The temperature of an electrically heated pipe varies in the radial direction and is defined by the following differential equation: d?T 1 dT dr2 +dr +S = 0 Where T is the temperature, r is the radial coordinate and S is the internal heat source. For a pipe with an inner radius of rinner = 0.04 [m), an outer radius of router = 0.1 (m] and an internal heat source of S = 200,000 ("C/m²), determine the temperature at r = 0.04, 0.06 and 0.08 (m). Solve this as a boundary value problem with = 12,000 ["C/m] at r = 0.04 [m] and T = 40 (C] at r = 0.1 [m). Use centered difference approximations of O(h?) on the derivative terms in the differential equation provided and use backward difference approximation of 0(h) on the Neumann boundary condition. Solve the matrix for temperatures using any method (MATLAB is also acceptable).
The temperature of an electrically heated pipe varies in the radial direction and is defined by the following differential equation: d?T 1 dT dr2 +dr +S = 0 Where T is the temperature, r is the radial coordinate and S is the internal heat source. For a pipe with an inner radius of rinner = 0.04 [m), an outer radius of router = 0.1 (m] and an internal heat source of S = 200,000 ("C/m²), determine the temperature at r = 0.04, 0.06 and 0.08 (m). Solve this as a boundary value problem with = 12,000 ["C/m] at r = 0.04 [m] and T = 40 (C] at r = 0.1 [m). Use centered difference approximations of O(h?) on the derivative terms in the differential equation provided and use backward difference approximation of 0(h) on the Neumann boundary condition. Solve the matrix for temperatures using any method (MATLAB is also acceptable).
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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![The temperature of an electrically heated pipe varies in the radial direction and is defined by the following
differential equation:
d?T 1 dT
+S = 0
dr2'r dr
Where T is the temperature, r is the radial coordinate and S is the internal heat source. For a pipe with
an inner radius of rnner = 0.04 [m), an outer radius of router = 0.1 (m] and an internal heat source of S =
200,000 ['C/m²), determine the temperature at r = 0.04, 0.06 and 0.08 [m). Solve this as a boundary value
dT
problem with = 12,000 ("C/m] at r = 0.04 [m] and T = 40 ('C] at r = 0.1 [m). Use centered difference
approximations of 0(h²) on the derivative terms in the differential equation provided and use backward
difference approximation of 0(h) on the Neumann boundary condition. Solve the matrix for
temperatures using any method (MATLAB is also acceptable).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69c0dee2-b8a1-46a9-ac56-4a3c0b1fd16b%2Fa9c78771-e3bb-49b0-a710-40894b443a85%2Fxmzwnnlf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The temperature of an electrically heated pipe varies in the radial direction and is defined by the following
differential equation:
d?T 1 dT
+S = 0
dr2'r dr
Where T is the temperature, r is the radial coordinate and S is the internal heat source. For a pipe with
an inner radius of rnner = 0.04 [m), an outer radius of router = 0.1 (m] and an internal heat source of S =
200,000 ['C/m²), determine the temperature at r = 0.04, 0.06 and 0.08 [m). Solve this as a boundary value
dT
problem with = 12,000 ("C/m] at r = 0.04 [m] and T = 40 ('C] at r = 0.1 [m). Use centered difference
approximations of 0(h²) on the derivative terms in the differential equation provided and use backward
difference approximation of 0(h) on the Neumann boundary condition. Solve the matrix for
temperatures using any method (MATLAB is also acceptable).
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