(Properties for type-R thermocouple are pure Pt) The type-R thermocouple is to m

Question

(Properties for type-R thermocouple are pure Pt) The type-R thermocouple is to measure a gas stream at 500 deg C and is initially at 20 deg C. The junction is formed by melting the ends of the two wires and forming a spherical bead which is 0.15 cm in diameter. Assume a convection heat transfer coefficient between the junction surface and the gas stream of 275 W/m2K.

a. How long whould it take for the junction to reach 99% of the gas stream temperature?

b. What possible design change can be done to reduce this time.

Explanation / Answer

Surface area A = 4*pi*r^2 = 4*3.14*(0.15/2)^2 = 0.07065 cm^2

Volume V = 4/3 *pi*r^3 = 4/3 *3.14 *(0.15/2)^3 = 0.001766 cm^3

For Pt, density rho = 21450 kg/m^3

For Pt, specific heat Cp = 130 J/kg-K

(T0 - T) / (T0 - T_amb) = e^(-hAt / rho*Cp*V)

a)

(20 - 0.99*500) / (20 - 500) = e^(-275*0.07065*10^-4 *t / (21450*130*0.001766*10^-6) )

Solving t = 0.0265 s

b)

Reduce the dia.

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