Analytical Heat Diffusion Theory by A. V. Luikov

By A. V. Luikov

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For each problem there exists a set of characteristic variables, in terms of which the problem should be investigated. A transition from the ordinary physical quantities to those of the complex kind, which are formed from the same quantities but in definite dimensionless combinations, gives important advantages. First, the number of variables decreases. Internal relations characterizing a process are more distinctly expressed in these quantities. 35 36 2. THEORY OF GENERALIZED VARIABLES In addition, the new variables also possess another advantage.

The surface temperature is constant during the whole heat transfer process. This may be achieved by special temperature control or with special conditions of heat transfer between the surroundings and the body surface (see the boundary condition of the third kind). 4) qt(r)=Ax). The simplest case of the boundary condition of the second kind is that of a constant heat flux

The definite combination ατ/Ρ of these quantities is of great importance. // is obvious that the expression ατ/Ρ represents a generalized variable which is usually referred to as the Fourier criterion or number ατ/Ρ = Fo. 12) Hence, it follows that the Fourier number has the meaning of generalized time. It may therefore be called as the homochronous number {homochronity means uniformity in time; if for two systems the relation P/a is constant, then for them homochronity obviously transforms into synchronity).

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