The fin efficiency, "fin is defined as the ratio of actual heat transfer rate, act from the fin at the point of attachment to the ideal heat transfer rate, ideal from the fin if the entire fin were at wall temperature T wall' That is, dT Mfin 9 act 9 ideal -KA dx x = 0 hCL(Twall - Tfluid) Derive the analytical form of the fin efficiency based on each analytical T(x) solution obtained in questions (1) and (3). Again, let a² = Ch ка when formulating your solution. (Use T, to represent Tfluid and T W to represent Twall in your response.) question (1) Mfin question (3) Fin = What do you notice about each analytical form? What happens as L, the length of the fin, increases in each case? For the solution obtained in question (1), as L increases, the fin efficiency |---Select--- For the solution obtained in question (3), as L increases, the fin efficiency ---Select--- That is, the amount of heat removed from the fin to the ambient fluid ---Select--- at positions further away from the point where the fin is attached to the wall, x = 0. That is, the amount of heat removed from the fin to the ambient fluid ---Select--- at positions further away from the point where the fin is attached to the wall, x = 0. ax e (T-1;)e2aL + e 2aL + If 1+e T(x) = T @ - 1+e T f 2aL Question #1 T(x) = T. Twe -al e - -al Te -T. -al + eal -al Te eax + + Tw - T₂ +eaI)2 Te-a² + ea + #
The fin efficiency, "fin is defined as the ratio of actual heat transfer rate, act from the fin at the point of attachment to the ideal heat transfer rate, ideal from the fin if the entire fin were at wall temperature T wall' That is, dT Mfin 9 act 9 ideal -KA dx x = 0 hCL(Twall - Tfluid) Derive the analytical form of the fin efficiency based on each analytical T(x) solution obtained in questions (1) and (3). Again, let a² = Ch ка when formulating your solution. (Use T, to represent Tfluid and T W to represent Twall in your response.) question (1) Mfin question (3) Fin = What do you notice about each analytical form? What happens as L, the length of the fin, increases in each case? For the solution obtained in question (1), as L increases, the fin efficiency |---Select--- For the solution obtained in question (3), as L increases, the fin efficiency ---Select--- That is, the amount of heat removed from the fin to the ambient fluid ---Select--- at positions further away from the point where the fin is attached to the wall, x = 0. That is, the amount of heat removed from the fin to the ambient fluid ---Select--- at positions further away from the point where the fin is attached to the wall, x = 0. ax e (T-1;)e2aL + e 2aL + If 1+e T(x) = T @ - 1+e T f 2aL Question #1 T(x) = T. Twe -al e - -al Te -T. -al + eal -al Te eax + + Tw - T₂ +eaI)2 Te-a² + ea + #
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
I need help with this problem described below and an explanation for the solution. (Differential Equations)
The problems involves 2 equations attached below:
Question 1's T(x) is Labelled in image below
Questions 3's T(x) is Labelled in image below
Transcribed Image Text:The fin efficiency, "fin is defined as the ratio of actual heat transfer rate, act from the fin at the point of attachment to the ideal heat transfer rate, ideal from the fin if the entire fin were at wall temperature T
wall'
That is,
dT
Mfin
9 act
9 ideal
-KA
dx x = 0
hCL(Twall - Tfluid)
Derive the analytical form of the fin efficiency based on each analytical T(x) solution obtained in questions (1) and (3). Again, let a² =
Ch
ка
when formulating your solution. (Use T, to represent Tfluid and T
W
to represent Twall in your response.)
question (1)
Mfin
question (3)
Fin
=
What do you notice about each analytical form? What happens as L, the length of the fin, increases in each case?
For the solution obtained in question (1), as L increases, the fin efficiency |---Select---
For the solution obtained in question (3), as L increases, the fin efficiency ---Select---
That is, the amount of heat removed from the fin to the ambient fluid ---Select--- at positions further away from the point where the fin is attached to the wall, x = 0.
That is, the amount of heat removed from the fin to the ambient fluid ---Select--- at positions further away from the point where the fin is attached to the wall, x = 0.
Transcribed Image Text:ax
e
(T-1;)e2aL
+
e
2aL
+ If
1+e
T(x) =
T
@
-
1+e
T
f
2aL
Question #1
T(x) =
T.
Twe
-al
e
-
-al
Te -T.
-al + eal
-al
Te
eax +
+ Tw
-
T₂
+eaI)2
Te-a² + ea
+
#
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