Problem 4 The heated rod from Problem 3 is subject to a volumetric heating h(x) = ho in units of [Wm³], as shown in the figure below. Under the heat supply the temperature of the rod changes along x with the temperature function T(x). The temperature T(x) is governed by the following equations: - d (−x (q(x)) + h(x) = 0 PDE dx \q(x) = − k dT (4) Fourier's law of heat conduction where q(x) is the heat flux through the rod and k is the (constant) thermal conductivity. Both ends of the bar are in contact with a heat reservoir at zero temperature. T(x) h(x) L 8
Problem 4 The heated rod from Problem 3 is subject to a volumetric heating h(x) = ho in units of [Wm³], as shown in the figure below. Under the heat supply the temperature of the rod changes along x with the temperature function T(x). The temperature T(x) is governed by the following equations: - d (−x (q(x)) + h(x) = 0 PDE dx \q(x) = − k dT (4) Fourier's law of heat conduction where q(x) is the heat flux through the rod and k is the (constant) thermal conductivity. Both ends of the bar are in contact with a heat reservoir at zero temperature. T(x) h(x) L 8
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
Related questions
Question
The heated rod from Problem 3 is subject to a volumetric heating
h(x) = h0
x
L
in units of [Wm−3
], as shown in the figure below. Under the
heat supply the temperature of the rod changes along x with the
temperature function T(x). The temperature T(x) is governed by the
following equations:
(
−
d
dx (q(x)) + h(x) = 0 PDE
q(x) = −k
dT
dx Fourier’s law of heat conduction
(4)
where q(x) is the heat flux through the rod and k is the (constant)
thermal conductivity. Both ends of the bar are in contact with a heat
reservoir at zero temperature.
Determine:
1. Appropriate BCs for this physical problem.
2. The temperature function T(x).
3. The heat flux function q(x).
![Problem 4
The heated rod from Problem 3 is subject to a volumetric heating
h(x) = ho in units of [Wm³], as shown in the figure below. Under the
heat supply the temperature of the rod changes along x with the
temperature function T(x). The temperature T(x) is governed by the
following equations:
-
d
(−x (q(x)) + h(x) = 0 PDE
dx
\q(x) = − k dT
(4)
Fourier's law of heat conduction
where q(x) is the heat flux through the rod and k is the (constant)
thermal conductivity. Both ends of the bar are in contact with a heat
reservoir at zero temperature.
T(x)
h(x)
L
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44771ccb-18ef-4ee9-9657-f17f9fc0e809%2F75019ebe-84b9-4a22-873e-9a8eda034050%2F1fl929r_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 4
The heated rod from Problem 3 is subject to a volumetric heating
h(x) = ho in units of [Wm³], as shown in the figure below. Under the
heat supply the temperature of the rod changes along x with the
temperature function T(x). The temperature T(x) is governed by the
following equations:
-
d
(−x (q(x)) + h(x) = 0 PDE
dx
\q(x) = − k dT
(4)
Fourier's law of heat conduction
where q(x) is the heat flux through the rod and k is the (constant)
thermal conductivity. Both ends of the bar are in contact with a heat
reservoir at zero temperature.
T(x)
h(x)
L
8
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