81 research outputs found
‘‘Cooling by Heating’’- Demonstrating the Significance of the Longitudinal Specific Heat
Heating a solid sphere at its surface induces mechanical stresses inside the sphere. If a finite amount of heat is supplied, the stresses gradually disappear as temperature becomes homogeneous throughout the sphere. We show that before this happens, there is a temporary lowering of pressure and density in the interior of the sphere, inducing a transient lowering of the temperature here. For ordinary solids this effect is small because c_{p}≅c_{V}. For fluent liquids the effect is negligible because their dynamic shear modulus vanishes. For a liquid at its glass transition, however, the effect is generally considerably larger than in solids. This paper presents analytical solutions of the relevant coupled thermoviscoelastic equations. In general, there is a difference between the isobaric specific heat c_{p} measured at constant isotropic pressure and the longitudinal specific heat c_{l} pertaining to mechanical boundary conditions that confine the associated expansion to be longitudinal. In the exact treatment of heat propagation, the heat-diffusion constant contains c_{l} rather than c_{p}. We show that the key parameter controlling the magnitude of the “cooling-by-heating“ effect is the relative difference between these two specific heats. For a typical glass-forming liquid, when the temperature at the surface is increased by 1 K, a lowering of the temperature at the sphere center of the order of 5 mK is expected if the experiment is performed at the glass transition. The cooling-by-heating effect is confirmed by measurements on a glucose sphere at the glass transition
The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation
In linear anisotropic elasticity, the elastic properties of a medium are
described by the fourth rank elasticity tensor C. The decomposition of C into a
partially symmetric tensor M and a partially antisymmetric tensors N is often
used in the literature. An alternative, less well-known decomposition, into the
completely symmetric part S of C plus the reminder A, turns out to be
irreducible under the 3-dimensional general linear group. We show that the
SA-decomposition is unique, irreducible, and preserves the symmetries of the
elasticity tensor. The MN-decomposition fails to have these desirable
properties and is such inferior from a physical point of view. Various
applications of the SA-decomposition are discussed: the Cauchy relations
(vanishing of A), the non-existence of elastic null Lagrangians, the
decomposition of the elastic energy and of the acoustic wave propagation. The
acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The
Cauchy part governs the longitudinal wave propagation. We provide explicit
examples of the effectiveness of the SA-decomposition. A complete class of
anisotropic media is proposed that allows pure polarizations in arbitrary
directions, similarly as in an isotropic medium.Comment: 1 figur
Investigation on microscale hygrothermal behavior of carbon nanotube‐reinforced polymer composite
LS-based and GL-based thermoelasticity in two dimensional bounded media: A Chebyshev collocation analysis
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