For fully turbulent flow in a long tube of diameter D, develop a relation between the ratio (L/?T)/D in terms of flow and heat transfer parameters, where L/?T is the tube length required to raise the bulk temperature of the fluid by ?T for fluids with Prandtl number of the order of unity or larger for liquid metals.
GIVEN
Fully developed turbulent flow in a long tube
Diameter = D
L/? T = Tube length required to raise the bulk temperature by ? T
FIND
A relationship for (L/?T)/D in terms of flow and heat transfer parameters using
(a) Equation 7.61 for fluids with Pr = 1
(b) liquid metals
ASSUMPTIONS
Steady state
Constant fluid properties
Uniform wall temperatures
SKETCH
Let
(a) for the Nusselt number
The rate of heat transfer to the fluid must equal the energy needed to raise the temperature of the fluid
by ?T
Checking the units
(b) From
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A refrigerator extracts 65.0 J of heat from a heat reservoir at 
If the coefficient of performance of the refrigerator is 2.50, then how much heat is discharged out of the refrigerator?
A. 125 J B. 91.0 J C. 75.0 J D. 55.0 J
A salesperson for insulation material claims that insulating exposed steam pipes in the basement of a large hotel will be cost effective. Suppose saturated steam at 5.7 bars flows through a 30-cm- OD steel pipe with a 3 cm wall thickness. The pipe is surrounded by air at 20°C. The convective heat transfer coefficient on the outer surface of the pipe is estimated to be 25 W/(m2 K). The cost of generating steam is estimated to be $5 per 109 J and the salesman offers to install a 5 cm thick layer of 85% magnesia insulation on the pipes for $200/m or a 10-cm-thick layer for $300/m. Estimate the payback time for these two alternatives assuming that the steam line operates all year long and make a recommendation to the hotel owner. Assume that the surface of the pipe as well as the
insulation have a low emissivity and radiative heat transfer is negligible.
GIVEN
Steam pipe in a hotel basement
Pipe outside diameter (Do) = 30 cm = 0.3 m
Pipe wall thickness (Ls) = 3 cm = 0.03 m
Surrounding air temperature (T?) = 20°C
Convective heat transfer coefficient (hc) = 25 W/(m2 K)
Cost of steam = $5/109J
Insulation is 85% magnesia
FIND
Payback time for
(a) Insulation thickness (LIa) = 5 cm = 0.05 m; Cost = $200/m
(b) Insulation thickness (LIb) = 10 cm = 0.10 m; Cost = $300/m
Make a recommendation to the hotel owner.
ASSUMPTIONS
The pipe and insulation are black (? = 1.0) The convective resistance on the inside of the pipe is negligible, therefore the inside pipe surface temperature
is equal to the steam temperature The pipe is made of 1% carbon steel Constant thermal conductivities
SKETCH
A heat engine has an efficiency of 35.0% and receives 150 J of heat per cycle
(a) How much work does it do in each cycle? (b) How much heat does it "waste" in each cycle?