... in an electrical
network. Kirchhoff’s laws, along with Ohm’s law, form the basis of circuit theory.
Born the son of a lawyer in Konigsberg, East Prussia, Kirchhoff entered
the University of Konigsberg ... large variety ofelectric circuits. Kirchhoff’s
lawswerefirst introduced in 1847 by theGermanphysicistGustav Robert
Kirchhoff (1824–1887). These laws are formally known as Kirchhoff’s
current ... chemist Robert Bunsen led to the
discovery of cesium in 1860 and rubidium in 1861. Kirchhoff was also credited with
the Kirchhoff law of radiation. Thus Kirchhoff is famous among engineers, chemists,
and...
... subject to the Terms of Use as given at the website.
FUNDAMENTALS OFELECTRIC SYSTEMS
FUNDAMENTALS OF
ELECTRIC SYSTEMS
CAPACITORS
Figure 1.1 illustrates a capacitor. It consists of two insulated ... Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.
FUNDAMENTALS OFELECTRIC SYSTEMS
FUNDAMENTALS OFELECTRIC SYSTEMS 1.9
FIGURE 1.9 Iron filings around a wire ... subject to the Terms of Use as given at the website.
FUNDAMENTALS OFELECTRIC SYSTEMS
TABLE 2.1 Characteristics of Soft Magnetic Materials
Saturation Amplitude Coercive Electrical Curie
Principal...
... ¼1
Examples
.
Field of real numbers R
.
Field of complex numbers C
.
Field of rational functions with real coefficients R(s)
.
Field of binary numbers
The set of integers Z with the standard notions of addition ... Circuits and Filters
The Circuits and Filters
Handbook
Third Edition
Fundamentals ofCircuits and Filters
Feedback, Nonlinear, and Distributed Circuits
Analog and VLSI Circuits
Computer Aided ... of det(M), often denoted by jMj, for M 2 F
232
. Consider
M ¼
m
11
m
12
m
21
m
22
(1:22)
The minor of m
ij
is defined to be the determinant of the submatrix which results from the removal of
row...
... resisted by a shear stress of 10 Pa due to the viscosity of the fluid. Assuming that the
velocity gradient of the fluid is constant, determine the coefficient of viscosity of the fluid.
Solution: ... does heat of fusion mean in casting?
Answer. Heat of fusion is the amount of heat energy required to transform the metal from solid
state to liquid state.
10.13 How does solidification of alloys ... volume of casting, and A = surface area of casting.
10.16 Identify the three sources of contraction in a metal casting after pouring.
Answer. The three contractions occur due to: (1) contraction of...
... dark because of the costs of
compliance. The costs to comply with Sarbox can be several million dollars, which can be a large
percentage of a small firms profits. A major cost of going dark ... this: “A firm has estimated that the cost of improving the safety of one of its products is $30
million. However, the firm believes that improving the safety of the product will only save $20
million ... costs of raising funds in the public market.
5. The treasurer’s office and the controller’s office are the two primary organizational groups that
report directly to the chief financial officer....
... Dimensions, thermal conductivity and surface temperatures of a concrete slab. Efficiency
of gas furnace and cost of natural gas.
FIND:
Daily cost of heat loss.
SCHEMATIC:
ASSUMPTIONS:
... if the thickness of the glass were doubled to match that of the air space. The
principal advantage of the double pane construction resides with the low thermal conductivity
of air (~ 60 times ... emissivity and temperature of a surface placed in a large, evacuated
chamber of prescribed temperature.
FIND: (a) Rate of surface radiation emission, (b) Net rate of radiation exchange between
surface...
... and thermal conductivity of steel tubes. Temperature of steam
flowing through the tubes. Thermal conductivity of insulation and emissivity of aluminum sheath.
Temperature of ambient air and surroundings. ... C.
=
<
COMMENTS:
Use of the critical insulation thickness in lieu of a thin coating has the effect of
reducing the maximum insulation temperature from 778.7
°
C to 318.2
°
C. Use of the critical insulation
thickness ... larger than those of the transistor.
PROBLEM 3.41
KNOWN:
Thin electrical heater fitted between two concentric cylinders, the outer surface of which
experiences convection.
FIND:
(a) Electrical power...
... guesses.
(2) Note that the rate of heat transfer by convection to the top surface of the rod must balance the rate of
heat transfer by conduction to the sides and bottom of the rod.
NOTE TO INSTRUCTOR:
... is
abcde
qqqqqq
′′′′′′
=++++
or in terms of conduction terms between nodes,
123457
qqqqqqq.
′′′′′′′
=+++++
Each of these rates can be written in terms of nodal temperatures and control volume ... as well as the rate of heat transfer by convection to the surface.
COMMENTS:
(1) Using the matrix-inversion method, the exact solution to the system of equations (1,
2, 3) of part (a) is T
1
...
... form of the FDEs for the
interior nodes. Use space and time increments of 37.5 mm and 1.2 s, respectively, for a 17-node
network. For the surface node 00, use the FDE derived in Section 2 of the ... at 1000
°
C (instead of a net radiant flux).
FIND:
(a) The temperatures T(0, 120 s) and T(0.15 m, 120s) using the finite-element software FEHT
for a surface emissivity of 0.94 and (b) Plot the ... steady-state temperature.
(2) Both the FEHT and IHT methods of solution give identical results. Their steady-state solutions
agree with the result of an energy balance on a time interval basis yielding...
... emissivity of Nichrome wire. Electrical
current. Temperature of air flow and surroundings. Velocity of air flow.
(a) Surface and centerline temperatures of the wire, (b) Effect of flow velocity and electric
current ... and thermal conductivity of steel pipe. Temperature of water flow in
pipe. Temperature and velocity of air in cross flow over pipe. Cost of producing hot water.
(a) Cost of daily heat loss from ... with use of the correlation for
D
Nu.
Initial temperature, power dissipation, diameter, and properties of a heating element.
Velocity and temperature of air in cross flow. Temperature of surroundings.
...
... conductivity of steel pipe. Temperature and velocity of water flow
in pipe. Temperature and velocity of air in cross flow over pipe. Cost of producing hot water.
FIND:
Daily cost of heat loss ... length. Pressure of
saturated steam.
FIND:
Outlet temperature and pressure of air. Mass rate of steam condensation.
SCHEMATIC:
ASSUMPTIONS:
(1) Steady-state, (2) Outer surface of annulus is adiabatic, ... the initial estimate of 325 K is reasonable
and iteration is not necessary. (2) For a steam flow rate of 0.01 kg/s, approximately 10% of the
outflow would be in the form of saturated liquid,...
... room, per unit length of the tube; effect on
quality, x, at outlet of 30 m length of tube; (b) Effect of radiation on heat transfer and quality of outlet
flow; (c) Effect of emissivity and insulation ... 9.72
KNOWN:
Velocity and temperature of air flowing through a duct of prescribed diameter. Temperature
of duct surroundings. Thickness, thermal conductivity and emissivity of applied insulation.
FIND:
...
PROBLEM 9.57
KNOWN: Length and diameter of tube submerged in paraffin of prescribed dimensions. Properties
of paraffin. Inlet temperature, flow rate and properties of water in the tube.
FIND: (a) Water...
... conditions, (3) Water flow rate is much larger than that of air.
ANALYSIS: (a) Assuming the flow rate of the water is much larger than that of air,
mincairp,c
CCmc.
==
&
Hence, the heat rate ... reduces the size of the heat exchanger.
PROBLEM 11.35
KNOWN:
Steam at 0.14 bar condensing in a shell and tube HXer (one shell, two tube passes consisting
of 130 brass tubes off length 2 m, D
i
... for the HXer, outlet temperature of cooling water, T
c,o
,
and condensation rate of the steam
h
m
; and (b) Compute and plot T
c,o
and
h
m
as a function of the
water flow rate 10
≤
c
m
...
... conductivities of a ceramic/metal composite. Emissivity of ceramic
surface. Temperatures of vacuum chamber wall and substrate lower surface. Receiving area of radiation
detector, distance of detector ... history of the
workpiece from the start of heating to the end of cooling; identify key features of the process;
determine the total time requirement; and justify the lumped-capacitance method of analysis.
SCHEMATIC:
ASSUMPTIONS:
... Table 12.1.
(c) After a long period of time, the surface will be at the temperature of the enclosure. This condition of
thermal equilibrium is described by Kirchoff’s law, for which
ε
=
α =
0.375.
<
Continued...
... emissivity of boiler tube. Thermal conductivity and emissivity of
ash deposit. Convection coefficient and temperature of gas flow over the tube. Temperature of
surroundings.
FIND:
(a) Rate of heat ... +=
<
COMMENTS:
Use of the foam insulation reduces the heat loss considerably. Note the significant
effect of radiation.
PROBLEM 13.97
KNOWN:
Electrical conductors in the form of parallel plates ... and T
2
.
(2) The resistance of a section of low density particle board 75 mm thick (L
1
+ L
2
+ L
3
) of area W
2
is
9615 K/W, which exceeds the total resistance of the composite by approximately...