In a biomedical processing plant, a newly developed liquid drug or medication that leaves a mixing chamber at 20°C needs to be heated to 70°C in a thermal curing process. This is achieved by heating the liquid media at the rate of 10 kg/h in a thin metallic circular pipe with a 10 mm inner diameter that is electrically heated by wrapping it in resistance wire and insulation. If the tube surface is heated with a constant heat flux of 5,100 W/m2, calculate the length of tubing needed for this heat exchange device and the inner surface temperature of the pipe at its exit. Assume fully developed convection, and verify this assumption after calculating the length. The physical properties of the fluid media are considered as follows: Cp= 4.0 kJ/(kg K), k= 0.5 W/(m K), ?= 0.002 Ns/m2, and
?=1000 kg/m3
GIVEN
• Diameter of copper tube (Di)= 10 mm = 0.01 m
• Cooling water inlet temperature (Tin)= 200C
• Cooling water flow rate ( m• )=10 kg/hr = 2.78*10-3 kg/s
• Cooling water outlet temperature (Tout)= 700C
• Surface heat flux(q’’) = 5100 W/m2
FIND
(a) Length of tubing needed for this heat exchange device.
(b) Inner surface temperature of pipe at exit.
PROPERTIES AND CONSTANTS
Given, for the fluid
Density (?) = 1000 kg/m3
Specific heat (cp) = 4000 J/(kg K)
Thermal conductivity (k) = 0.5 W/(m K)
Absolute viscosity (?) = 0.002 (Ns)/m2
The Reynold’s Number for given flow is
Thus the flowrate is in laminar region.
Thus, for a fully developed flow at constant wall temperature Nu=4.364
Thus the average heat transfer coefficient between water and pipe is 218.5 W/(m2 K).
The rate of heat transfer to the cooling water is given by
Thus the length of device required for this heat exchanger is 3.47 m.
At, pipe exit for constant heat flux
Thus inner surface temperature of pipe at exit is 93.30C.
The length at which flow becomes fully developed is
Since, the pipe length is 3.47 m the fully developed flow assumption is correct.
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