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6-75
Review problems
6-106E Prantl number is to be determined for a given set of properties.
Assumptions None.
Properties The given properties are: cp = 0.5 Btu/lbm·R, k = 2 Btu/h·ft·R,
= 0.3 lbm/ft·s.
Analysis The Prandtl number is
s/h)(3600s)lbm/ftR)(0.3Btu/lbm(0.5
cp
6-107 Determine whether the flow is laminar or turbulent over a flat plate for different fluids at a given temperature.
Assumptions 1 Transition from laminar to turbulent flow over the flat plate occurs at a Reynolds number of 5 × 105
Properties The properties of the fluids are evaluated at 50°C. For Air: ν = 1.798 10−5 m2/s (Table A-15). For CO2:
ν = 9.714 10−6 m2/s (Table A-16). For Water: = 988.1 kg/m3, = 0.547 10−3 kg/m·s → ν = / = 5.536 10−7 m2/s
(Table A-9). For Engine oil (unused): ν = 1.671 10−4 m2/s (Table A-13).
Analysis The Reynolds number for the plate is
VL
6-77
6-109 The Coutte flow of a fluid between two parallel plates is considered. The temperature distribution is to be sketched
and determined, and the maximum temperature of the fluid, as well as the temperature of the fluid at the contact surfaces with
the lower and upper plates are to be determined.
Assumptions Steady operating conditions exist.
Properties The viscosity and thermal conductivity of the fluid are given to be
= 0.8 Ns/m2 and kf = 0.145 W/mK. The
thermal conductivity of lower plate is given to be kp = 1.5 W/mK.
Analysis: (a) The sketch of temperature distribution is given in the figure. We observe from this figure that there are different
slopes at the interface (y = 0) because of different conductivities (kp > kf). The slope is zero at the upper plate (y = L) because
of adiabatic condition.
(b) The general solution of the relevant
differential equation is obtained as follows:
2
2
2
V
dT
V
Td
L
V
dy
du
V
L
y
u
−
−
=⎯→⎯=
V
Insulation
6-79
14.000
169003
0.1703
0.0119
15.000
181075
0.1763
0.0123
16.000
193147
0.1820
0.0127
17.000
205218
0.1876
0.0131
18.000
217290
0.1931
0.0134
19.000
229362
0.1984
0.0138
20.000
241433
0.2035
0.0142
21.000
253505
0.2085
0.0145
22.000
265576
0.2135
0.0149
23.000
277648
0.2182
0.0152
24.000
289720
0.2229
0.0155
25.000
301791
0.2275
0.0158
26.000
313863
0.2320
0.0162
27.000
325935
0.2365
0.0165
28.000
338006
0.2408
0.0168
29.000
350078
0.2451
0.0171
30.000
362150
0.2493
0.0174
31.000
374221
0.2534
0.0176
32.000
386293
0.2574
0.0179
33.000
398365
0.2614
0.0182
34.000
410436
0.2654
0.0185
35.000
422508
0.2692
0.0187
36.000
434580
0.2730
0.0190
37.000
446651
0.2768
0.0193
38.000
458723
0.2805
0.0195
39.000
470795
0.2842
0.0198
40.000
482866
0.2878
0.0200
41.000
494938
0.2914
0.0203
41.210
497473
0.2921
0.0203
41.420
500008
0.2929
0.0204
6-80
6-111 Object 1 and object 2 with same shape and geometry, but different characteristic lengths, are placed in airflow of
different free stream velocities at 1 atm and 20°C. The average convection heat transfer coefficient for object 2 is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Properties are constant.
Analysis The relation for Nusselt, Prandtl, and Reynolds numbers is given as
hL
cp
VL
6-83
6-115 A flat flat is subjected to air flow, and the drag force acting on it is measured. The electrical power needed to maintain
the prescribed heater surface temperature of 80°C is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The edge effects are negligible.
Properties The properties of air at 50C and 1 atm are (Table A-15)
= 1.092 kg/m3, cp=1.007 kJ/kg-K, Pr = 0.7228
Analysis For flat plates, the drag force is equivalent to friction force. The average friction coefficient Cf can be determined
from
m/skg 1
N 2.0
F
V
2
f
2
6-84
Fundamentals of Engineering (FE) Exam Problems
6-116 The transition from laminar flow to turbulent flow in a forced convection situation is determined by which one of the
following dimensionless numbers?
(a) Grasshof (b) Nusselt (c) Reynolds (d) Stanton (e) Mach
6-117 The ______ number is a significant dimensionless parameter for forced convection and the _____ number is a
significant dimensionless parameter for natural convection.
(a) Reynolds, Grashof (b) Reynolds, Mach (c) Reynolds, Eckert
(d) Reynolds, Schmidt (e) Grashof, Sherwood
6-118 In any forced or natural convection situation, the velocity of the flowing fluid is zero where the fluid wets any
stationary surface. The magnitude of heat flux where the fluid wets a stationary surface is given by
(a)
)( wallfluid TTk −
(b)
wall
dy
dT
k
(c)
wall
2
2
dy
Td
k
(d)
wall
dy
dT
h
(e) None of them
wall
dy
dT
6-119 The coefficient of friction Cf for a fluid flowing across a surface in terms of the surface shear stress,
s, is given by
(a) 2
V2 /
s (b) 2
s /
V2
(c) 2
s /
V2T (d) 4
s /
V2 (e) None of them
6-120 Most correlations for the convection heat transfer coefficient use the dimensionless Nusselt number, which is defined
as
(a) h / k (b) k / h (c) hLc / k (d) kLc / h (e) k/
cp
6-86
6-124 In turbulent flow, one can estimate the Nusselt number using the analogy between heat and momentum transfer
(Colburn analogy). This analogy relates the Nusselt number to the coefficient of friction, Cf, as
(a) Nu = 0.5 Cf Re Pr1/3 (b) Nu = 0.5 Cf Re Pr2/3 (c) Nu = Cf Re Pr1/3
(d) Nu = Cf Re Pr2/3 (e) Nu = Cf Re1/2 Pr1/3
6-125, 6-126 Design and Essay Problems
