Consider the heat equation dtu = əx2u with solutions defined on 0 s x s 1 and boundary conditions uº(0) = 0,u(1) = 0. Find explicit solutions of the form u(t,x) = v(t)w(x) satisfying the initial condition u(x, t = 0) = COS

Consider the heat equation dtu = əx2u with solutions defined on 0 s x s 1 and boundary conditions uº(0) = 0,u(1) = 0. Find explicit solutions of the form u(t,x) = v(t)w(x) satisfying the initial condition u(x, t = 0) = COS

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Consider the heat equation
dtu = Əx2u
with solutions defined on 0 <xs 1 and boundary conditions u°(0) = 0,u(1) = 0.
Find explicit solutions of the form
u(t,x) = v(t)w(x)
satisfying the initial condition
u(x, t = 0)
= COS

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A Figure illustrates the tube-flow system. The heat transfer under developed flow conditions when the flow remains laminar. The wall temperature is Tw, the center of the tube temperature is Te the radius of the tube is re, and the velocity at the center of the tube is uo. The velocity distribution equation is: 1 uo Prove that: 1 aT uor. T - T= a ax 4 ro Start the solution of the equation : P{żar drjuc,T 1 a ()- aT 1 әт ur дr ar « дх