PARABOLIC PROFILE IN HEAT-CONDUCTION PROBLEMS. 3. SEMI-BOUNDED SPACE WITH A DEFINITE EXTERNAL HEAT FLOW

Some approaches to the optimization of the exponent n of the parabolic temperature profi le for a semi-bounded space with the second-kind boundary condition, implying the prescription of an external heat fl ow, are considered. An optimization scheme involving the minimization of a new error norm estimating the absolute value of a temperature deviation, more effi cient than the scheme of T. Myers with minimization of the Langford norm, as well as new hybrid integral methods are proposed. With the use of these methods, parabolic solutions have been obtained on the basis of the temperature momentum integral in different modifi cations and the heat-fl ow momentum integral, and these solutions defi ne the surface temperature with a very high accuracy. As an illustrative example, the problem on the heat conduction of a semi-bounded space with a defi nite pulsating heat fl ow at its surface, whose time change is defi ned by a quadratic parabola, was considered. The approximation errors of the parabolic solutions obtained using the hybrid integral methods proposed comprise hundredths and thousandths of a percent, and they are smaller by one to two orders of magnitude than the errors of the analogous solutions obtained by the known heat balance integral method and refi ned integral method, involving the optimization of the exponent of a parabolic temperature profi le on the basis of minimization of the Langford norm, and by the combined integral method
   
Author:  V. A. Kot
Keywords:  temperature-disturbance front, temperature momentum integral, heat-fl ow momentum integral, heat balance integral method, hybrid integral method
Page:  986