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Theory of space-time dissipative elasticity and scale effects

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Lurie S. A., Belov P. A.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
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2013
|
tom 2
166-178
EN
In this article a model of irreversible dynamic thermoelasticity of an ideal continuua is constructed from an elasticity theory of asymmetrical, transversely isotropic in time direction, dissipative defectless 4D-continuum. In the model the fourth component of the 4D-displacement vector is locally irregular time R. The kinematic model comprises 3D-tensor of distortion, 3Dvector of velocity, 3D-gradient vector of local irregular time and entropy in unified tensor object which is an asymmetrical 4D-tensor of distortion of second rank. Consequently, the force model comprises 3D-tensor of stress, 3D-vector of impulses, 3D-vector of heat flow and temperature in unified tensor object which is an asymmetrical 4D-stress tensor of second rank. Hooke’s law equations have been formulated which connect components of asymmetrical 4D-tensors of stress and distortion. Physical interpretations have been given to the tensors’ components of thermomechanical properties of formulated continuum. Therefore, the article formulate an irreversible dynamic thermoelasticity covariant model of ideal (defectless) continua in which basic kinematic and force variables are components of unified tensor objects and theory is represented by 4D-vector equation. Sedov’s equation has been derived and resulted into Euler’s equations, space projections of which determine motion equations, and time projection determines heat conductivity equation as well as the whole spectrum of the space-time boundary value problems. The proposed theory allows one to describe the scale effects in the thermal processes and opens prospects for studying the scale effects of the coupled dynamic thermoelasticity and its nanoscience applications. A temperature-scale refinement can also broaden the range of applicability of the law of heat conduction in solids to allow for design of small-sized components, devices and nano-systems.
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Non-Fourier heat removal from hot nanosystems through graphene layer

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Sellitto A., Alvarez F. X.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
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2012
|
tom 1
38-47
EN
Nonlocal effects on heat transport beyond a simple Fourier description are analyzed in a thermodynamical model. In the particular case of hot nanosystems cooled through a graphene layer, it is shown that these effects may increase in a ten percent the amount of removed heat, as compared with classical predictions based on the Fourier law.
3
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Mesoscopic description of boundary effects in nanoscale heat transport

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Àlvarez F. X., Cimmelli V. A., Jou D., Sellitto A.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
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2012
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tom 1
112-142
EN
We review some of the most important phenomena due to the phonon-wall collisions in nonlocal heat transport in nanosystems, and show how they may be described through certain slip boundary conditions in phonon hydrodynamics. Heat conduction in nanowires of different cross sections and in thin layers is analyzed, and the dependence of the thermal conductivity on the geometry, as well as on the roughness is pointed out. We also analyze the effects of the roughness of the surface of the pores on the thermal conductivity of porous silicon. Thermoelectric effects are considered as well. In memory of Professor Carlo Cercignani
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