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 dx (g(x)) + h(x) = 0 PDE q(x) = −kdx -кат (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 00
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
d
following equations:
−
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).
Side Note: Please see that both ends of bar are in contact with a heat reservoir at zero temperature so the boundary condition at the right cannot be du/dx=0 because its not thermally insulated. Thank you
![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
dx
(g(x)) + h(x) = 0 PDE
q(x) = −kdx
-кат
(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
00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44771ccb-18ef-4ee9-9657-f17f9fc0e809%2Fe1ce306d-337a-427d-a684-00807125d427%2Foarrr4_processed.png&w=3840&q=75)
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