Solve the following:
Q: A long constantan wire of 1-mm diameter is butt welded to the surface of a large copper block, forming a thermo-couple junction. The wire behaves as a fin, permitting heat to flow from the surface, thereby depressing the sensing junction temperature Tj below that of the block To.
(a) If the wire is in air at 25°C with a convection coefficient of 10W/m2 · K, estimate the measurement error (Tj - To) for the thermocouple when the block is at 125°C.
(b) For convection coefficients of 5, 10, and 25 W/m2 · K, plot the measurement error as a function of the thermal conductivity of the block material over the range 15 to 400W/m · K. Under what circumstances is it advantageous to use smaller diameter wire?
