Heat transfer course
Topics to prepare for the next seminar on chapter 8:
1. For laminar flow in tubes we define a hydraulic entrance length. Compare this length to
the length required for flow over a flat plate to develop a boundary layer equal to half the
pipe diameter. Comments?
2. Compare hydraulic and thermal entrance lengths for tube flow of different fluids.
Comments? Implications for heat exchanger design?
3. Reducing tube diameter in heat exchangers is a way of increasing the heat transfer
coefficients. However, pressure drop will also increase. This may be compensated by
decreasing the tube length and connecting several tubes in parallel. Assume that we want
to keep the pressure drop, the mass flow and the in- and outlet temperature constant.
Compare the heat transfer coefficients we would get with different tube diameters.
Compare also the total volume of the tubes, the total tube area and the tube lengths.
Choose the parameters so that you investigate both the laminar and the turbulent regimes.
For the comparison, disregard the entrance section of the tubes.
4. Estimate the heat transfer coefficient in ambient air at 20°C in a long tube with d=10
mm for different air velocities from 1 to 10 m/s. Compare the heat transfer
coefficient calculated to that in a slot between parallel plates at the distance d = 10
mm.
5. A heat pump collects heat from the ground by a ground coil consisting of tubes
buried in the ground. The tubes are filled with a propylene glycol-solution which is
pumped through the coil and through the evaporator of the heat pump. The
concentration of the glycol solution must be high enough to avoid freezing. Assume
that the ground coil is 100 m, that the tube diameter is 3.5 cm and that the flow
velocity is 1.5 m/s. Assume also that the tube wall temperature is -8°C (throughout
the coil) and the glycol solution is -15°C as it enters the ground coil. Calculate the
heat transfer coefficient in the ground coil, the temperature of the glycol as it leaves the
coil and the absorbed power for two different concentrations of the propylene glycol
solution, 32.5% and 48%. The thermal properties of the glycol can in both cases be
taken at -15°C (see table).
Conc.
Density Spec heat Th. cond.
Kin. visc. Dyn. visc. Prandtl
3
Kg/m
kJ/kg K
W/m K
m2/s
Ns/m2
no
32,5%
1039
3,87
0,438
17,3 10-6
18,0 10-3
197
-6
-3
48%
1057
3,55
0,392
47 10
50 10
450
6. A coaxial heat exchanger consists of an inner tube with the inner diameter 9 mm and
the wall thickness 1 mm inserted into an outer tube with an inner diameter of 13
mm. The heat exchanger is used for cooling oil, which is flowing at a rate of 1 liter
per minute through the annulus between the inner and outer tubes. In the inner tube
water is flowing in the opposite direction at a rate of 4 liters per minute. In the
nominal case, the inlet temperature of the oil is 100°C and of the water 60°C. The oil
should be cooled to 80°C. How long does the heat exchanger have to be? For the
calculation the following properties can be used: Oil: Density =850 kg/m3, heat
capacity =2,1 kJ/(kg K), thermal conductivity =0,14 W/(m K), kinematic viscosity
=37∙10-6 m2/s. Water: Density= 980 kg/m3, heat capacity =4,19 kJ/(kg K), thermal
conductivity =0,66 W/(m K), kinematic viscosity =0,43∙10-6 m2/s. Possible entrance
effects are not considered to give a conservative result. Also, the thermal resistance in
the wall is neglected.