=ider some specific examples of the influence of e heated plate. The differential equation is Eq. _ds are insulated Eq. (3.3.9). Consider the follo mperature.
=ider some specific examples of the influence of e heated plate. The differential equation is Eq. _ds are insulated Eq. (3.3.9). Consider the follo mperature.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
#3
Transcribed Image Text:The next exercises consider various app
problems.
(3) Let us consider some specific examples of the influence of the ambient temper-
ature on the heated plate. The differential equation is Eq. (3.3.10) and assume
that the ends are insulated Eq. (3.3.9). Consider the following profiles for the
ambient temperature.
(a)
(b)
Eq.
bq.
T(x)/a
α,
for L/2< |2x - L| <L,
To(x) =
2a - 4a (2x/L − 1)², for |2x - L| < L/2.
Construct the solutions and compare the results by graphing them.
Answer: The temperature profiles for the two cases are shown below for the
choice BL = 5.
T(x)/a
2
1.5
0.5
2
1.5
1
1
0
0.5
0
0
0
To(x) = a + a sin
0.2
(4) Repeat the previous exercise but now assume the boundary conditions are given
solby Eq. (3.3.21).
Answer: The temperature profiles for the two cases are shown below for the
choice BL-5, Ta/a = 1 and To/a = 2.
0.4
0.2
(*).
x/L
0.4
x/L
0.6
(a)
(b)
0.8
0.6
0.8
value
1
1
A
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