A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a²u a?u = 0. ax2 ' ay2 Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (Ae x + Be-Px)(C cos py + D sin py).

A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a²u a?u = 0. ax2 ' ay2 Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (Ae x + Be-Px)(C cos py + D sin py).

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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Question

to find the steady state tempreature by assuming the solution to be of the given form

A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The
temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let
u(x, y) denote the temperature satisfying the equation
a?u a?u
0.
ax2' ay2
||
Find the steady state temperature u(x, y), by assuming the solution to be of the form
u(x, y) = (AePx + Be-P*)(C cos py + D sin py).
-px

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