
Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Question
Chapter 2, Problem 2.64P
To determine
The sketch of temperature distribution within a rod at the initial time, at the steady state and at two intermediate times.
The sketch of temperature distribution on the same graph within a second rod which has higher thermal conductivity at the same times.
The rod which will approach steady state condition sooner and the boundary conditions.
Expert Solution & Answer

Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A countershaft carrying two V-belt pullets is shown in the figure. Pulley A receives power
from a motor through a belt with the belt tensions shown. The power is transmitted through
the shaft and delivered to the belt on pulley B. Assume the belt tension on the loose side
(T1) at B is 30% of the tension on the tight side (T2).
(a) Determine the tension (i.e., T₂ and T₁) in the belt on pulley B, assuming the shaft is
running at a constant speed.
(b) Find the magnitudes of the bearing reaction forces, assuming the bearings act as
simple supports.
(c) Draw shear-force and bending moment diagrams for the shaft (in XZ and XY plane
if needed).
(d) Calculate the maximum moments at points A and B respectively and find the point
of maximum bending moment (A or B).
(e) Find maximum stresses (tensile, compressive, and shear stresses) at the identified
point of maximum moment (hint: principal and max shear stresses)
8 dia.
9
400lbf
50lbf
45°
1.5 dia.
T₂
B
Units in inches
T₁
10 dia.
The cantilevered bar in the figure is made from a ductile material and is statically loaded
with F,, = 200 lbf and Fx = F₂ = 0. Analyze the stress situation in rod AB by obtaining
the following information. Note that the stress concentration factors are neglected in the
following questions (Kt and Kts=1).
(a) Determine the precise location of the critical stress element.
(b) Sketch the critical stress element and determine magnitudes and direction for all
stresses acting on it. (Transverse shear may only be neglected if you can justify this
decision.)
(c) For the critical stress element, determine the principal stresses and maximum shear
stress.
6 in
1-in dia.
B
+1-
in
in
2 in
5 in
A laminated thick-walled hydraulic cylinder was fabricated by shrink-fitting
jacket having an outside diameter of 300mm onto a SS 304 steel tube having an inside
diameter of 100mm and an outside diameter of 200mm as shown in the figure. The
interference (8) was 0.15mm. When the Young's modulus for both SS304 and 1020 steel
is the same as 200GPa, and the Poisson's ratio is also the same as 0.3 for both materials,
find the followings.
Initially 100 mm
Initially 200 mm
Initially 300 mm
SS 304
1020 steel
(a) P; (interfacial contact stress)
(b) The maximum stresses (σ, and σ+) in the laminated steel cylinder resulting from the
shrink fit.
Chapter 2 Solutions
Introduction to Heat 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 r1 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 - Prob. 2.9PCh. 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 - Prob. 2.13PCh. 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 - Prob. 2.17PCh. 2 - Prob. 2.18PCh. 2 - Consider a 300mm300mm window in an aircraft. For a...Ch. 2 - Prob. 2.20PCh. 2 - Use IHT 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 - Prob. 2.24PCh. 2 - Prob. 2.25PCh. 2 - At a given instant of time, the temperature...Ch. 2 - Prob. 2.27PCh. 2 - Uniform internal heat generation at q.=5107W/m3 is...Ch. 2 - Prob. 2.29PCh. 2 - The steady-state temperature distribution in a...Ch. 2 - The temperature distribution across a wall 0.3 m...Ch. 2 - Prob. 2.32PCh. 2 - Prob. 2.33PCh. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 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 - One-dimensional, steady-state conduction with no...Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.43PCh. 2 - Prob. 2.44PCh. 2 - Beginning with a differential control volume in...Ch. 2 - A steam pipe is wrapped with insulation of inner...Ch. 2 - Prob. 2.47PCh. 2 - Prob. 2.48PCh. 2 - Two-dimensional, steady-state conduction occurs in...Ch. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 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 - Prob. 2.57PCh. 2 - Prob. 2.58PCh. 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 - Prob. 2.62PCh. 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 - Prob. 2.68PCh. 2 - The steady-state temperature distribution in a...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Auto Controls Design a proportional derivitivecontroller for a plant orsystemthat satisfies the following specifications : 1. is steady-state error is less than 2 % for a ramp input. 2.) Damping ratio (zeta) is greater than 0.7have determined the 3. Once youvalue of kp and kd, then plotthe response of the compensated(with controller) and uncompensated( without the controller, only the plantsystem using MATLAB.arrow_forwardAuto Controls (a) Refer to the above figure .What kind of controller is it ? (b) simplify the block diagramto derive the closed loop transfer function of the system. (C) What are the assumptions thatare needed to make to findthe controller gain ? What arethe value of Kp , Ti and Td ?arrow_forwardAuto Controls Design a PID controller for thefollowing system so that the modified system satisfies the followingspecifications : 1. settling time ,ts = 1.96 s and % Overshoot Mp = 70.7 % Assume a non-dominant pole at s = -15 to solve the problem The plot the compensated andThen plot the uncompensated system in MATLAB. what can you see from the plot ? what is your observation ?arrow_forward
- Fourth year Monthly exam\3 2024-2025 Power plant Time: 1 Hr Q1. A gas turbine power plant operates on a modified Brayton cycle consisting of two-stage compression with intercooling to the initial temperature between stages, two-stage expansion with reheating to the maximum cycle temperature, and two regenerative heat exchangers. The following data is given: Inlet air temperature: 300 K Maximum cycle temperature: 1400 K Pressure ratio across each compressor stage: 4 Pressure ratio across each turbine stage: 4 Isentropic efficiency of compressors and turbines: 85% Effectiveness of each regenerator: 80% a) Draw a schematic and T-s diagram of the cycle. b) Determine the thermal efficiency of the cycle. c) Calculate the net specific work output (in kJ/kg). d) Discuss the impact of regenerators on the cycle performance. Examiner Prof. Dr. Adil Al-Kumaitarrow_forwardAuto Controls The figure is a schematic diagram of an aircraft elevator control system. The input to the systemin the deflection angle of the control lever , and the output is the elevator angle phi.show that for each angle theta of the control lever ,there is a corresponding elevator angle phi. Then find Y(s)/theta(s) and simplify the resulting transfer function . Also note from the diagram that y and phi is relatedarrow_forwardLiquid hexane flows through a counter flow heat exchanger at 5 m3/h as shown in Figure E5.5.The hexane enters the heat exchanger at 90°C. Water, flowing at 5 m3/h, is used to cool the hexane.The water enters the heat exchanger at 15°C. The UA product of the heat exchanger is found to be2.7 kW/K. Determine the outlet temperatures of the hot and cold fluids and the heat transfer ratebetween them using LMTD method.arrow_forward
- Determine the fluid outlet temperatures and the heat transfer rate for the counter flow heatexchanger described in Problem 3 using the ε-NTU model. Assume that the properties can beevaluated at the given fluid inlet temperatures.arrow_forwardSection View - practice Homework 0.5000 3.0000 2,0000 1.0000arrow_forwardDrawing the section view for the following multiview drawing AutoCAD you see the section pratice I need to show how to autocadarrow_forward
- A boiler with 80% efficiency produces steam at 40bar and 500 C at a rate of 1.128kg/s. The temperature of the feed water is raised from 25 C to 125 C in the economizer and the ambient air is drawn to the boiler at a rate of 2.70 kg/s at 16 C. The flue gases leave the chimney at rate of 3 kg/s at 150 C with specific heat of 1.01 kJ/kg.K. The dryness fraction of steam collected in the steam drum is 0.95. 1- Determine the heat value of the fuel. 2- The equivalence evaporation. 3- Draw the heat balance sheet.arrow_forwardA rotating shaft is made of 42 mm by 4 mm thick cold-drawn round steel tubing and has a 6 mm diameter hole drilled transversely through it. The shaft is subjected to a pulsating torque fluctuating from 20 to 160 Nm and a completely reversed bending moment of 200 Nm. The steel tubing has a minimum strength of Sut = 410 MPa (60 ksi). The static stress-concentration factor for the hole is 2.4 for bending and 1.9 for torsion. The maximum operating temperature is 400˚C and a reliability of 99.9% is to be assumed. Find the factor of safety for infinite life using the modified Goodman failure criterion.arrow_forwardI need help with a MATLAB code. This code just keeps running and does not give me any plots. I even reduced the tolerance from 1e-9 to 1e-6. Can you help me fix this? Please make sure your solution runs. % Initial Conditions rev = 0:0.001:2; g1 = deg2rad(1); g2 = deg2rad(3); g3 = deg2rad(6); g4 = deg2rad(30); g0 = deg2rad(0); Z0 = 0; w0 = [0; Z0*cos(g0); -Z0*sin(g0)]; Z1 = 5; w1 = [0; Z1*cos(g1); -Z1*sin(g1)]; Z2 = 11; w2 = [0; Z2*cos(g2); -Z2*sin(g2)]; [v3, psi3, eta3] = Nut_angle(Z2, g2, w2); plot(v3, psi3) function dwedt = K_DDE(~, w_en) % Extracting the initial condtions to a variable % Extracting the initial condtions to a variable w = w_en(1:3); e = w_en(4:7); Z = w_en(8); I = 0.060214; J = 0.015707; x = (J/I) - 1; y = Z - 1; s = Z; % Kinematic Differential Equations dedt = zeros(4,1); dedt(1) = pi*(e(3)*(s-w(2)-1) + e(2)*w(3) + e(4)*w(1)); dedt(2) = pi*(e(4)*(w(2)-1-s) + e(3)*w(1) - e(1)*w(3)); dedt(3) = pi*(-e(1)*(s-w(2)-1) - e(2)*w(1) + e(4)*w(3));…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning

Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license