A computer code is being developed to analyze a 12.5-mm-diameter, cylindrical sensor used to deter- mine ambient air temperature. The sensor experiences free convection while positioned horizontally in quiescent air at Too = 27°C. For the temperature range from 30 to 80°C, derive an expression for the
(a) Neglecting radiation heat loss, calculate the heat flux qe" 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% mag- nesia insulation (k = 0.050 W/m · K) having a sur- face emissivity of s = 0.60, compute and plot the required heat flux qe" as a function of insulation thickness in the range from 0 to 20 mm. For this range, compute and plot the convection and radia- tion heat rates per unit tube length as a function of insulation thickness.