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Concept explainers
Solve the nondimensional transient heat conduction equation in two dimensions, which represents the transient temperature distribution in an insulated plate. The governing equation is
where
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Initial conditions |
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Solve using the alternating direction-implicit technique. Write a computer program to implement the solution. Plot the results using a three-dimensional plotting routine where the horizontal plan contains the x and y axes and the z axis is the dependent variable u. Construct several plots at various times, including the following: (a) the initial conditions; (b ) one intermediate time, approximately halfway to steady state; and (c ) the steady-state condition.
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Chapter 32 Solutions
Numerical Methods for Engineers
- Q4*) (make sure you first understand question P5) Discuss the extremisation of the integral I = = √(2(y + 2) ³y' + (x − 7)) c You may find point (iv) in § 3.5 relevant. dx.arrow_forwardQ6*) Describe the plane paths of light in the two-dimensional media in which the light velocities are given respectively by (a) c = a/y, (b) c = a/√y, where a > 0, y > 0.arrow_forwardlim 1 x→0x3 3 So²² 6 tln(1+t) t4 +4 .dt 2arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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