EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 29, Problem 2P
Use Liebmann's method to solve for the temperature of the square heated plate in Fig. 29.4, but with the upper boundary condition increased to
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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.
03 A thin rod of 3 cm length having a thermal diffusivity coefficient (a) of 0.835 cm²/s is
initially kept at a temperature of 0 °C. The rod is insulated at all points except at its ends
which are kept at all times at T(0) -5 °C and T(3) = 10 °C. Use the explicit method to solve
for the temperature distribution in the rod at t= 0.2 second using the following information;
Ax=1 cm, At = 0.1 second, and λ = a At/Ax².
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Question: Which series helps us to derive the discretized form of the governing equations?
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Chapter 29 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 29 - 29.1 Use Liebmann’s method to solve for the...Ch. 29 - 29.2 Use Liebmann’s method to solve for the...Ch. 29 - 29.3 Compute the fluxes for Prob. 29.2 using the...Ch. 29 - Repeat Example 29.1, but use 49 interior nodes...Ch. 29 - Repeat Prob. 29.4, but for the case where the...Ch. 29 - 29.6 Repeat Examples 29.1 and 29.3, but for the...Ch. 29 - Prob. 7PCh. 29 - 29.8 With the exception of the boundary...Ch. 29 - Write equations for the darkened nodes in the grid...Ch. 29 - 29.10 Write equations for the darkened nodes in...
Ch. 29 - Apply the control-volume approach to develop the...Ch. 29 - Derive an equation like Eq. (29.26) for the case...Ch. 29 - 29.13 Develop a user-friendly computer program to...Ch. 29 - Employ the program from Prob. 29.13 to solve...Ch. 29 - Employ the program from Prob. 29.13 to solve Prob....Ch. 29 - Use the control-volume approach and derive the...Ch. 29 - 29.17 Calculate heat flux for node in Fig. 29.13...Ch. 29 - 29.18 Compute the temperature distribution for...Ch. 29 - 29.19 The Poisson equation can be written in...
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