Heat regimes in a medium with non-linear transport processes and spatial heat production

On one approach to the definition of Burnett kinetic coefficients of dense charged matter

“…Note that other modifications of ν ei can be used depending on the nature of the dense charged system. So the approximation ln Λ = ln[1 + (3 2/Γ) 2 ] (Γ = e 2 (k B T r D ) −1 ) is useful for the non-ideal plasma region (T ∼ 10 4 -10 1) in comparison with the data of work [17] for the linear transport coefficients for the non-ideal charged matter shows that the inclusion of the Burnett coefficients corresponds to the appearance of the members with a small parameter at the highest derivatives in the system of conservation equations at moderate gradients of the hydro-dynamic variables.…”

“…Note that in this case the application of the description in the framework of continuous media in the study of the structure of the shock wave front is not always correct because in front of Kn there can be ∼ 1 (Kn is the Knudsen number, this parameter should be 1 for the continuum description). Therefore a detailed comparison was provided between traditional models and the Burnett model of description of heat and mass transfer under the conditions of fuel element of a Gas Core Nuclear Reactor (GCNR) [11,17], where a dense matter flow is realized at moderate gradients of the hydro-dynamic variables and there is a heat source. This comparison shows the qualitative difference between of the inclusion of the Burnett approach in modeling, when the gradients of the hydro-dynamic parameters are very large ( [13] with the gradients in the front of the shock wave) and when the gradients of the hydro-dynamical variables are moderate (then the parameter is small at the highest derivative in the conservation equations as for the modelling of heat and mass transfer in the fuel element of GCNR [11,17]).…”

“…Therefore a detailed comparison was provided between traditional models and the Burnett model of description of heat and mass transfer under the conditions of fuel element of a Gas Core Nuclear Reactor (GCNR) [11,17], where a dense matter flow is realized at moderate gradients of the hydro-dynamic variables and there is a heat source. This comparison shows the qualitative difference between of the inclusion of the Burnett approach in modeling, when the gradients of the hydro-dynamic parameters are very large ( [13] with the gradients in the front of the shock wave) and when the gradients of the hydro-dynamical variables are moderate (then the parameter is small at the highest derivative in the conservation equations as for the modelling of heat and mass transfer in the fuel element of GCNR [11,17]). To determine this difference and the need of using the Burnett approximation, the stability of the traditional model (in the framework of linear transport laws), describing heat and mass transfer, was studied in the special case of a fuel cell of a GCNR upon the inclusion of Burnett transport processes.…”