APPROXIMATE STUDY OF THE THERMAL SHOCK.
POLITECNICO DI TORINO (ITALY) ISTITUTO DI MECCANICA APPLICATA AERODINAMICA E GASDINAMICA
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The present method allows us to find a priori, simply and immediately, an approximate expression of the transient temperature distribution in infinite bodies with plane, cylindrical and spherical geometry. The temperature is given as a function of a penetration, whose variation with time is obtained by means of the integral method. The results, obtained for problems whose exact solution is known, prove the accuracy of the present method and allow its extension to still unsolved problems. Some technically interesting boundary conditions also nonlinear ones as in natural convection and black body radiation are examined. The non-linear boundary conditions make practically unsolvable the partial differential equation of the transient heat conduction, but do not involve any complication in the present method. This method always leads to a first order ordinary differential equation with separable variables. The second part is concerned with a method for the determination of temperature profiles in finite bodies slab, hollow cylinder and hollow sphere. The evolution of the temperature profile is well described by modifying the expressions used in the case of infinite bodies. Application of the proposed method is recommended by its optimal agreement with known exact results. Author