EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 31, Problem 4P
Use Galerkin's method to develop an element equation for a steady-state version of the advection-diffusion equation described in Prob. 30.7. Express the final result in the format of Eq.
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I.C
02/A/ Use the Crank-Nicolson method to solve for the temperature distribution of a long thin rod
with a length of 10 cm and the following values: k = 0.49 cal/(s cm °C), Ax = 2 cm, and At =
st 0.1 s. Initially the temperature of the rod is 0°C and the boundary conditions are fixed for all times
at 7(0, t) = 100°C and 7(10, t) = 50°C. Note that the rod is aluminum with C = 0.2174 cal/g °C)
and p = 2.7 g/cm³. List the tridiagonal system of equations and determined the temperature up
to 0.1 s.
Find the temperature at the interior node given in the following figure
100 °C
75 °C
0 °C
9"
%3D
25 °C
6"
Using the Lieberman method and relaxation factor of 1.2, the temperature estimated after first iterations is:
Select one:
а.
60.00
b. 45.19
С.
50.00
A generic property is being transported through a fluid of constant cross-sectional area at
steady-state. The concentration of the property, IT, at point 1, is 0.015 / unit volume. The
concentration of the property, T, at point 2 is 0.0075 / unit volume. Points 1 and 2 are 2
m apart. The constituitive property, ô, however, is not constant.... Rather it is a function
of I according to:
8 = 0.15 + 1.65 I
a.) Derive an integrated form of the equation for steady-state flux, y
Chapter 31 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 31 - 31.1 Repeat Example 31.1, but for and a uniform...Ch. 31 - Repeat Example 31.2, but for boundary conditions...Ch. 31 - Apply the results of Prob. 31.2 to compute the...Ch. 31 - Use Galerkins method to develop an element...Ch. 31 - Prob. 5PCh. 31 - 31.6 Develop a user-friendly program to model the...Ch. 31 - 31.7 Use Excel to perform the same computation as...Ch. 31 - Use MATLAB or Mathcad to develop a contour plot...Ch. 31 - 31.9 Use Excel to model the temperature...Ch. 31 - 31.10 Use MATLAB or Mathcad to develop a contour...
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