Open AccessIntegral methods of solving heat-conduction problems: a new concept (Dirichlet condition)
Author(s) -
В. А. Кот
Publication year - 2019
Publication title -
doklady nacionalʹnoj akademii nauk belarusi
Language(s) - English
Resource type - Journals
eISSN - 2524-2431
pISSN - 1561-8323
DOI - 10.29235/1561-8323-2019-63-4-485-495
Subject(s) - thermal conduction , mathematics , bounded function , quadratic equation , exponent , relativistic heat conduction , mathematical analysis , heat kernel , norm (philosophy) , heat equation , integral equation , function (biology) , parabola , heat transfer , heat flux , thermodynamics , physics , geometry , linguistics , philosophy , evolutionary biology , biology , political science , law
On the basic of consideration of the heat-conduction problem for a semi-bounded space with a temperature profile defined by a parabola with an exponent n, a new concept of construction of constitutive involves the introduction of a local function for a heat ow or for the temperature, with is determined from the heat-conduction equation. The approach proposed made it possible to obtain a number of new integral relation: an improved integral for the temperature momentum, an integral of a quadratic heat ow, and an integral of a quadratic temperature function. Two Schemes of optimizing the exponent n with the use of the error norms E1 and are proposed. As compared to the Langford norm, the indicated error norms made it possible to substantially increase the approximation accuracy of solutions of the problem posed.