1-61
Solving Engineering Problems
1-108C (a) Despite the convenience and capability the engineering software packages offer, they are still just tools, and they
will not replace the traditional engineering courses. They will simply cause a shift in emphasis in the course material from
mathematics to physics. (b) They are of great value in engineering practice, however, as engineers today rely on software
packages for solving large and complex problems in a short time, and perform optimization studies efficiently.
1-109 We are to determine a positive real root of the following equation using EES: 3.5x3 – 10x0.5 – 3x = −4.
1-110 We are to solve a system of 2 equations and 2 unknowns using EES.
1-111 We are to solve a system of 3 equations with 3 unknowns using EES.
1-112 We are to solve a system of 3 equations with 3 unknowns using EES.
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Special Topic: Thermal Comfort
1-113C The metabolism refers to the burning of foods such as carbohydrates, fat, and protein in order to perform the
necessary bodily functions. The metabolic rate for an average man ranges from 108 W while reading, writing, typing, or
1-114C The metabolic rate is proportional to the size of the body, and the metabolic rate of women, in general, is lower than
1-115C Asymmetric thermal radiation is caused by the cold surfaces of large windows, uninsulated walls, or cold products
on one side, and the warm surfaces of gas or electric radiant heating panels on the walls or ceiling, solar heated masonry
1-116C (a) Draft causes undesired local cooling of the human body by exposing parts of the body to high heat transfer
1-117C Stratification is the formation of vertical still air layers in a room at difference temperatures, with highest
1-118C It is necessary to ventilate buildings to provide adequate fresh air and to get rid of excess carbon dioxide,
contaminants, odors, and humidity. Ventilation increases the energy consumption for heating in winter by replacing the warm
1-63
Review Problems
1-119 The windows of a house in Atlanta are of double door type with wood frames and metal spacers. The average rate of
heat loss through the windows in winter is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat losses associated with the infiltration of air through the
Q
Window
1-120 The range of U-factors for windows are given. The range for the rate of heat loss through the window of a house is to
be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat losses associated with the
infiltration of air through the cracks/openings are not considered.
Analysis The rate of heat transfer through the window can be determined from
)(
windowoverallwindow oi TTAUQ −=
where Ti and To are the indoor and outdoor air temperatures, respectively, Uoverall is the U-
factor (the overall heat transfer coefficient) of the window, and Awindow is the window area.
Substituting,
Maximum heat loss:
W378=−−= C)]8(20)[m 8.1C)(1.2 W/m25.6( 22
max window,
Q
Minimum heat loss:
W76=−−= C)]8(20)[m 8.1C)(1.2 W/m25.1( 22
min window,
Q
Discussion Note that the rate of heat loss through windows of identical size may differ by a factor of 5, depending on how
the windows are constructed.
Q
Window
20C
-8C
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1-121 A room is to be heated by 1 ton of hot water contained in a tank placed in the room. The minimum initial temperature
of the water is to be determined if it to meet the heating requirements of this room for a 24-h period.
Assumptions 1 Water is an incompressible substance with constant specific heats. 2 Air is an ideal gas with constant specific
heats. 3 The energy stored in the container itself is negligible relative to the energy stored in water. 4 The room is maintained
at 20°C at all times. 5 The hot water is to meet the heating requirements of this room for a 24-h period.
Properties The specific heat of water at room temperature is c = 4.18 kJ/kg·°C (Table A-9).
Analysis Heat loss from the room during a 24-h period is
1-122 Engine valves are to be heated in a heat treatment section. The amount of heat transfer, the average rate of heat
transfer, the average heat flux, and the number of valves that can be heat treated daily are to be determined.
Assumptions Constant properties given in the problem can be used.
Properties The average specific heat and density of valves are given to be cp = 440 J/kg.C and
= 7840 kg/m3.
Analysis (a) The amount of heat transferred to the valve is simply the change in its internal energy, and is determined from
)( 12
−== TTmcUQ p
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1-123 A cylindrical resistor on a circuit board dissipates 0.8 W of power. The amount of heat dissipated in 24 h, the heat flux,
and the fraction of heat dissipated from the top and bottom surfaces are to be determined.
Assumptions Heat is transferred uniformly from all surfaces.
Analysis (a) The amount of heat this resistor dissipates during a 24-hour period is
kJ 69.1= Wh19.2=== h) W)(248.0(tQQ
(since 1 Wh = 3600 Ws = 3.6 kJ)
(b) The heat flux on the surface of the resistor is
2
2
2
cm 764.2513.2251.0cm) cm)(2 4.0(
4
cm) 4.0(
2
4
2=+=+=+=
DL
D
As
2
W/cm0.289
=== 2
cm 764.2
W80.0
s
sA
Q
q
(c) Assuming the heat transfer coefficient to be uniform, heat transfer is proportional to the surface area. Then
the fraction of heat dissipated from the top and bottom surfaces of the resistor becomes
(9.1%)or
764.2
251.0
total
basetop
total
basetop 0.091=== −−
A
A
Q
Q
Discussion Heat transfer from the top and bottom surfaces is small relative to that transferred from the side surface.
1-124 The heat generated in the circuitry on the surface of a 3-W silicon chip is conducted to the ceramic substrate. The
temperature difference across the chip in steady operation is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Thermal properties of the chip are constant.
Properties The thermal conductivity of the silicon chip is given to be
k = 130 W/mC.
Q
Resistor
0.8 W
Q
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1-125 A circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.06 W. All the heat generated in
the chips is conducted across the circuit board. The temperature difference between the two sides of the circuit board is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Thermal properties of the board are constant. 3 All the heat generated in
the chips is conducted across the circuit board.
Properties The effective thermal conductivity of the board is given to be
1-126 An electric resistance heating element is immersed in water initially at 20°C. The time it will take for this heater to
raise the water temperature to 80°C as well as the convection heat transfer coefficients at the beginning and at the end of the
heating process are to be determined.
Assumptions 1 Steady operating conditions exist and thus the rate of heat loss from the wire equals the rate of heat
generation in the wire as a result of resistance heating. 2 Thermal properties of water are constant. 3 Heat losses from the
water in the tank are negligible.
Properties The specific heat of water at room temperature is c = 4.18 kJ/kgC (Table A-9).
Analysis When steady operating conditions are reached, we have
W800
generated == EQ
. This is also equal to the rate of heat
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1-127 A standing man is subjected to high winds and thus high convection coefficients. The rate of heat loss from this man
by convection in still air at 20°C, in windy air, and the wind chill temperature are to be determined.
Assumptions 1 A standing man can be modeled as a 30-cm diameter, 170-cm long vertical cylinder with both the top and
bottom surfaces insulated. 2 The exposed surface temperature of the person and the convection heat transfer coefficient is
constant and uniform. 3 Heat loss by radiation is negligible.
Analysis The heat transfer surface area of the person is
1-128 The surface temperature of an engine block that generates 50 kW of power output is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Temperature inside the engine compartment is uniform. 3 Heat transfer
by radiation is not considered.
Analysis With a net engine efficiency of 35%, which means 65% of the generated power output are heat loss by convection:
kW 5.32)35.01)(kW 50()1(
outconv =−=−=
WQ
From Newton’s law of cooling, the heat transfer by convection is given as
)(
conv
−= TThAQss
Rearranging, the engine block surface temperature is
C 841=+
=+= C 157
)m 950C)( W/m50(
W105.32
22
3
conv
.
T
hA
Q
T
s
s
Discussion Due to the complex geometry of the engine block, hot spots are likely to occur with temperatures much higher
than 841 °C.
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1-129 Electric power required to maintain the surface temperature of an electrical wire submerged in boiling water at 115ºC.
Assumptions 1 Steady operating conditions exist. 2
Convection heat transfer coefficient is uniform. 3 Heat
transfer by radiation is negligible. 4 Heat losses from the
boiler are negligible.
Analysis From an overall energy balance on the electrical
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1-70
1-131 A cylindrical fuel rod is cooled by water flowing through its encased concentric tube. The surface temperature of
the fuel rod must be maintained below 300°C and the convection heat transfer coefficient is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat generation in the fuel rod is uniform.
Analysis The total heat transfer area of the fuel rod is
DLAs
=
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1-132 The rate of radiation heat transfer between a person and the surrounding surfaces at specified temperatures is to be
determined in summer and in winter.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer by convection is not considered. 3 The person is completely
surrounded by the interior surfaces of the room. 4 The surrounding surfaces are at a uniform temperature.
Properties The emissivity of a person is given to be = 0.95
Analysis Noting that the person is completely enclosed by the surrounding surfaces, the net rates of radiation heat transfer
from the body to the surrounding walls, ceiling, and the floor in both cases are:
1-133 The base surface of a cubical furnace is surrounded by black surfaces at a specified temperature. The net rate of
radiation heat transfer to the base surface from the top and side surfaces is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The top and side surfaces of the furnace closely approximate black
surfaces. 3 The properties of the surfaces are constant.
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1-73
1-136 The glass cover of a flat plate solar collector with specified inner and outer surface temperatures is considered. The
fraction of heat lost from the glass cover by radiation is to be determined.
Assumptions 1 Steady operating conditions exist since the surface temperatures of the glass remain constant at the specified
values. 2 Thermal properties of the glass are constant.
Properties The thermal conductivity of the glass is given to be k = 0.7 W/mC.
Analysis Under steady conditions, the rate of heat transfer through the glass by conduction is
C)25(28
−
T