Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 3, Problem 3.46P
To determine
Consider the water heater We wish to determine the energy needed to compensate for heat losses incurred while the water is stored at the prescribed temperature of 55-degreeC. The cylindrical storage tank (with flat ends) has a capacity of 100 gal, and foamed urethane is used to insulate the side and end walls from ambient air at an annual average temperature of 20-degree C. The resistance to heat transfer is dominated by conduction in the insulation and by free convection in the air, for which h 2 W/m2 middot K. If electric resistance heating is used to compensate for the losses and the cost of electric power is $0.18/kWh, specify tank and insulation dimensions for which the annual cost associated with the heat losses is less than $50.
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Problem 6.
ART TAT
Consider the cylindrical pipe shown in the figure. Heat is being generated in the pipe wall at a rate
of R in units of W/m³, and the thermal conductivity of the wall is k, the heat transfer coefficients
at the inside and outside of the pipe are h; and ho, respectively.
At a given location along the pipe axis, the temperature of the fluid flowing inside of the pipe is Ti
and that at the outside is To
i.
ii.
Find the expression for the temperature distribution in the pipe wall.
Find the total heat transfer rate from the pipe to both fluids.
VI.2 A coolant is transported in a pipe with external wall temperature of -30 °C and with outer
diameter of 10 cm. The tube is thermally isolated by two layers: 1) an internal layer of
foamed polypropylene with thermal conductivity of 0.08 W.m.K and thickness of 10 cm,
and 2) an external felt layer with thermal conductivity of 0.05 W.m.K and thickness of 5
cm. Temperature of the outer surface is 25 °C. Calculate the heat flow from the
surroundings to the tube with length of 100 m. What is the temperature on the boundary
between polypropylene and felt layers?
Result: The heat flow from the surroundings is approx. 1.77 kW. Temperature between
layers of isolation is 8.8 °C.
3. A 3 in O.D. aluminum tube (k=133 BTU/h ft°F) has 16
longitudinal fins spaced around its outside surface as shown
below. The fins are .06 in thick and extend 2 in from the outside
surface of the tube. If the outside surface of the tube wall is at
200F, the surrounding air is at 70°F and the convective heat
transfer coefficient is 15 BTU/h ft°F, determine the percent
increase in heat transfer for the finned pipe over that for the
unfinned pipe.
Note: longitudinal fins are rectangular fins that extend along the
length of the tube. Figure shows view looking down the tube
Chapter 3 Solutions
Introduction to Heat Transfer
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