Nonstationary heating of a fixed granular mass

Application of an equivalent equation to description of heat- and mass-exchange processes determined by differential equations in the domain with a moving boundary

“…We initially (and this is principal) transform operators rather than independent variables. In so doing, we can say, referring to the results of [6,7], that the proposed elliptic equations with fixed boundaries of the domain of their definition describe the process with the same degree of accuracy as the initial system of equations (1)-(2) whose domain of solutions contains a moving boundary.…”

“…A distinctive feature of this investigation is that we are dealing with a disperse (two-component) system the basic heat and mass-transfer equations in which, depending on the medium's structure, have been formulated thus far on their own special principles and often have their own form in different space-time domains [10]. Such a situation, as has been shown in [6,7,10], enables one to change equation types (parabolic, hyperbolic, elliptic), with the accuracy of description of the process being preserved. The equation type itself is often a relative notion [22].…”

“…The equation type itself is often a relative notion [22]. This circumstance differentiates the problems considered here from the classical ones [12][13][14][15][16][17][18][19][20][21] for which the methods of the present work (as [6,7,10]) should be interpreted as those approximate with certain specific properties. In the classical variants, the moving boundary is present as an initially given condition in the boundary-value problem (replacements of variables, which "arrest" boundary motion (see, e.g., [14]), with a possible change in the form of equations are not taken into account).…”

“…It is stated in [6,7] that further terms in expansion (4) introduce only certain refinements of no fundamental importance into the solution of Eq. (5).…”

“…For this purpose we must replace the sought function C → C − C 0 [4]. Following [6,7], we construct the EE, formally expanding relation (2) in an operator series…”