Mathematical model of a vacuum box electric furnace for online computation: A nonlinear ordinary differential equation model and experimental verification

Authors

1 Shahrood University of Technology

2 Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

Mathematical modeling plays an important role in designing and optimizing of heat transfer systems. Due to radiation heat transfer mode in a vacuum environment, the behavior of the system is very nonlinear. In this paper, a new nonlinear ODE model for a vacuum box heat chamber is developed which is suitable for online computation, and the validity of the model is investigated using an experimental set. A specific input is given to the both mathematical model and the experimental set. With some of this data, system parameters are extracted using the genetic algorithm. Then, the behavior of the mathematical model and the experimental system with the extracted parameters are compared using cycles that have not been used in optimization. The comparison shows the accuracy of the proposed mathematical model. Then, to examine the model more closely and to observe the effect of model parameters on system behavior, the Monte Carlo method was used to analyze the overall sensitivity of the model. For this purpose, Latin hypercube sampling and partial rank correlation coefficients have been used to rank the parameters. The results show that the thermal conductivity of insulators is the most important parameter affecting the behavior of the system.

Keywords

References

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Journal of Solid and Fluid Mechanics
Volume 12, Issue 1
March and April 2022
Pages 145-157

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