Summary
This note presents an exact solution for the stress and displacement field in an unbounded and transversely constrained elastic medium resulting from the motion of a plane heat source travelling through the medium at constant speed in the direction normal to the source plane.
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Abbreviations
- ρ :
-
mass density
- κ :
-
diffusivity
- θ :
-
thermal conductivity
- Q :
-
heat emitted by plane heat source per unit time per unit area
- ν :
-
speed of propagation of plane heat source
- μ :
-
shear modulus
- ν :
-
Poisson's ratio
- T :
-
temperature
- σ x, σy, σz :
-
normal stress components
- u x, uy, uz :
-
displacement components
- c :
-
speed of irrotational waves
- t :
-
time
- x, y, z :
-
Cartesian coordinates
- ζ=x−vt :
-
moving coordinate
References
Nowacki, W., Thermoelasticity, Pergamon Press, 1962.
Fox, N., Appl. sci. Res. A 13 (1964) 144.
Carslaw, H. S. and J. C. Jaeger, Conduction of Heat in Solids. 2nd Ed., Oxford University Press, 1959.
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Reismann, H. The moving, plane heat source in an elastic medium. Appl. sci. Res. 15, 216–220 (1966). https://doi.org/10.1007/BF00411557
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DOI: https://doi.org/10.1007/BF00411557