Question

The temperature of a flowing gas is to be measured with a thermocouple junction and wire stretched between two legs of a sting, a wind tunnel test fixture. The junc- tion is formed by butt-welding two wires of different material, as shown in the schematic. For wires of diame- ter D = 125 pm and a convection coefficient of h = 700 W/ m K, determine the minimum separation distance between the two legs of the sting, L=L +L, to ensure that the sting temperature does not influence the junction temperature and, in turn, invalidate the gas temperature measurement. Consider two different types of thermocouple junctions consisting of (i) copper and constantan wires and (ii) chromel and alumel wires. Evaluate the thermal conductivity of copper and con- stantan at T = 300 K. Use kom - 19 W/mK and ka= 29 W/m-K for the thermal conductivities of the chromel and alumel wires, respectively. Thermocouple junction Gas kr. Sting

Answer 1

he Too m Faom dable '- at T= 3ook : - k 401 w/m. k Copben . k= 23 w/m.k Coni fantan Given chnomel AJumel k 23 wmk infinitely log in Asume that the two wiie^ act V a ( Henc the Condition : . Ac L,4 6 L2 4 6 must be satis fied where 2 Ac = A (125x 1 X P (126x 1) 333 x 10

Fos Constantan wines'- Copber and Y2 L1 4 6 Oo135 L2 4 6 2 7oo x 3 33 x (õ6 Minimum Seþenatión distanca charomel and alumel asijs: . Fosi /2 ( 3 x 2-27x (53 4-24xi0 -3 4. 6 oro 393x16G ( L2 Y2 4 6 5-23x(03 Min Seperation ckstana!- L=J. 47 mm L L2