An approximate modeling of 1d transient heat transfer in a gray participating medium

Transient combined radiative and conductive heat transfer is very crucial for glass thermoforming industry. Real time control of the process is presently under consideration for better glass manufacture with less defects. Solution of transient combined radiative and conductive heat transfer in glass requires the solution of radiative transfer equation, which usually takes hours to converge using latest finite volume codes. This paper formulates a polynomial approximation of the radiative part for real time applications. A state space model of the transient conductive and radiative heat transfer is presented. All the states of the model is shown to be observable with measurement only at one surface. The method is faster and takes few seconds to reach steady state with little deviation from the finite element solution. Formulation of the discretization is shown for one dimensional gray medium. Numerical simulation is presented for a case close to glass thermoforming with different radiative sources. A comparison with finite element solutions is also presented and it demonstrates the efficiency of this numerical tool.