Ak. Belyaev et Va. Palmov, THERMODYNAMIC DERIVATION OF THE HEAT-CONDUCTION EQUATION AND THE DYNAMIC BOUNDARY-VALUE PROBLEM FOR THERMOELASTIC MATERIALS AND FLUIDS, Acta mechanica, 114(1-4), 1996, pp. 27-37
It is shown that the dynamic boundary value problem and the heat condu
ction equation for some simple materials are derivable from the first
and second laws of thermodynamics. The dynamic boundary value problem,
the heat conduction equation and two variational principles are deriv
ed for thermoelastic materials with time-dependent properties, for the
case when the volume and surface forces are not ''dead'', and when th
e free energy of the material depends upon the temperature. It is also
shown that the conventional form of the heat conduction equation for
geometrically nonlinear anisotropic elastic media does not satisfy the
principle of material frame indifference. A new form of the heat cond
uction equation is offered. The heat conduction equation for the Navie
r-Stokes fluid and the dynamic boundary value problem for an elastic f
luid are obtained. The elastic fluid is proved to be the only simple f
luid without ''memory''.