By Michel Frémond (auth.)
Predictive theories of phenomena related to part switch with purposes in engineering are investigated during this quantity, e.g. solid-liquid part swap, quantity and floor harm, and section swap concerning temperature discontinuities. Many different part switch phenomena comparable to solid-solid section swap fit reminiscence alloys and vapor-liquid part switch also are explored. Modeling is predicated on continuum thermo-mechanics. This contains a renewed precept of digital energy introducing the facility of the microscopic motions answerable for section switch. This development yields a brand new equation of movement with regards to microscopic motions, past the classical equation of movement for macroscopic motions. the hot idea sensibly improves the section swap modeling. for instance, while hot rain falls on frozen soil, the harmful black ice phenomenon could be comprehensively anticipated. moreover, novel equations expect the evolution of clouds, that are themselves a mix of air, liquid water and vapor.
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Predictive theories of phenomena regarding part swap with functions in engineering are investigated during this quantity, e. g. solid-liquid section swap, quantity and floor harm, and section swap related to temperature discontinuities. Many different section swap phenomena resembling solid-solid section switch suit reminiscence alloys and vapor-liquid part swap also are explored.
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Extra info for Phase Change in Mechanics
1 The Stefan Problem The classical ice–water phase change or the Stefan problem [2, 34, 96, 149, 200], introduces as state quantities the temperature T and the liquid or water volume fraction β , [3, 133]. 1) with δ E = gradT and χ = T . Let us comment the different terms of Ψ and Φ : • −CT ln T is responsible for heat storage (C is the heat capacity). • −β (L/T0 )(T − T0 ) is a linear function with respect to β : its derivative being constant with respect to β defines a threshold (we prove below that when (T − T0 ) < 0 the solid phase, the ice, is present and when (T − T0 ) > 0, the liquid phase, the water, is present).
Let us recall that the temperatures T are positive because they are the traces on the discontinuity surface of the volume temperatures which are positive. We assume that the average temperature T is positive. The particular case where T = 0 is investigated in . 28) and [H · N] = 0. 29) where we recall that e is the specific internal energy. [U] + m 2 [U ]. 31) where, UN = U · N, Vrel = U − W is the velocity with respect to the discontinuity surface, whose velocity is W, v = VN = Vrel · N, the relative normal velocity.
With the small perturbation assumption, the constitutive laws are σ = β1 (λv (trε˙ )1 + 2 μvε˙ ) + β2 (λe (trε )1 + 2μe ε ) − p1, B1 B2 ∈ − TL0 θ 0 + ∂ IK (β ) + c ∂β 1 −p , ∂t 1 λ Hi = kgradβi , Q = − gradT, T L θ s = C(1 + ) + β1 , T0 T0 where the deformations ε and temperatures θ at power 2 have been neglected in agreement with the small deformation assumption (see Appendix B). 4. An other way to have simple constitutive laws is to assume that the voids are filled with vapor with heat capacity C and thermal conductivity λ .
Phase Change in Mechanics by Michel Frémond (auth.)