A small device is used to measure the surface temperature of an object. A thermocouple bead of diameter \(D=120 \mu \mathrm{m}\) is positioned a distance \(z=100 \mu \mathrm{m}\) from the surface of interest. The two thermocouple wires, each of diameter \(d=25 \mu \mathrm{m}\) and length \(L=300 \mu \mathrm{m}\), are held by a large manipulator that is at a temperature of \(T_{m}=23^{\circ} \mathrm{C}\).

If the thermocouple registers a temperature of \(T_{\text {tc }}=29^{\circ} \mathrm{C}\), what is the surface temperature? The thermal conductivities of the chromel and alumel thermocouple wires are \(k_{\mathrm{Ch}}=19 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and \(k_{\mathrm{Al}}=29 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), respectively. You may neglect radiation and convection effects.

Transcribed Image Text:

Air Manipulator, T d L D. T Thermocouple bead T