The conduction heat transfer in an extended surface, known as a fin, yields the following equation for the temperature T, if the temperature distribution is assumed to be one-dimensional in x, where x is the distance from the base of the fin, as shown in figure: To Fin →→X T(X) d²T hp dx² KA h,T Heat Loss (T-T 0 dT dx Here, p is the perimeter of the fin, being 2R for a cylindrical fin of radius R; A is the cross-sectional area, being R2 for a cylindrical fin; k is the At x = 0: T=T₁ dT At x=L: dx =0 thermal conductivity of the material; T is the ambient fluid temperature; and h in the convective heat transfer coefficient. The boundary conditions are as follows: = 0 where L is the length of the fin. Solve this equation to obtain 7(x) by using Euler's method for R=1cm, h=20 W/m².K, k = 15 W/m-K, L = 25 cm, T=80°C, and T = 20°C.

The conduction heat transfer in an extended surface, known as a fin, yields the following equation for the temperature T, if the temperature distribution is assumed to be one-dimensional in x, where x is the distance from the base of the fin, as shown in figure: To Fin →→X T(X) d²T hp dx² KA h,T Heat Loss (T-T 0 dT dx Here, p is the perimeter of the fin, being 2R for a cylindrical fin of radius R; A is the cross-sectional area, being R2 for a cylindrical fin; k is the At x = 0: T=T₁ dT At x=L: dx =0 thermal conductivity of the material; T is the ambient fluid temperature; and h in the convective heat transfer coefficient. The boundary conditions are as follows: = 0 where L is the length of the fin. Solve this equation to obtain 7(x) by using Euler's method for R=1cm, h=20 W/m².K, k = 15 W/m-K, L = 25 cm, T=80°C, and T = 20°C.

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

The conduction heat transfer in an extended surface, known as a fin, yields
the following equation for the temperature T, if the temperature distribution
is assumed to be one-dimensional in x, where x is the distance from the
base of the fin, as shown in figure:
To
Fin
>X
T(x)
h,T
Heat Loss
d²T_hp (T-T) = 0
dx² ΚΑ
dT
dx
= 0
Here, p is the perimeter of the fin, being 2R for a cylindrical fin of radius
R; A is the cross-sectional area, being R2 for a cylindrical fin; k is the
At x = 0: T = T₁
dT
At x=L:
:0
dx
thermal conductivity of the material; T is the ambient fluid temperature;
and h in the convective heat transfer coefficient. The boundary conditions
are as follows:
where L is the length of the fin. Solve this equation to obtain 7(x) by using
Euler's method for R=1cm, h= 20 W/m².K, k = 15 W/m-K, L = 25 cm,
T₁ = 80°C, and T = 20°C.

Hint:
By nondimensionalzing the governing equation, you can apply the
numerical results obtained to a wide range of physical parameters, given
here as k, A, L, h, p, and T.
Use dimensionless temperature and distance X, defined as follows:
0 =
●
T-T
To-To
Format for submitting projects:
• Abstract
● Nomenclature
• Introduction
Analysis: Derivation of Equations
Results (Tables, Graphs)
• Discussion of Results
● Conclusions
● References
Program Listing
The governing equation then becomes
d²0 hpL²
= -0 = P²0
dx² ΚΑ
Here, P is a dimensionless parameter that characterizes the problem.
X =
X
L
where P =
hp
ΚΑ
L

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