Analysis of thermal regimes in media with bulk heat release

Nonlinear Transport Processes in Non‐Ideal Media

“…These comparisons can determine the "stability" of traditional model of heat and mass transfer under the described complication of transport processes modelling. Numerical analysis of traditional and Burnett models was provided using computer code for multiparameter nonlinear investigation (see [14] for detail) based on singularity theory. Codes for solving of the initial and state problems for the systems of equations (6) were also used to analyze the models.…”

“…Since the equation (9) is degenerated at k 1 = 0 and k 3 = 0, so there are four quadrants at the map plane (k 1 , k 3 ) to be investigated separately. The investigation should be provided by numerical and analytical methods (Tikhonov criterion [14], see references therein) because it is difficult to realize numerically limits k 1 → ±0 and k 3 → ±0 in different quadrants. Analytical investigation will show in particular that solutions of (9) at k 3 → 0 converge or don't converge to solutions of (9) at k 3 = 0 (that is "soft" or "rough" scenario is realized at turning on of the parameter k 3 ).…”

“…Thermo-physical constants of this plasma in the system of conservation equations have a number of peculiarities (see, e.g. [2,14] and references therein).…”

“…The dimensionless coefficients k 2 − k 4 can be small compared with k 1 for our case with moderate gradients of the hydrodynamic parameters, since in this case the contribution of Burnett coefficients in corresponding currents is small compared to the contribution of the ordinary transport coefficients. Therefore, in the next section of the article should also explore the solution (9) with a small parameter at the highest derivative using the Tikhonov criterion [14]. Note that the third order of equation (9) is the consequence of the definition of the impulse current through nonlinear Burnett coefficients.…”

“…In this case www.cpp-journal.org a path-following method was used to get bifurcation diagrams and maps. The method is applied to a complex hierarchy of systems of equations which is constructed in a framework of singularity theory [14]. Let k 4 = 0 (K 1 = −u (0)α 1 = 0) for simplicity below.…”