Question

In the final stages of production, a pharmaceutical is sterilized by heating it from 25 to 75C 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

Answer 1

Answer:

The answer is "$12682.267\ \ \frac{W}{m^2}$"

Explanation:

Calculating the mass flow rate of fluid:

$m= \rho AV$

   $= \rho \frac{\pi}{4} D^2\ V\\\\= 100 \times \frac{\pi}{4} \times (0.0127)^2\times 0.2\\\\=0.0253 \ \frac{kg}{s}$

Calculating the amount of heat transfer.

$q =m\timesC_p(T_{m,0}-T_{m,i})$

  $=0.0253 \times 4000 (75-25)\\\\=0.0253 \times 4000(50)\\\\=0.0253 \times 200,000 \\\\= 5060 \ W$

Calculating the required value for heat flux:

$q"=\frac{q}{A_s}$

   $=\frac{q}{\pi DL}\\\\= \frac{5060}{\pi \times 0.0127 \times 10}\\\\= 12682.267 \frac{W}{m^2}$