ON A REFINED HEAT CONDUCTION THEORY FOR MICROPERIODIC LAYERED SOLIDS
Titel:
ON A REFINED HEAT CONDUCTION THEORY FOR MICROPERIODIC LAYERED SOLIDS
Auteur:
Ignaczak, Jozef Baczynski, Zbigniew F.
Verschenen in:
Journal of thermal stresses
Paginering:
Jaargang 20 (1997) nr. 7 pagina's 749-771
Jaar:
1997-10-01
Inhoud:
A refined averaged theory of a rigid heat conductor with a microperiodic structure is used to solve a one-dimensional initial boundary value problem of heat conduction in a periodically layered plate with a large number of homogeneous isotropic layers. In such a theory, the temperature θ = θ(x,t) (0 ≤ x ≤ L, t ≥ 0)is approximated by θ(x,t) = θ0(x,t) + η(x)θ1(x,t) where θ0(x,t) is a temperature-corrector and η = η(x) is a prescribed microshape function; and the functions θ0 = θ0(x,t) and θ1 = theta;1(x,t) are to be found by solving an initial-boundary value problem described by a system of linear partial differential equations with averaged coefficients subject to suitable initial and boundary conditions. A uniqueness theorem for the averaged problem is proved and two closed-form solutions for a periodically layered semispace are obtained. One of the two solutions represents the temperature field in the layered semispace due to a sudden heating of the boundary plane, while the other stands for the temperature field in the layered semispace produced by laser surface heating. Numerical examples are included.
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