Solve the following problem:
Q: A thin-walled tube of 20-mm diameter passes hot fluid at a mean temperature of 45°C in an experimental flow loop. The tube is mounted horizontally in quiescent air at a temperature of 15°C. To satisfy the stringent temperature control requirements of the experiment, it was decided to wind thin electrical heating tape on the outer surface of the tube to prevent heat loss from the hot fluid to the ambient air.
(a) Neglecting radiation heat loss, calculate the heat flux q; that must be supplied by the electrical tape to ensure a uniform fluid temperature.
(b) Assuming the emissivity of the tape is 0.95 and the surroundings are also at 15°C, calculate the required heat flux.
(c) The heat loss may be reduced by wrapping the heating tape in a layer of insulation. For 85% magnesia insulation (k = 0.050 W/m · K) having a surface emissivity of 8 = 0.60, compute and plot the required heat flux q; as a function of insulation thickness in the range from 0 to 20 mm. For this range, compute and plot the convection and radiation heat rates per unit tube length as a function of insulation thickness.
