A Simple Quasi-2D Numerical Model of a Thermogage Furnace

A simple quasi-2D model for the temperature distribution in a graphite tube furnace is presented. The model is used to estimate the temperature gradients in the furnace at temperatures above which contact sensors can be used, and to assist in the redesign of the furnace heater element to improve the temperature gradients. The Thermogage graphite tube furnace is commonly used in many NMIs as a blackbody source for radiation thermometer calibration and as a spectral irradiance standard. Although the design is robust, easy to operate and can change temperature rapidly, it is limited by its effective emissivity of typically 99.5–99.8%. At NMIA, the temperature gradient along the tube is assessed using thermocouples up to about 1,500°C, and the blackbody emissivity is calculated from this. However, at higher operating temperatures (up to 2,900°C), it is impractical to measure the gradient, and we propose to numerically model the temperature distributions used to calculate emissivity. In another paper at this conference, the model is used to design an optimized heater tube with improved temperature gradients. In the model presented here, the 2-D temperature distribution is simplified to separate the axial and radial temperature distributions within the heater tube and the surrounding insulation. Literature data for the temperature dependence of the electrical and thermal conductivities of the graphite tube were coupled to models for the thermal conductivity of the felt insulation, particularly including the effects of allowing for a gas mixture in the insulation. Experimental measurements of the temperature profile up to 1,500°C and radial heat fluxes up to 2,200°C were compared to the theoretical predictions of the model and good agreement was obtained.