PARABOLIC PROFILE IN HEAT-CONDUCTION PROBLEMS. 1. SEMI-BOUNDED SPACE WITH A SURFACE OF CONSTANT TEMPERATURE

A new approach to the construction of constitutive integral relations, involving the introduction into consideration of local functions for a heat fl ow or a temperature determined directly from the differential heat-conduction equation, is proposed. With the use of this approach, new integral relations: the temperature-momentum integral of single modifi cation, the temperature-momentum integral of double modifi cation, the heat-fl ow integral, and the temperature-function integral, have been obtained. On the basis of these integrals as well as the integral method of heat balance and the refi ned integral method, different variants of the hybrid integral method realized with the use of manifold integral relations were investigated. In addition to the Langford norm, new error norms were introduced into consideration. The parabolic solutions obtained possess much better qualities compared to those of the analogous known solutions
   
Author:  V. A. Kot
Keywords:  temperature-disturbance front, integral method of heat balance, temperature-momentum integral, heat fl ow integral, temperature-function integral, hybrid integral method
Page:  1391