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The cross-section of a long conducting duct is shown in the following figure. Three of the sides are held at V = 0 and the bottom side is held at V = V. yA V.- Find a non-zero equation for V(x, y) that satisfies three of the four boundary conditions. Recall that for arbitrary constants A, B,C, D, and m the following four equations satisfy Laplace's equation in 2-D cartesian coordinates. 1. V(r, y) = (A cosh mx + B sinh mx) (C cos my+D sin my) 2. V(x, y) 3. V (x, y) = (Aem + Be-ma)(C cos my + D sin my) 4. V(x, y) = = (A cos mx + B sin mx)(C cosh my +D sinh my) %3D (A cos mx + B sin mx) (Cemy + De-my

The cross-section of a long conducting duct is shown in the following figure. Three of the sides are held at V = 0 and the bottom side is held at V = V. yA V.- Find a non-zero equation for V(x, y) that satisfies three of the four boundary conditions. Recall that for arbitrary constants A, B,C, D, and m the following four equations satisfy Laplace's equation in 2-D cartesian coordinates. 1. V(r, y) = (A cosh mx + B sinh mx) (C cos my+D sin my) 2. V(x, y) 3. V (x, y) = (Aem + Be-ma)(C cos my + D sin my) 4. V(x, y) = = (A cos mx + B sin mx)(C cosh my +D sinh my) %3D (A cos mx + B sin mx) (Cemy + De-my

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The cross-section of a long conducting duct is shown in the following figure. Three of the sides are held at V = 0 and the bottom side is held at V = V.. a Vo a Find a non-zero equation for V(x, y) that satisfies three of the four boundary conditions. Recall that for arbitrary constants A, B,C, D, and m the following four equations satisfy Laplace's equation in 2-D cartesian coordinates. 1. V (x, y) 2. V (x, y) = (A cos mx + B sin mx)(C cosh my + D sinh my) 3. V (x, y) = (Aema + Be¬ma)(C cos my + D sin my) 4. V (x, y) = (A cos mx + B sin mæ) (Cemy + De¬my) (A cosh mx + B sinh mx) (C cos my + D sin my) of 2
Transcribed Image Text:The cross-section of a long conducting duct is shown in the following figure. Three of the sides are held at V = 0 and the bottom side is held at V = V.. a Vo a Find a non-zero equation for V(x, y) that satisfies three of the four boundary conditions. Recall that for arbitrary constants A, B,C, D, and m the following four equations satisfy Laplace's equation in 2-D cartesian coordinates. 1. V (x, y) 2. V (x, y) = (A cos mx + B sin mx)(C cosh my + D sinh my) 3. V (x, y) = (Aema + Be¬ma)(C cos my + D sin my) 4. V (x, y) = (A cos mx + B sin mæ) (Cemy + De¬my) (A cosh mx + B sinh mx) (C cos my + D sin my) of 2
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