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Temperature in a cooled, heat-generating cylinder

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The temperature and heat flux distributions in a long circular cylinder with a central circular channel surrounded by a ring of k equally spaced circular channels are determined for the case of a uniform generation of heat in the cylinder material. The solution of the problem is accomplished by constructing and combining two temperature systems. The first of these has a pole of order n at the centre of each eccentric channel and possesses an invariance that allows the boundary conditions to be met simultaneously at the surface of each eccentric channel, and the second is the familiar solution in n-th degree circular harmonics for the hollow cylinder with heat generation and an arbitrary symmetrical temperature distribution. Curves are presented for a variety of cases to demonstrate the effect of the various parameters that appear in the solution.

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Abbreviations

a :

Inner radius, divided by outer radius

b :

Radius of centres of eccentric channels, divided by outer radius

c :

Outer radius of cylinder

H :

Heat generation rate, BTU/hr./in.3

κ :

Thermal conductivity, BTU/hr./in./deg. F

r, ρ :

Radial co-ordinates

k :

Number of equally spaced eccentric channels

T :

Temperature, deg. F (a subscript S refers to channel surface)

z, ζ :

Complex variables

α1, α2:

Boundary condition parameters

λ :

Radius of eccentric channels, divided by b

φ, θ :

Angular coordinates

Φ :

Heat flux, BTU/hr./in.2

References

  1. Schneider, P. J., Conduction Heat Transfer, Addison-Wesley Publishing Co., Cambridge, 1955.

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  2. Sparrow, E. M., Trans. Amer. Soc. Mech. Engrs. C 82 (1960) 389.

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  3. Howland, R. C. J., Proc. Camb. Phil. Soc. 30 (1934) 315.

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Authors and Affiliations

  1. Bettis Atomic Power Laboratory, Westinghouse Electric Corporation, Pittsburgh 30, Pennsylvania, U.S.A.

    H. Kraus

Authors
  1. H. Kraus
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Kraus, H. Temperature in a cooled, heat-generating cylinder. Appl. sci. Res. 10, 419 (1961). https://doi.org/10.1007/BF00411935

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  • DOI: https://doi.org/10.1007/BF00411935

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