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
icon
Related questions
Question
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
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
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,