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

The required heat flux = 12682.268 W/m²

Step-by-step 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 (\pi)/(4)D^2V`

`m = 1000 * (\pi)/(4) * ( 0.0127)^2 * 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`

`q`

`q`

q" = 12682.268 W/m²

The required heat flux = 12682.268 W/m²