Abstract
The finite integral transform method is used to obtain the solution of unsteady heat conduction problems for a hollow sphere with a moving internal boundary and various boundary conditions at the outer surface. For the solution of the problems of interest integral transform formulas are presented with kernels (16), (20), and (24) and the corresponding inversion formulas (18), (22), (26), (29) and characteristic equations (17), (21), (25), (28), (31), (33).
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Abbreviations
- a,λ :
-
thermal diffusivity and conductivity
- tϕ :
-
temperature of phase transformation
- ρ :
-
density
- α :
-
heat transfer coefficient
- Q:
-
total quantity of heat passing through inner boundary
- F:
-
latent heat of phase transformation
- Fo(1,τ)=aτ/R 21 , Fo(i,τ)=ατ/r 2i , Fo(i,τ i)=ατa i/r 2i :
-
Fourier numbers
- Bi2=αR2/λ:
-
Biot number
References
G. A. Surkov and V. I. Krylovich, Inzh. -fiz. zhurn., No. 6, 1964.
G. A. Surkov, Inzh. -fiz. zhurn., no. 3, 1964.
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Surkov, G.A. Transient heat conduction in hollow spheres with a moving inner boundary. Journal of Engineering Physics 8, 324–328 (1965). https://doi.org/10.1007/BF00828744
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DOI: https://doi.org/10.1007/BF00828744