High-precision numerical value method for solving interval heat convection diffusion problem

Abstract

The invention discloses a high-precision numerical value method for solving an interval heat convection diffusion problem. The high-precision numerical value method comprises the following steps: establishing a heat transfer control equation of the heat convection diffusion problem; introducing an interval variable to represent the uncertainty of an input parameter in a heat transfer model, and establishing an interval control equation of the heat convection diffusion problem; utilizing a Legendre polynomial expansion to carry out approximate representation on temperature response in the interval control equation; according to tensor product operation, determining a collocation point set in a high-dimension space; utilizing a finite element program to calculate the temperature response of all collocation points, establishing a linear equation set in regard to an expansion coefficient in a temperature response approximate expression, and adopting a least square method to solve; and on the basis of the smoothness of a polynomial function, determining an extreme point of the temperature response approximate expression, and obtaining the upper bound and the lower bound of interval temperature response. The high-precision numerical value method can systematically solve the heat convection diffusion problem with interval uncertainty parameters and effectively improves the calculation precision of the interval numerical value method.

Description

technical field [0001] The invention belongs to the field of mechanical engineering, and in particular relates to a high-precision numerical method for solving an interval heat convection diffusion problem. Background technique [0002] In nature and various production technology fields, heat transfer through fluid flow is an extremely common physical phenomenon. Especially in the manufacturing process of industrial equipment such as aerospace, energy and chemical industry, and precision products such as electronic devices, how to effectively realize heat transfer has become an important aspect of product design. Much of the existing research on thermal analysis is conducted for deterministic models without considering the uncertainties of the model input parameters. In actual engineering, due to the limitations of the manufacturing process, measurement errors, and cognitive limitations, the physical parameters of the structure, such as material properties, external loads, ...

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Problems solved by technology

[0004] The technical problem to be solved by the present invention is: to overcome the deficiencies existing in the prior art in solving the heat convection diffusion problem, fully consider the interval uncertain factors in the heat transfer problem, and propose a prediction The high-precision numerical calculation method of the temperature response interval variation range can systematically solve the problem of temperature field prediction with interval uncertain parameters, and further reduce the calculation cost of traditional sampling methods while ensuring calculation accuracy

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