Purified water, flowing at the rate of 45 kg/h is to be heated from 25°C to 75°C in a food processing plant before it is mixed with thickened tomato puree for sauce production. A thin-walled, 1.25 cm diameter, stainless steel tube is used, which is maintained at a constant surface temperature of 175°C by immersing it in a hot mineral bath. Calculate the length of tubing required and determine whether the forced convection inside the tube is fully developed or has entrance effects. Also, what is the frictional loss?
GIVEN
• Diameter of steel tube (Di)= 1.25 cm = 0.0125 m
• Cooling water inlet temperature (Tin)= 250C
• Cooling water flow rate ( m• )=45 kg/h=0.0125 kg/h
• Water outlet temperature (Tout)= 750C
• Surface temperature(Ts)=1750C
FIND
(a) Length of tubing required.
(b) whether the forced convection inside tube is fully developed or has entrance effects
PROPERTIES AND CONSTANTS
Density (?) = 988.1 kg/m3
Specific heat (cp) = 4178 J/(kg K)
Thermal conductivity (k) = 0.647 W/(m K)
Absolute viscosity (?) = 555.1 × 10–6 (Ns)/m2
Prandtl Number (Pr) = 3.55
The Reynold’s Number for given flow is
Thus the flowrate is in transition region. For the problem we can consider it as laminar flow regime.
For Ts=1750C, finding LMTD given in we have
Now, we have from
We have,
Thus from second correlation of we get
Thus from second correlation we have
Now, solving the problem iteratively we get
On further iterating we reach the final solution of L=1.70 m which is the required length of the pipe.
and c h= 316.35 W/(m2 K).
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