Radiation-compensating thermocouple pair. The temperature of a flame is critical in almost any application. An affordable method is of course using a thermometer. Some thermometers can work under oxidizing environments even when temperatures are well above 1000 C. An example is the K-type thermocouple. At such temperatures, however, any thermometer would start glowing red-hot, which means that it loses a significant amount of heat by radiation. One way to compensate for radiation losses is to use two thermocouples with different wire diameters, as below.

By making reasonable assumptions for a pair of thermocouples of the same type engulfed in a flat laminar diffusion flame, develop an expression for the gas temperature in the flame. The expression will be a function of the temperatures read by the thermocouples, wire diameters and ambient temperature.