Refractories and Industrial Ceramics Vol. 42, Nos.3–4, 2001 UDC 536.2.023 V. V. Kolomeitsev, E. F. Kolomeitseva, O. V. Kolomeitseva, and S. A. Suvorov Translated from Ogneupory i Tekhnicheskaya Keramika, No. 4, pp. 35 – 36, April, 2001. The relation between a spatio-temporal change of tem- The following relations hold for Eq. (4): perature in a three-dimensional nonstationary temperature (,xy, z,t) vT (xy , , z,t) “field” is derived from the First Law of Thermodynamics 0 (5) 2 2 (,xy, z,t) v T (xy , , z, t ). and the Biot – Fourier law and is expressed by a differential equation of heat conduction, which, in the absence of inter- One will note that the physical meaning of the wave nal heat sources, takes the form function, as implied by Eq. (4), is the rate of change of the T 1 temperature field. div() grad T (1) Combining Eqs. (2), (3), and (4) gives tc 11 T T 0. (6) for = f (T ) and c = const, or a t u t = a T, (2) Differential equation (6) contains only derivatives of temperature with respect to time; its solution we represent in
Refractories and Industrial Ceramics – Springer Journals
Published: Oct 9, 2004
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