In the final stages of production, a pharmaceutical is sterilized by heating it from 25 to 75 degree c as it moves at 0.2 m/s through a straight thin-walled stainless steel tube of 12.7-mm diameter. a uniform heat flux is maintained by an electric resistance heater wrapped around the outer surface of the tube. if the tube is 10 m long, what is the required heat flux? if fluid enters the tube with a fully developed velocity profile and a uniform temperature profile. what is the surface temperature at the tube exit and at a distance of 0.5 m from the entrance? fluid properties may be approximated as p = 1000 kg/m^3, c = 4000 j/kg. k. m = 2 x 10^-3 kg/s. m, k = 0.8 w/m. k, and pr = 10.