The influence of the temperature dependence of thermal conductivity and emissivity on the temperature field in a photoacoustic cell with two-layer samples

Abstract

Based on the system of nonlinear equations of thermal conductivity for stationary temperatures of the gas layer, substrate, the first and the second layers of samples with a volumetric optical absorption coefficient, the features of the formation of a stationary temperature field in the photoacoustic cell have been investigated. Analytical expressions for the temperature field of the gas layer, two layers of the sample and the substrate, as well as a system of interrelated nonlinear algebraic equations for the steady-state temperature of the irradiated and rear surfaces of the first layer and the boundary between the second layer β and the substrate have been obtained. The numerical solution of the system of nonlinear algebraic equations shows that with the increase of the absorption coefficient of the corresponding layer and the gradual transition from the condition β_il_i <1 ( li is the layer thickness) to the condition β_il_i ≥1, heating increases significantly, and the dependences of the characteristic temperatures on the intensity of the incident beam I0 become nonlinear. It is shown that the sign of the thermal coefficient of the temperature dependence of emissivity significantly affects the dependences of the temperature increment of the surfaces of all layers on the intensity of the incident beam.