Condición de Estabilidad Numérica para un Operador en Diferencias Finitas Utilizado para el Problema Inverso de Conducción de Calor

Fernando B. Sánchez Sarmiento

doi:10.70567/mc.v41i15.80

Authors

Fernando B. Sánchez Sarmiento Universidad Austral, Facultad de Ingeniería, Laboratorio de Investigación, Desarrollo y Transferencia de la Universidad Austral (LIDTUA). Pilar, Argentina.

DOI:

https://doi.org/10.70567/mc.v41i15.80

Keywords:

IHCP, Numerical stability, well-posed problems

Abstract

Inverse heat conduction problems are known as ill-posed problems. That is, the problem has no solution, its solution is not unique or the solution is not stable. To discuss this assumption, this work presents an analysis of the numerical stability of a finite difference operator used for the inverse problem. The analysis is carried out for the one-dimensional transient problem with symmetry of revolution in which we want to know the boundary condition (temperature or heat flow curve) when the temperature at the center of the solid is known. This problem corresponds to the ISO 9950 test used to determine the cooling characteristic of tempering industrial oils. It is concluded that the operators are conditionally stable. The existence and uniqueness of the solution was previously demonstrated. With this work, it is shown that this inverse heat conduction problem can be well posed, depending on the numerical parameters.

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