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1254. A square plate of side a has one side maintained at temperature f(z) and the others at zero, as indicated in Fig. 12-9. Show that the steady-state temperature at any point of the plate is given by u(z, v) = kez krz dz sin kry f(z) sin ainh sinh (ke Obtain the result for f(z) = t, a constant.

1254. A square plate of side a has one side maintained at temperature f(z) and the others at zero, as indicated in Fig. 12-9. Show that the steady-state temperature at any point of the plate is given by u(z, v) = kez krz dz sin kry f(z) sin ainh sinh (ke Obtain the result for f(z) = t, a constant.

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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1254. A square plate of side a has one side maintained at temperature f(z) and the others at zero, as indicated in Fig. 12-9. Show that the steady-state temperature at any point of the plate is given by S Ha) sin? kez krz kry u(z, v) = sinh (kr) dz sin ainh Obtain the result for f(z) = t, a constant.
Transcribed Image Text:1254. A square plate of side a has one side maintained at temperature f(z) and the others at zero, as indicated in Fig. 12-9. Show that the steady-state temperature at any point of the plate is given by S Ha) sin? kez krz kry u(z, v) = sinh (kr) dz sin ainh Obtain the result for f(z) = t, a constant.
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