Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 7, Problem 7.42P
Consider a thin,
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1. Consider a new wind tunnel to test and utilise the effects of boundary layer conditions
in order to maintain the velocity of a fluid. Laminar airflow enters a square duct design
through a 0.25m² opening, as is shown in Figure 1. Because the boundary layer
displacement thickness increases in the direction of flow, it is necessary to increase the
cross-sectional size of the duct if a constant U=1 m/s velocity to be maintained outside
the boundary layer. Assume standard air temperature in the calculation.
U =
1 m/s
0.25 m2
d(x)
1 m/s
Figure 1
a) Determine the expression of the duct size, d, in consideration to maintain the
velocity outside the boundary layer.
b) Plot a graph of the duct size, d, as a function of x for 0
Problem 6. A boundary layer is developing for uniform flow of air at STP over a flat plate as shown. The free-stream
flow outside the boundary layer has an undisturbed velocity of U = 50 m/s. The plate has a width of b = 3.0 m
perpendicular to the schematic. A control volume (CV) with control surfaces (ab), (bc), (cd), and (ad) is defined as shown.
Assume that the flow in the boundary layer is turbulent at surface (cd) with a 1/7th power-law velocity profile and a
boundary layer disturbance thickness of 8 = 2.0 cm. For surfaces (ab), (bc), and (cd), calculate (a) mass flowrate and
(b) momentum transported (in Newtons). (c) Determine the drag for the flat plate at surface (ad).
U
U
control volume
u(y)
boundary-layer region
flat plate
a
Problem 6. A boundary layer is developing for uniform flow of air at STP over a flat plate as shown. The free-
stream flow outside the boundary layer has an undisturbed velocity of U = 50 m/s. The plate has a width of
b = 3.0 m perpendicular to the schematic. A control volume (CV) with control surfaces (ab), (bc), (cd), and (ad) is
defined as shown. Assume that the flow in the boundary layer is turbulent at surface (cd) with a 1/7th power-law
velocity profile and a boundary layer disturbance thickness of = 2.0 cm. For surfaces (ab), (bc), and (cd),
calculate (a) mass flowrate and (b) momentum transported (in Newtons). (c) Determine the drag for the flat plate
at surface (ad).
y
U
control volume
boundary-layer region
a
flat plate
d
U
δ
u(y)
Chapter 7 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 7 - Consider the following fluids at a film...Ch. 7 - Engine oil at 100C and a velocity of 0.1 m/s flows...Ch. 7 - Consider steady, parallel flow of atmospheric air...Ch. 7 - Consider a liquid metal (Pr1), with free stream...Ch. 7 - Consider the velocity boundary layer profile for...Ch. 7 - Consider a steady, turbulent boundary layer on and...Ch. 7 - Consider flow over a flat plate for which it is...Ch. 7 - A flat plate of width 1 m is maintained at a...Ch. 7 - An electric air heater consists of a horizontal...Ch. 7 - Consider atmospheric air at 25C and a velocity of...
Ch. 7 - Repeat Problem 7.11 for the case when the boundary...Ch. 7 - Consider water at 27°C in parallel flow over an...Ch. 7 - Explain under what conditions the total rate of...Ch. 7 - In fuel cell stacks, it is desirable to operate...Ch. 7 - The roof of a refrigerated truck compartment is of...Ch. 7 - The top surface of a heated compartment consists...Ch. 7 - Calculate the value of the average heat transfer...Ch. 7 - The proposed design for an anemometer to determine...Ch. 7 - Steel (AISI 1010) plates of thickness =6mm and...Ch. 7 - Consider a rectangular fin that is used to cool a...Ch. 7 - The Weather Channel reports that it is a hot,...Ch. 7 - In the production of sheet metals or plastics, it...Ch. 7 - An array of electronic chips is mounted within a...Ch. 7 - A steel strip emerges from the hot roll section of...Ch. 7 - In Problem 7.23. an anemometer design was...Ch. 7 - One hundred electrical components, each...Ch. 7 - The boundary layer associated with parallel flow...Ch. 7 - Forced air at 250C and 10 m/s is used to cool...Ch. 7 - Air at atmospheric pressure and a temperature of...Ch. 7 - Consider a thin, 50mm50mm fuel cell similar to...Ch. 7 - The cover plate of a flat-plate solar collector is...Ch. 7 - An array of 10 silicon chips, each of length...Ch. 7 - A square (10mm10mm) silicon chip is insulated on...Ch. 7 - A circular pipe of 25-mm outside diameter is...Ch. 7 - An L=1-m- long vertical copper tube of inner...Ch. 7 - A long, cylindrical, electrical heating element of...Ch. 7 - Consider the conditions of Problem 7.49, but now...Ch. 7 - Pin fins are to be specified for use in an...Ch. 7 - Prob. 7.52PCh. 7 - Prob. 7.53PCh. 7 - Hot water at 500C is routed from one building in...Ch. 7 - In a manufacturing process, long aluminum rods of...Ch. 7 - Prob. 7.58PCh. 7 - To determine air velocity changes, it is proposed...Ch. 7 - Determine the convection heat loss from both the...Ch. 7 - Prob. 7.63PCh. 7 - Prob. 7.64PCh. 7 - Prob. 7.67PCh. 7 - A thermocouple is inserted into a hot air duct to...Ch. 7 - Consider a sphere with a diameter of 20 mm and a...Ch. 7 - Prob. 7.76PCh. 7 - A spherical, underwater instrument pod used to...Ch. 7 - Worldwide. over a billion solder balls must be...Ch. 7 - Prob. 7.80PCh. 7 - Prob. 7.81PCh. 7 - Consider the plasma spray coating process of...Ch. 7 - Prob. 7.83PCh. 7 - Tissue engineering involves the development of...Ch. 7 - Consider temperature measurement in a gas stream...Ch. 7 - Prob. 7.89PCh. 7 - A preheater involves the use of condensing steam...Ch. 7 - Prob. 7.91PCh. 7 - A tube bank uses an aligned arrangement of...Ch. 7 - A tube bank uses an aligned arrangement of...Ch. 7 - Repeat Problem 7.94, but with NL=7,NT=10, and...Ch. 7 - Heating and cooling with miniature impinging jets...Ch. 7 - A circular transistor of 10-mm diameter is cooled...Ch. 7 - A long rectangular plate of AISI 304 stainless...Ch. 7 - A cryogenic probe is used to treat cancerous skin...Ch. 7 - Prob. 7.103PCh. 7 - Prob. 7.104PCh. 7 - Prob. 7.105PCh. 7 - Consider the packed bed of aluminum spheres...Ch. 7 - Prob. 7.108PCh. 7 - Prob. 7.109PCh. 7 - Prob. 7.111PCh. 7 - Packed beds of spherical panicles can be sintered...Ch. 7 - Prob. 7.114PCh. 7 - Prob. 7.116PCh. 7 - Prob. 7.117PCh. 7 - Prob. 7.118PCh. 7 - Prob. 7.119PCh. 7 - Prob. 7.120PCh. 7 - Dry air at 35°C and a velocity of 20 m/s flows...Ch. 7 - Prob. 7.123PCh. 7 - Benzene, a known carcinogen, has been spilled on...Ch. 7 - Prob. 7.125PCh. 7 - Prob. 7.126PCh. 7 - Condenser cooling water for a power plant is...Ch. 7 - Prob. 7.128PCh. 7 - In a paper-drying process, the paper moves on a...Ch. 7 - Prob. 7.131PCh. 7 - Prob. 7.132PCh. 7 - Prob. 7.133PCh. 7 - Prob. 7.134PCh. 7 - Prob. 7.136PCh. 7 - It has been suggested that heat transfer from a...Ch. 7 - Prob. 7.138PCh. 7 - Cylindrical dry-bulb and wet-bulb thermometers are...Ch. 7 - The thermal pollution problem is associated with...Ch. 7 - Cranberries are harvested by flooding the bogs in...Ch. 7 - A spherical drop of water, 0.5 mm in diameter, is...Ch. 7 - Prob. 7.143PCh. 7 - Prob. 7.144PCh. 7 - Prob. 7.145PCh. 7 - Prob. 7.146PCh. 7 - Prob. 7.147PCh. 7 - Consider an air-conditioning system composed of a...Ch. 7 - Prob. 7.149P
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- Experimental measurements of the convection heat transfer coefficient for a square bar in cross flow yielded the following values: Assume that the functional form of the Nusselt number is Nu = C*Rem*Prn, where C, m, and n are constants. Also, assume that air temperature does not change in the following problem.A. What will be the convection heat transfer coefficient for a similar bar with L = 1 m when V = 15 m/s?B. What will be the convection heat transfer coefficient for a similar bar with L = 1 m when V = 30 m/s?arrow_forwardIn elementary mechanical fluidarrow_forwardProblem 1. A smooth plate with length L = 3.0 m and width 6 = 0.90 m moves through still air at STP at a velocity of U = 4.5 m/s that is aligned with L. Calculate the following for a boundary layer that stays laminar and for one that trips to turbulent at the leading edge: (a) boundary layer disturbance thickness, &, at x = 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 m from the leading edge of the plate, (b) wall shear stress, Tw, at those x- locations, and (c) friction drag, FD,f, on one side of plate. (d) Calculate percent decrease in drag for laminar versus turbulent boundary layer.arrow_forward
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