r2 N Тоо 8 Pipe at Tb Fin The temperature distribution T(r) in an annular fin of inner radius 11 and outer radius 12 is described by the ordinary differential equation: d² dT r. dr² - - FT + T = rm² (T - T∞) = 0 where r is the radial distance from the centerline of the pipe and m² is a function of the heat transfer coefficient, thermal conductivity, and thickness of the annulus and is a known constant. Using central differences, work out the finite difference representation of the differential equation in recursion form. Save this, as you will need to scan or take a photo and upload it as proof of your work. == For Ar=0.1, m² 21, and r = 0.8, what are the left off-diagonal terms that you would insert into a coefficient matrix to solve this problem? In other words, what are the coefficients for Ti-1 for all the interior (meaning non-boundary) nodes?
r2 N Тоо 8 Pipe at Tb Fin The temperature distribution T(r) in an annular fin of inner radius 11 and outer radius 12 is described by the ordinary differential equation: d² dT r. dr² - - FT + T = rm² (T - T∞) = 0 where r is the radial distance from the centerline of the pipe and m² is a function of the heat transfer coefficient, thermal conductivity, and thickness of the annulus and is a known constant. Using central differences, work out the finite difference representation of the differential equation in recursion form. Save this, as you will need to scan or take a photo and upload it as proof of your work. == For Ar=0.1, m² 21, and r = 0.8, what are the left off-diagonal terms that you would insert into a coefficient matrix to solve this problem? In other words, what are the coefficients for Ti-1 for all the interior (meaning non-boundary) nodes?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:r2
N
Тоо
8
Pipe at Tb
Fin
The temperature distribution T(r) in an annular fin of inner radius 11 and outer radius 12 is described by the ordinary
differential equation:
d²
dT
r.
dr²
-
-
FT + T = rm² (T - T∞) = 0
where r is the radial distance from the centerline of the pipe and m² is a function of the heat transfer coefficient, thermal
conductivity, and thickness of the annulus and is a known constant.
Using central differences, work out the finite difference representation of the differential equation in recursion form. Save this,
as you will need to scan or take a photo and upload it as proof of your work.
==
For Ar=0.1, m²
21, and r = 0.8, what are the left off-diagonal terms that you would insert into a coefficient matrix to
solve this problem? In other words, what are the coefficients for Ti-1 for all the interior (meaning non-boundary) nodes?
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