By A. V. Luikov
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Extra info for Analytical Heat Diffusion Theory
25) The function Gz represents the temperature distribution in an infinite plate (0 < χ < /) at the moment τ if the temperature at the initial moment is equal to zero and at this moment the quantity of heat Q = bey is evolved instantaneously at the point ξ. The application of the method of sources to the solution of several concrete problems will be shown later. 3 Integral Transform Methods a. Operational Methods. Solutions obtained by classical methods are not always convenient for calculations.
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. A prescribed value of a complex of quantities may be obtained as a result of an infinite number of various combinations of the physical quantities making up the complex. Consequently, not just a single set but an infinite set of initial physical quantities satisfies the fixed values of the new variables.
The First Calculation Method. Crossing the surface element dS during the time dx9 the amount of heat transfer is equal to -À(dt/dn)dSdT. 1) should be integrated over the whole surface S and time interval AT: AQ=- Γ2 J τι f J (S) l(dt\dn) dS dT. 2) then simplifies to AQ = Q2 - Ôi = - λΞ Γ 2 (dt/dn) άτ. 3) 32 1. PHYSICAL FUNDAMENTALS OF HEAT TRANSFER b. The Second Calculation Method. The surface element dS during the time dx receives from the surrounding medium the amount of heat a(ta-t8)dSdx. 4) To determine the total amount AQ received by the whole surface of a body, Eq.