Machine Tool Practices
11th Edition
ISBN: 9780134985848
Author: Richard R. Kibbe; Roland O. Meyer; Jon Stenerson; Kelly Curran
Publisher: Pearson Education (US)
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Chapter A.5, Problem 2ST
To determine
The comparison between third angleand first angle method
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Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three
consecutive timesteps.
1.0
0.8-
0.6
0.4-
0.2
0.0
00
-0.2
-0.4
-0.6-
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
Figure 3: Advection equation, solution for three different timesteps.
Question 2
Figure 3 shows the numerical solution of the advection equation for a scalar u along x at three
consecutive timesteps.
1.0
0.8-
0.6-
0.4-
0.2-
0.0-
-0.2-
-0.4-
-0.6
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
Figure 3: Advection equation, solution for three different timesteps.
a) Provide an explanation what conditions and numerical setup could explain the curves. Identify
which of the three curves is the first, second and third timestep.
b) Consider explicit schemes with central and upwind discretisations. Explain how each of these
candidate discretisations could produce the behaviour shown in Figure 3.
c) Determine the CFL number that was used in the simulation for each of the candidate schemes for
all possible updates.
Assume that the timestep and mesh-width used are constant. Read the data to two digits of
accuracy from Figure 4 shown at the end of the question, which is an enlarged version of Figure 3.
Demonstrate your method and input data for one calculation, but then use a…
Chapter A Solutions
Machine Tool Practices
Ch. A.1 - Prob. 1STCh. A.1 - Prob. 2STCh. A.1 - Companies are looking for people with good...Ch. A.1 - Prob. 4STCh. A.1 - Prob. 5STCh. A.1 - Prob. 6STCh. A.1 - Prob. 7STCh. A.1 - Prob. 8STCh. A.2 - Prob. 1STCh. A.2 - Prob. 2ST
Ch. A.2 - Prob. 3STCh. A.2 - Prob. 4STCh. A.2 - Prob. 5STCh. A.2 - Prob. 6STCh. A.2 - Prob. 7STCh. A.3 - What is the primary piece of safety equipment in...Ch. A.3 - Prob. 2STCh. A.3 - Prob. 3STCh. A.3 - Prob. 4STCh. A.3 - What hazards exist from coolants, oils, and...Ch. A.3 - Prob. 6STCh. A.3 - Prob. 7STCh. A.3 - Prob. 8STCh. A.3 - Prob. 9STCh. A.3 - Prob. 10STCh. A.3 - Prob. 11STCh. A.4 - Define the term pitch diameter.Ch. A.4 - Name two ways to measure a thread.Ch. A.4 - What is the rule of thumb for the length of...Ch. A.4 - Describe when class two fits are used.Ch. A.4 - Describe UNC and UNF.Ch. A.4 - What is the formula for calculating the OD of a...Ch. A.4 - When are stud bolts used?Ch. A.4 - Prob. 8STCh. A.4 - Explain two reasons why flat washers are used.Ch. A.4 - What is the purpose of a helical spring lock...Ch. A.4 - When is an internal-external tooth lock washer...Ch. A.4 - When are dowel pins used?Ch. A.4 - When are taper pins used?Ch. A.4 - When are roll pins used?Ch. A.4 - What are retaining lings?Ch. A.4 - Prob. 16STCh. A.4 - Prob. 17STCh. A.4 - Prob. 18STCh. A.5 - Prob. 1STCh. A.5 - Prob. 2STCh. A.5 - Prob. 3STCh. A.5 - Prob. 4STCh. A.5 - Prob. 5STCh. A.5 - Prob. 6STCh. A.6 - Prob. 1STCh. A.6 - Prob. 2STCh. A.6 - Prob. 3STCh. A.6 - Prob. 4STCh. A.6 - Prob. 5STCh. A.6 - Prob. 6STCh. A.6 - Prob. 7STCh. A.6 - Prob. 8STCh. A.6 - Prob. 9STCh. A.6 - Prob. 10STCh. A.7 - Prob. 1STCh. A.7 - Prob. 2STCh. A.7 - Prob. 3STCh. A.7 - Prob. 4STCh. A.7 - Prob. 5STCh. A.7 - Prob. 6STCh. A.7 - Prob. 7STCh. A.7 - Prob. 8STCh. A.7 - Prob. 9STCh. A.7 - Prob. 10STCh. A.8 - Prob. 1STCh. A.8 - Prob. 2STCh. A.8 - Prob. 3STCh. A.8 - Prob. 4STCh. A.8 - Prob. 5STCh. A.8 - Prob. 6STCh. A.8 - Prob. 7STCh. A.8 - Prob. 8STCh. A.8 - Prob. 9STCh. A.8 - Prob. 10STCh. A.8 - Prob. 11STCh. A.9 - Prob. 1.1QCCh. A.9 - Prob. 1.2QCCh. A.9 - Prob. 1.3QCCh. A.9 - Prob. 1.4QCCh. A.9 - Prob. 1.5QCCh. A.9 - Prob. 1.6QCCh. A.9 - Prob. 2.1QCCh. A.9 - Prob. 2.2QCCh. A.9 - Prob. 3.1QCCh. A.9 - Prob. 3.2QCCh. A.9 - Prob. 4.1QCCh. A.9 - Prob. 4.2QCCh. A.9 - Prob. 4.3QCCh. A.9 - Prob. 1STCh. A.9 - Prob. 2STCh. A.9 - Prob. 3STCh. A.9 - Prob. 4STCh. A.9 - Prob. 5STCh. A.9 - Prob. 6ST
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- 1.1 Consider the fireclay brick wall of Example 1.1 that is operating under different thermal conditions. The tem- perature distribution, at an instant in time, is T(x) = a+ bx where a 1400 K and b = -1000 K/m. Determine the heat fluxes, q", and heat rates, q, at x = 0 and x = L. Do steady-state conditions exist?arrow_forward2.4 To determine the effect of the temperature dependence of the thermal conductivity on the temperature dis- tribution in a solid, consider a material for which this dependence may be represented as k = k₁ + aT where k, is a positive constant and a is a coefficient that may be positive or negative. Sketch the steady-state temperature distribution associated with heat transfer in a plane wall for three cases corresponding to a > 0, a = 0, and a < 0.arrow_forward1.21 A one-dimensional plane wall is exposed to convective and radiative conditions at x = 0. The ambient and sur- rounding temperatures are T = 20°C and Tur = 40°C, respectively. The convection heat transfer coefficient is h=20 W/m² K, and the absorptivity of the exposed sur- face is α=0.78. Determine the convective and radiative heat fluxes to the wall at x = 0 if the wall surface tem- perature is T, = 24°C. Assume the exposed wall surface is gray, and the surroundings are large.arrow_forward
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