In an experiment, the temperature of a hot gas 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 42 percent of the initial temperature difference must be within 5 s. The properties of the thermocouple junction are k = 35 W/m•K, rho = 8500 kg/m3, and cp = 320 J/kg•K. If the heat transfer coefficient between the thermocouple junction and the gas is 250 W/m2•K, determine the diameter of the junction.

The diameter of the junction is 5.06 mm

Explanation:

Given that:

ρ = 8500 kg/m³

k = 35 W/m.k

the heat transfer coefficient between the thermocouple junction and the gas  =

The initial temperature difference (t₀) = 42% = 0.42

t = 5 s

Substituting values:

The diameter of the junction is 5.06 mm

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