On the theory of hydrodynamic thermal explosion. (English. Russian original) Zbl 0754.76023

Sov. Phys., Dokl. 36, No. 2, 122-124 (1991); translation from Dokl. Akad. Nauk SSSR 316, No. 4, 856-860 (1991).
(From the introduction.) In this paper, the authors investigate the phenomenon of a hydrodynamic thermal explosion. It is shown that the phenomenon does not necessarily occur, since the unsteady thermal process leading to a thermal explosion is described by an equation in which the source terms have the same form as in the steady case. In the case of motion of the liquid the unsteady process is described by a system of two nonlinear equations in which the source terms depend essentially on the unsteady flow velocity profile and, therefore, it is possible that in unsteady flow a strong enough dissipative heat source leading to a hydrodynamic thermal explosion may not occur. This question is resolved by the solution, discussed by us below, of the unsteady problem for supercritical values of a parameter \(\kappa\).


76D99 Incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)