Chapter 3, Problem 3.114P

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 junction is formed by butt-welding two wires of different material, as shown in the schematic. For wires of diameter $D=125\text{μm}$ and a convection coefficient of $h=700{\text{W/m}}^{\text{2}}\cdot \text{K,}$ determine the minimum separationdistance between the two legs of the sting, $L=L_1+L_2,$ 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 constantan at $T=300\text{K}\text{.}$ Use $k_{\text{Ch}}=19\text{W/m}\cdot \text{K}$ and $k_{\text{A1}}=29\text{W/m}\cdot \text{K}$ for the thermal conductivities of the chromel and alumel wires. respectively.