
c nt
&A
Fourier series coefficients ; wall conduction parameter; hydraulic diameter; t YY Y+,
a,
EH,
u.’
eigenfunction; Reynolds number; radius of zero shear; temperature; radial temperature function; velocity; y’@?C Q/P1 i dbn dum ;
Subscripts ave, in, a, 1, m, n, 0, W,
average; inlet; annulus ; inner waI1; mean ; harmonic index; outer wall; wall.
INTRODUCTION
t This work was performed under U.S. Atomic Energy Commission Contract AT(O4-3)-189, Project Agreement 29. 2 Atomic Power Equipment Department, General Electric Company, San Jose, California. 5 Mechanical Engineering Department, Stanford University, Stanford, California.
THE CIRCULAR tube annulus is one of the more
important flow passage geometries for heattransfer systems, ranking closely behind the circular tube in engineering applications. It has
1187
1188
W. A.
SUTHERLAND
and W.
M.
KAYS
been shown by Reynolds et al. [l] that the thermal boundary condition for flow through an annulus can be reduced to four fundamental solutions. Of the large
Pergamon Press 1964.
Printed in Great Britain
HEAT TRANSFER IN AN ANNULUS WITH VARIABLE CIRCUMFERENTIAL HEAT FLUX?
W. A. SUTHERLAND:
and W. M. KAYS§
(Received 10 March 1964)
Abstract-An analysis of heat transfer in a concentric circular tube annulus with an arbitrarily prescribed heat flux around the periphery of either wall, or both walls, is presented. Solutions have been obtained for the hydrodynamically and thermally fully developed condition for constant heat rate per unit of tube length, for both the laminar and turbulent flow regimes. With these results, the ensuing temperature variation around either wall may be predicted. Contrary to what might be expected, the waI1 temperature variation is very substantial in turbulent as well as laminar flow. An example shows the importance of this effect.
NOMENCLATURE a, b, A, B,
&
c nt
&A
Fourier series coefficients ; wall conduction parameter; hydraulic diameter; t YY Y+,
a,
EH,
u.’
eigenfunction; Reynolds number; radius of zero shear; temperature; radial temperature function; velocity; y’@?C Q/P1 i dbn dum ;
Subscripts ave, in, a, 1, m, n, 0, W,
average; inlet; annulus ; inner waI1; mean ; harmonic index; outer wall; wall.
INTRODUCTION
t This work was performed under U.S. Atomic Energy Commission Contract AT(O4-3)-189, Project Agreement 29. 2 Atomic Power Equipment Department, General Electric Company, San Jose, California. 5 Mechanical Engineering Department, Stanford University, Stanford, California.
THE CIRCULAR tube annulus is one of the more
important flow passage geometries for heattransfer systems, ranking closely behind the circular tube in engineering applications. It has
1187
1188
W. A.
SUTHERLAND
and W.
M.
KAYS
been shown by Reynolds et al. [l] that the thermal boundary condition for flow through an annulus can be reduced to four fundamental solutions. Of the large
References: W. C. REYNOLDS, E. LUNDBERG P. A. MCCUEN, R. and Heat transfer in annular passages-general formulation of the problem for arbitrarily prescribed wall temperatures or heat fluxes, ht. J. Heat Mass Transfer 6, 483493 (1963). (1963). (1963). Transfer 6, 531-557 (1963). Math. Me& 31, 208 (1951). 8. R. JENKINS,Variation of the eddy conductivity R