Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 2, Problem 2.64P
To determine
The temperature distribution within the rod at different condition.
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find the laplace transform for the
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2(1-e)
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S
12)
k
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14) f(t)=1, 0
Find the solution of the following Differential Equations
Using Laplace Transforms
1) 4y+2y=0.
y(0)=2.
y'(0)=0.
2) y+w²y=0,
(0)=A,
y'(0)=B.
3) +2y-8y 0.
y(0)=1.
y'(0)-8.
4)-2-3y=0,
y(0)=1.
y'(0)=7.
5) y-ky'=0,
y(0)=2,
y'(0)=k.
6) y+ky'-2k²y=0,
y(0)=2,
y'(0) = 2k.
7) '+4y=0,
y(0)=2.8
8) y+y=17 sin(21),
y(0)=-1.
9) y-y-6y=0,
y(0)=6,
y'(0)=13.
10) y=0.
y(0)=4,
y' (0)=0.
11) -4y+4y-0,
y(0)=2.1.
y'(0)=3.9
12) y+2y'+2y=0,
y(0)=1,
y'(0)=-3.
13) +7y+12y=21e".
y(0)=3.5.
y'(0)=-10.
14) "+9y=10e".
y(0)=0,
y'(0)=0.
15) +3y+2.25y=91' +64.
y(0)=1.
y'(0) = 31.5
16)
-6y+5y-29 cos(2t).
y(0)=3.2,
y'(0)=6.2
17) y+2y+2y=0,
y(0)=0.
y'(0)=1.
18) y+2y+17y=0,
y(0)=0.
y'(0)=12.
19) y"-4y+5y=0,
y(0)=1,
y'(0)=2.
20) 9y-6y+y=0,
(0)-3,
y'(0)=1.
21) -2y+10y=0,
y(0)=3,
y'(0)=3.
22) 4y-4y+37y=0,
y(0)=3.
y'(0)=1.5
23) 4y-8y+5y=0,
y(0)=0,
y'(0)=1.
24)
++1.25y-0,
y(0)=1,
y'(0)=-0.5
25) y 2 cos(r).
y(0)=2.
y'(0) = 0.
26)
-4y+3y-0,
y(0)=3,
y(0) 7.
27) y+2y+y=e
y(0)=0.
y'(0)=0.
28) y+2y-3y=10sinh(27),
y(0)=0.
y'(0)=4.
29)…
Auto Controls
A union feedback control system has the following open loop transfer function
where k>0 is a variable proportional gain
i. for K = 1 , derive the exact magnitude and phase expressions of G(jw).
ii) for K = 1 , identify the gaincross-over frequency (Wgc) [where IG(jo))| 1] and phase cross-overfrequency [where <G(jw) = - 180]. You can use MATLAB command "margin" to obtain there quantities.
iii) Calculate gain margin (in dB) and phase margin (in degrees) ·State whether the closed-loop is stable for K = 1 and briefly justify your answer based on the margin . (Gain marginPhase margin)
iv. what happens to the gain margin and Phase margin when you increase the value of K?you
You can use for loop in MATLAB to check that.Helpful matlab commands : if, bode, margin, rlocus
NO COPIED SOLUTIONS
Chapter 2 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - Assume steady-state, one-dimensional conduction in...Ch. 2 - A hot water pipe with outside radius r, has a...Ch. 2 - A spherical shell with inner radius r1 and outer...Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - A composite rod consists of two different...Ch. 2 - A solid, truncated cone serves as a support for a...Ch. 2 - To determine the effect of the temperature...Ch. 2 - A young engineer is asked to design a thermal...Ch. 2 - A one-dimensional plane wall of thickness 2L=100mm...
Ch. 2 - Consider steady-state conditions for...Ch. 2 - Consider a plane wall 100 mm thick and of thermal...Ch. 2 - A cylinder of radius ro, length L, and thermal...Ch. 2 - In the two-dimensional body illustrated, the...Ch. 2 - Consider the geometry of Problem 2.14 for the case...Ch. 2 - Steady-state, one-dimensional conduction occurs in...Ch. 2 - An apparatus for measuring thermal conductivity...Ch. 2 - An engineer desires to measure the thermal...Ch. 2 - Consider a 300mm300mm window in an aircraft. For a...Ch. 2 - Consider a small but known volume of metal that...Ch. 2 - Use INT to perform the following tasks. Graph the...Ch. 2 - Calculate the thermal conductivity of air,...Ch. 2 - A method for determining the thermal conductivity...Ch. 2 - Compare and contrast the heat capacity cp of...Ch. 2 - A cylindrical rod of stainless steel is insulated...Ch. 2 - At a given instant of time, the temperature...Ch. 2 - A pan is used to boil water by placing it on a...Ch. 2 - Uniform internal heat generation at q=5107W/m3 is...Ch. 2 - Consider a one-dimensional plane wall with...Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - The temperature distribution across a wall 0.3 m...Ch. 2 - Prob. 2.33PCh. 2 - One-dimensional, steady-state conduction with...Ch. 2 - Derive the heat diffusion equation, Equation 2.26,...Ch. 2 - Derive the heat diffusion equation, Equation 2.29....Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - cylindrical system illustrated has negligible...Ch. 2 - Beginning with a differential control volume in...Ch. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - For a long circular tube of inner and outer radii...Ch. 2 - Passage of an electric current through a long...Ch. 2 - Two-dimensional. steady-state conduction occurs in...Ch. 2 - An electric cable of radius r1 and thermal...Ch. 2 - A spherical shell of inner and outer radii ri and...Ch. 2 - A chemically reacting mixture is stored in a...Ch. 2 - A thin electrical heater dissipating 4000W/m2 is...Ch. 2 - The one-dimensional system of mass M with constant...Ch. 2 - Consider a one-dimensional plane wall of thickness...Ch. 2 - A large plate of thickness 2L is at a uniform...Ch. 2 - The plane wall with constant properties and no...Ch. 2 - Consider the steady-state temperature...Ch. 2 - A plane wall has constant properties, no internal...Ch. 2 - A plane wall with constant properties is initially...Ch. 2 - Consider the conditions associated with Problem...Ch. 2 - Consider the steady-state temperature distribution...Ch. 2 - A spherical particle of radius r1 experiences...Ch. 2 - Prob. 2.64PCh. 2 - A plane wall of thickness L=0.1m experiences...Ch. 2 - Prob. 2.66PCh. 2 - A composite one-dimensional plane wall is of...Ch. 2 - Typically, air is heated in a hair dryer by...Ch. 2 - Prob. 2.69P
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- Auto Controls A union feedback control system has the following open loop transfer function where k>0 is a variable proportional gain i. for K = 1 , derive the exact magnitude and phase expressions of G(jw). ii) for K = 1 , identify the gaincross-over frequency (Wgc) [where IG(jo))| 1] and phase cross-overfrequency [where <G(jw) = - 180]. You can use MATLAB command "margin" to obtain there quantities. iii) Calculate gain margin (in dB) and phase margin (in degrees) ·State whether the closed-loop is stable for K = 1 and briefly justify your answer based on the margin . (Gain marginPhase margin) iv. what happens to the gain margin and Phase margin when you increase the value of K?you You can use for loop in MATLAB to check that.Helpful matlab commands : if, bode, margin, rlocus NO COPIED SOLUTIONSarrow_forwardAuto Controls Hand sketch the root Focus of the following transfer function How many asymptotes are there ?what are the angles of the asymptotes?Does the system remain stable for all values of K NO COPIED SOLUTIONSarrow_forward-400" 150" in Datum 80" 90" -280"arrow_forward
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