Question

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

Answer 1

Answer:

The required heat flux = 12682.268 W/m²

Explanation:

From the given information:

The initial = 25°C

The final = 75°C

The volume of the fluid = 0.2 m/s

The diameter of the steel tube = 12.7 mm = 0.0127 m

The fluid properties for density $\rho$ = 1000 kg/m³

The mass flow rate of the fluid can be calculated as:

$m = pAV$

$m = \rho \dfrac{\pi}{4}D^2V$

$m = 1000 \times \dfrac{\pi}{4} \times ( 0.0127)^2 \times 0.2$

$m = 0.0253 \ kg/s$

To estimate the amount of the heat by using the expression:

$q = mc_p(T_{final}-T_{initial})$

q = 0.0253 × 4000(75-25)

q = 101.2 (50)

q = 5060 W

Finally, the required heat of the flux is determined by using the formula:

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

$q" = \dfrac{q}{\pi D L}$

$q" = \dfrac{5060}{\pi \times 0.0127 \times 10}$

q" =  12682.268 W/m²

The required heat flux = 12682.268 W/m²