By A. V. Luikov
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Extra resources for Analytical Heat Diffusion Theory
Two types of dimensionless variables are therefore distinguished. ) is the simplest type of a variable. 1 The group ατ//2 may be designated as a criterion or a number depending on the nature of τ. When τ is a current time the group is a dimensionless number. When τ is a known fixed quantity (for example, the period of temperature oscillation) the group is referred to as a criterion. 42 2. THEORY OF GENERALIZED VARIABLES If a parameter corresponding to a certain variable is not given, then the complex, consisting of a variable and some different parameters, is constructed, for example ατ/Ι2 where I2/a is a complex of different parameters having the dimension of time.
1) In a number of problems, where f(k9 y, z) is a known function, a uniform temperature distribution is assumed at the initial moment; then t(x, y, z, 0) = t0 = const. 3) ts(r)=f(r) where ί8(τ) is the temperature at the body surface. , 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).
Biot criterion Bi = HR = R α/λ Kirpichev criterion Ki = <7const^M('a — 'o) Kondratiev criterion Kn = R2(m/a) Predvoditelev criterion Pd = (dOJdFo)max Pomerantsev criterion Po = WR2ß(ta — t0) Fourier criterion Fo' = apllnR2 where p = period of temperature oscillation Numbers Nusselt number Nu = al/λ Fourier number Fo = ατ/R2 Thus, the solution of a problem should be presented in the form of dimensionless quantities which define unknown dimensionless variables as functions of independent dimensionless variables with similarity criteria 44 2.
Analytical Heat Diffusion Theory by A. V. Luikov