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International Journal of Heat and mass Transfer, Vol. 54 (2011) 2602-2608.
M. J. Peet , H. S. Hasan and H. K. D. H. Bhadeshia1
Published in the International Journal of Heat and Mass Transfer Vol. 54 (2011) page 2602-2608 doi:10.1016/j.ijheatmasstransfer.2011.01.025
Abstract A model of thermal conductivity as a function of temperature and steel composition has been produced using a neural network technique based upon a Bayesian statistics framework. The model allows the estimation of conductivity for heat transfer problems, along with the appropriate uncertainty. The performance of the model is demonstrated by making predictions of previous experimental results which were not included in the process which leads to the creation of the model. Keywords: Thermal Conductivity, Steel, Bayes, Neural Network, Heat treatment, Mathematical models, Physical properties, Temperature, Commercial alloys, Matthiessen’s rule
Prediction of thermal conductivity of 2steel 1∗
1
Introduction
There are many situations in design or in process modelling where it would be useful to know the thermal conductivity of the steel being used, and how it would change as a function of temperature. With the lack of any quantitative model the usual recourse is to look for a similar composition contained in published tables of data [1, 2, 3]. However, in the absence of a quantitative model it is not possible to assess the validity of this procedure. Thermal conductivity controls the magnitude of the temperature gradients which occur in components during manufacture and use. In structural components subjected to thermal cycling, these gradients lead to thermal stresses. During heat treatment the conductivity limits the size of components that can be produced with the desired microstructure, since transformation depends on cooling rate and temperature. A suitable model of thermal conductivity should help to improve the design of steels and understanding of heat treatment, solidification
M. J. Peet , H. S. Hasan and H. K. D. H. Bhadeshia1
Published in the International Journal of Heat and Mass Transfer Vol. 54 (2011) page 2602-2608 doi:10.1016/j.ijheatmasstransfer.2011.01.025
Abstract A model of thermal conductivity as a function of temperature and steel composition has been produced using a neural network technique based upon a Bayesian statistics framework. The model allows the estimation of conductivity for heat transfer problems, along with the appropriate uncertainty. The performance of the model is demonstrated by making predictions of previous experimental results which were not included in the process which leads to the creation of the model. Keywords: Thermal Conductivity, Steel, Bayes, Neural Network, Heat treatment, Mathematical models, Physical properties, Temperature, Commercial alloys, Matthiessen’s rule
Prediction of thermal conductivity of 2steel 1∗
1
Introduction
There are many situations in design or in process modelling where it would be useful to know the thermal conductivity of the steel being used, and how it would change as a function of temperature. With the lack of any quantitative model the usual recourse is to look for a similar composition contained in published tables of data [1, 2, 3]. However, in the absence of a quantitative model it is not possible to assess the validity of this procedure. Thermal conductivity controls the magnitude of the temperature gradients which occur in components during manufacture and use. In structural components subjected to thermal cycling, these gradients lead to thermal stresses. During heat treatment the conductivity limits the size of components that can be produced with the desired microstructure, since transformation depends on cooling rate and temperature. A suitable model of thermal conductivity should help to improve the design of steels and understanding of heat treatment, solidification
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