A 6-cm by 5-cm rectangular silver plate has being uniformly generated at each point at the rate cal cm3 9 = 1.5 ·· sec. Let x represent the distance along the edge of the plate of length 6 cm and y be the distance along the edge of the plate of length 5 cm. Suppose the temperature u along the edges is kept at the following temperatures: 0 ≤ x ≤ 6, u(x,0) = x(6 − x), u(x, 5) = 0, u(0, y) = y(5-y), u(6,y) = 0, 0 ≤ y ≤ 5, where the origin lies at the corner of the plate with coordinates (0,0) and the edges lie along the positive x- and y-axes. The steady-state temperature u = = u(x, y) satisfies Poisson's equation: q K 0 < x < 6, 0 < y < 5, Uxx (x, y) + Uyy (x, y) = == cal where K, the thermal conductivity, is 1.04 cm deg sec difference method (given on page 6 of the lecture notes) with Ax Approximate the temperature u(x, y) using the finite = 3 and Ay = 2.5.
A 6-cm by 5-cm rectangular silver plate has being uniformly generated at each point at the rate cal cm3 9 = 1.5 ·· sec. Let x represent the distance along the edge of the plate of length 6 cm and y be the distance along the edge of the plate of length 5 cm. Suppose the temperature u along the edges is kept at the following temperatures: 0 ≤ x ≤ 6, u(x,0) = x(6 − x), u(x, 5) = 0, u(0, y) = y(5-y), u(6,y) = 0, 0 ≤ y ≤ 5, where the origin lies at the corner of the plate with coordinates (0,0) and the edges lie along the positive x- and y-axes. The steady-state temperature u = = u(x, y) satisfies Poisson's equation: q K 0 < x < 6, 0 < y < 5, Uxx (x, y) + Uyy (x, y) = == cal where K, the thermal conductivity, is 1.04 cm deg sec difference method (given on page 6 of the lecture notes) with Ax Approximate the temperature u(x, y) using the finite = 3 and Ay = 2.5.
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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Transcribed Image Text:A 6-cm by 5-cm rectangular silver plate has being uniformly generated at each point at the rate
9 = 1.5
• sec. Let x represent the distance along the edge of the plate of length 6 cm and y be the
distance along the edge of the plate of length 5 cm. Suppose the temperature u along the edges is kept at
cal
cm³
the following temperatures:
0 ≤ x ≤ 6,
u(x, 0) = x(6 − x),
u(0, y) = y(5 −y),
0 ≤ y ≤ 5,
where the origin lies at the corner of the plate with coordinates (0,0) and the edges lie along the positive x-
and y-axes. The steady-state temperature u = u u(x, y) satisfies Poisson's equation:
0 < x < 6, 0 < y < 5,
u(x, 5) = 0,
u(6,y) = 0,
q
Uxx (x, y) + Uyy (x, y) = ——
K'
cal
where K, the thermal conductivity, is 1.04
difference method (given on page 6 of the lecture notes) with Ax = 3 and Ay = 2.5.
cm.deg.sec
Approximate the temperature u (x, y) using the finite
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