Abstract
The problem consists of determining the temperature distribution and the thermal stresses in an annulus partly filled with a cold fluid with free convection in air as the outer thermal-boundary condition. An iterative computer solution provided temperature distributions which were compared to those measured experimentally. Analytical calculations of the stresses using Fourier series expression for the temperature distribution agreed with experimental results by photothermoelasticity.
The stress-intensity factors determined by photothermoelasticity for partly filled annuli with a crack extending radially 1/5 of the wall thickness were compared with approximate analytical methods.
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Abbreviations
- a :
-
inner radius, in.
- b :
-
outer radius, in.
- A, B :
-
Fourier cosine coefficients of the surface temperatures
- Bi :
-
Biot number (hr/k), dimensionless
- d :
-
distance of liquid level from center of annulus, in.
- E :
-
modulus of elasticity, psi
- f :
-
material-fringe constant, psi/fringe/in.
- h :
-
film coefficient of heat transfer, BTU/hr-ft2-° F
- k :
-
thermal conductivity of annulus, BTU/hr-ft2-°F/in.
- K 1 :
-
stress-intensity factor for the opening mode,\(psi - \sqrt {in.} \)
- K 2 :
-
stress-intensity factor for the shearing mode,\(psi - \sqrt {in.} \)
- r :
-
radius, in.
- T :
-
temperature, °F
- α:
-
coefficient of linear expansion, in./in.-°F
- δ ij :
-
Kronecker delta
- θ:
-
polar angle, deg
- θ0 :
-
angle at which the liquid level intercepts the interior boundary of the annulus, deg
- τ:
-
maximum shear stress, psi
- τ n :
-
average value of the maximum shear stress τ used to normalize the stresses, psi
- σ:
-
stress, psi
- a :
-
ambient
- i :
-
inner surface
- l :
-
liquid
- o :
-
outer surface
- v :
-
vapor
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Emery, A.F., Barrett, C.F. & Kobayashi, A.S. Temperature distributions and thermal stresses in a partially filled annulus. Experimental Mechanics 6, 602–608 (1966). https://doi.org/10.1007/BF02326828
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DOI: https://doi.org/10.1007/BF02326828