Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Textbook Question
Chapter 13.1, Problem 5E
Solve the exterior Dirichlet problem for a circular plate of radius c if u(c, θ) = f (θ), 0 < θ < 2π. In other words, find the steady-state temperature u(r, θ) in a plate that coincides with the entire xy-plane in which a circular hole of radius c has been cut out around the origin and the temperature on the circumference of the hole is f (θ). See Figure 13.1.4. [Hint: Assume that the temperature is bounded as r → ∞.]
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Chapter 13 Solutions
Differential Equations with Boundary-Value Problems
Ch. 13.1 - In Problems 1 4 find the steady-state temperature...Ch. 13.1 - In Problems 1 4 find the steady-state temperature...Ch. 13.1 - In Problems 1– 4 find the steady-state temperature...Ch. 13.1 - In Problems 1 4 find the steady-state temperature...Ch. 13.1 - Solve the exterior Dirichlet problem for a...Ch. 13.1 - Find the steady-state temperature u(r, θ) in a...Ch. 13.1 - Find the steady-state temperature u(r, θ) in a...Ch. 13.1 - Find the steady-state temperature u(r, θ) in the...Ch. 13.1 - Find the steady-state temperature u(r, ) in the...Ch. 13.1 - Find the steady-state temperature u(r, ) in the...
Ch. 13.1 - Find the steady-state temperature u(r, ) in the...Ch. 13.1 - If the boundary conditions for the annular plate...Ch. 13.1 - Find the steady-state temperature u(r, θ) in the...Ch. 13.1 - Find the steady-state temperature u(r, θ) in the...Ch. 13.1 - Find the steady-state temperature u(r, ) in the...Ch. 13.1 - Prob. 16ECh. 13.1 - Find the steady-state temperature u(r, ) in the...Ch. 13.1 - The plate in the first quadrant shown in Figure...Ch. 13.1 - Consider the annular plate in Figure 13.1.7....Ch. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.2 - Find the displacement u(r, t) in Example 1 if f...Ch. 13.2 - A circular membrane of unit radius 1 is clamped...Ch. 13.2 - Find the steady-state temperature u(r, z) in the...Ch. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Find the steady-state temperature u(r, z) in the...Ch. 13.2 - Find the steady-state temperatures u(r, z) in the...Ch. 13.2 - Find the steady-state temperatures u(r, z) in the...Ch. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - When there is heat transfer from the lateral side...Ch. 13.2 - Find the steady-state temperature u(r, z) in a...Ch. 13.2 - A circular plate is a composite of two different...Ch. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - In this problem we consider the general casethat...Ch. 13.3 - Solve the BVP in Example 1 if f()={50,0/20,/2....Ch. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Find the steady-state temperature u(r, ) within a...Ch. 13.3 - The steady-state temperature in a hemisphere of...Ch. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13 - Find the steady-state temperature u(r, θ) in a...Ch. 13 - Find the steady-state temperature in the circular...Ch. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Find the steady-state temperature u(r, ) in the...Ch. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Find the steady-state temperature u(r, z) in the...Ch. 13 - Prob. 10RECh. 13 - Find the steady-state temperature u(r, θ) in a...Ch. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Find the steady-state temperature u(r, θ) in the...Ch. 13 - Find the steady-state temperature u(r, z) in a...Ch. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RE
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