SELF-SIMILAR HEAT WAVES FROM A CONCENTRATED OR SPATIAL SOURCE IN AN ENVIRONMENT WITH NON-HOMOGENEOUS THERMAL-PHYSICAL PARAMETERS
B. P. Tikhomirov
VANT. Ser.: Mat. Mod. Fiz. Proc 2010. Вып.2. С. 40-50.
The problems about an instantaneous concentrated source in an environment with distributed physical parameters, as well as the problem about a special spatial source are considered. The issue of joining known self-similar solutions on the plane interface of environments with different thermal-physical characteristics is discussed in the paper. The obtained conditions of solutions` agreement allow us to estimate the part of the released energy to the left and to the right from the interface surface.
In the problem about a spatial source the combustion function, proportional to the energy and inversely proportional to the time, was taken as the source. Note, that this problem includes the problem of instantaneous concentrated source as a particular case.
The precise solution was built with account for the radiation energy density for setting the problems with planar, cylindrical and spherical symmetries and the mentioned combustion function.
The examples of model problems for testing the calculation techniques of non-linear thermal conductivity in non-homogeneous environment without account and with account for the combustion function are given in the paper.Keywords: concentrated and spatial sources, thermal wave, interface, matching of self-similar solutions, model test problems.
|
English
