### Exact Analytical Solutions in Closed Recurrent form for the Non-Stationary Linear Inverse Heat Conduction Problem for Bodies of One-Dimensional Geometry with Boundary Conditions on One And Two Surfaces

#### Lobanov Igor Evgenievich 1*

1 Technical Sciences, Moscow Aviation Institute, Moscow, Russia

### Abstract

In this paper, we obtained exact analytical solutions for the non-stationary linear inverse heat conduction problem for bodies of one-dimensional geometry with boundary conditions on one surface, as well as on two surfaces for a plane body, a hollow cylinder, and a hollow sphere, obtained in a closed recurrent form. The recurrent form of the solution of the non-stationary linear inverse heat conduction problem for bodies of one-dimensional geometry with boundary conditions on one surface, as well as on two surfaces for a plane body, hollow cylinders and spheres, presented in the article is a solution in a closed form from a single position, which is not always perhaps explicitly.

### Keywords

Thermal Conductivity, Analytical, Non-stationary, Linear, One-dimensional, Inverse Problem, Surface, Border Conditions, Unilateral, Bilateral, Recurrent , Flat, Spherical, Cylindrical

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