On simulation of heat transmission in dynamically deformed media | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 6 > №3 / 2000 / Pages: 436-444

On simulation of heat transmission in dynamically deformed media

, ,


We simulate the processes of dynamical deformation of linear media followed by heat transmission. We use the general assumptions on kinematic constraints and employ the variational formalism. For a medium with nonholonomic constraints (irreversible processes), we determine a general structure of nonholonomic constraints and derive a mathematical model of the medium in the form of variational equations; at that, we derive the system of governing equations and the system of equations of motion and heat transfer. For one particular case of nonholonomic constraints, we provide an identification of constants for the medium’s model such that these constants can be determined via the known physical constants of the material (a modulus of elasticity, a density, a speed of sound, etc.). We demonstrate that for the physically linear media, when it is possible to assume that the general displacements are continuous, the process of heat transmission becomes of inertial type. Hence, we simulate a new type of resonance temperature effects. In order to derive the model, we apply the Sedov variational approach, the variants of which were efficiently used when simulating the holonomic and nonholonomic media by L.I. Sedov and his followers.