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ABSTRACT
In this paper, the geometry boundary of furnace inner wall is identified by an inverse method of three-step scheme without iteration. First, based on the concept of virtual area, a matrix equation of heat conduction problems is formed by the boundary element method (BEM). Then, the boundary conditions of discrete nodes on the virtual boundary can be obtained by the least-square error method. Finally, the geometry boundary of the furnace inner wall is identified by searching the isothermal curve in the domain, which is composed of the actual and virtual boundaries. Numerical results show that the present method has the high accuracy and the good adaptability for identifying a more complex shape. Moreover, the measurement error, the position, and the number of measurement points have very little impact on the results.
Nomenclature
| Q | = | heat flux vector |
| N | = | number of point |
| r | = | radius of circle |
| T | = | temperature vector |
| Γ | = | boundary of problem |
| Ω | = | domain of problem |
| ε | = | standard deviation |
| ω | = | random variable |
| ∇2 | = | Laplace operator |
| x | = | spatial coordinate point |
| (x1, x2) | = | Cartesian coordinate of node x |
| Subscripts | = | |
| a | = | actual |
| b | = | boundary |
| e | = | estimated |
| I | = | inner |
| m | = | measurement |
| o | = | outer |
| T | = | transposition of vector |
| v | = | virtual |
Nomenclature
| Q | = | heat flux vector |
| N | = | number of point |
| r | = | radius of circle |
| T | = | temperature vector |
| Γ | = | boundary of problem |
| Ω | = | domain of problem |
| ε | = | standard deviation |
| ω | = | random variable |
| ∇2 | = | Laplace operator |
| x | = | spatial coordinate point |
| (x1, x2) | = | Cartesian coordinate of node x |
| Subscripts | = | |
| a | = | actual |
| b | = | boundary |
| e | = | estimated |
| I | = | inner |
| m | = | measurement |
| o | = | outer |
| T | = | transposition of vector |
| v | = | virtual |