In an experiment, the temperature of a hot air stream is to be measured by a thermocouple with a spherical junction. Due to the nature of this experiment, the response time of the thermocouple to register 99 percent of the initial temperature difference must be within 5s. The properties of the thermocouple junction are k = 35 W/m · K, ρ = 8500 kg/m³, and c_p = 320 J/kg · K. The hot air has a free stream velocity and temperature of 3 m/s and 140°C, respectively. If the initial temperature of the thermocouple junction is 20°C, determine the thermocouple junction diameter that would satisfy the required response time of 5s. Use the lumped system analysis to determine the time required for the thermocouple to register 99 percent of the initial temperature difference.

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Air flow, V Th 001 Thermocouple junction D