=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.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 8CR
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#3

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
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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