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Simultaneous estimation of the emissivity and the temperature-dependent thermal conductivity and specific heat in a semitransparent plane layer by an inverse method

Zmywaczyk J.

Archives of Thermodynamics

2006

Vol. 27, no. 3

39-62

A model of transient ID conduction-radiation heat transfer in absorbing, emitting and isotropically scattering grey medium with boundary conditions of the third kind for temperature has been considered in this paper. It has been assumed that boundaries of the plane layer of thickness L were of diffusive character. To solve the boundary-value problem a finite difference method (FDM) together with a two-flux method (TFM) based on the Schuster-Schwarzschild approximation was used. In the inverse formulation of the problem it has been accepted as the unknown quantities the total panchromatic hemispherical emissivity [epsilon][1] of the sample surface exposed to external incident radiation and the temperature-dependent thermal conductivity k(T) and specific heat c[p](T) of the sample material. The coefficient inverse heat transfer problem (CIHTP) was solved iteratively using the Levenberg-Marquardt algorithm to find a minimum of a mean square functional J involving residuals between the measured and calculated temperatures. It has been found that the final time of measurements t[f] should be correlated with the disturbance magnitude ZAB so as to reduce uncertainty of the estimated parameters.

Reduction of an effective thermal conductivity in the aspect of two flux model for absorbing, emitting and scattering media

Koniorczyk P., Zmywaczyk J., Kowalski M.

Archives of Thermodynamics

2004

Vol. 25, no. 4

19-29

The present paper deals with numerical analysis of the steadystate problem of the 'thickness effect curve' in semitransparent media, where simultaneos radiation and conduction heat transfer takes place. The analysis is conducted with the aid of a Two Flux Method (TFM) for absorbing, emitting and scattering media. Results are compared with the exact solution obtained fom a 1-D coupled radiation and conduction heat transfer model (RTE) in an emitting, absorbing as well as scattering medium.