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• Find the solution (U(x, y)) for the following partial differential equations A square plate is bounded by x = 0, x = a,y = 0 and y = a. Apply the Laplace's equation a?u a?u + = 0 əx² ' əy² to determine the potential distribution u(x, y) over the plate, subject to the following boundary conditions u(0, у) %3D 0, и(а, у) %3D 0, 0 < y < a 4), 0

• Find the solution (U(x, y)) for the following partial differential equations A square plate is bounded by x = 0, x = a,y = 0 and y = a. Apply the Laplace's equation a?u a?u + = 0 əx² ' əy² to determine the potential distribution u(x, y) over the plate, subject to the following boundary conditions u(0, у) %3D 0, и(а, у) %3D 0, 0 < y < a 4), 0

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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• Find the solution (U(x, y)) for the following partial differential equations A square plate is bounded by x = 0, x = a,y = 0 and y = a. Apply the Laplace's equation au a?u = 0 əx² ' əy² to determine the potential distribution u(x, y) over the plate, subject to the following boundary conditions u (0, у) %3D 0, и(а, у) %3D 0, 0 < y < a = TTX 2nx и(х, 0) %3 0, и(х, а) + 2 sin - a 0 < x < a, = uo ( sin а where is a constant. Also show that the temperature at the center of the plate is given by: uosinh sinh t
Transcribed Image Text:• Find the solution (U(x, y)) for the following partial differential equations A square plate is bounded by x = 0, x = a,y = 0 and y = a. Apply the Laplace's equation au a?u = 0 əx² ' əy² to determine the potential distribution u(x, y) over the plate, subject to the following boundary conditions u (0, у) %3D 0, и(а, у) %3D 0, 0 < y < a = TTX 2nx и(х, 0) %3 0, и(х, а) + 2 sin - a 0 < x < a, = uo ( sin а where is a constant. Also show that the temperature at the center of the plate is given by: uosinh sinh t
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