A thermocouple with a spherical junction diameter of 1 mm is used for measuring the temperature of a hydrogen gas stream. The properties of the thermocouple junction are k = 35 W/m · K, ρ = 8500 kg/m³, and c_p = 320 J/kg · K. The hydrogen gas, behaving as an ideal gas at 1 atm, has a free stream temperature of 2008C. If the initial temperature of the thermocouple junction is 10°C, evaluate the time for the thermocouple to register 99 percent of the initial temperature difference at different free stream velocities of the hydrogen gas. Using the EES (or other) software, perform the evaluation by varying the free stream velocity from 1 to 100 m/s. Then, plot the thermocouple response time and the convection heat transfer coefficient as a function of free stream velocity. 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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H₂ gas flow, V To, h 007 Thermocouple junction -D = 1 mm