1. Figure.1 depicts a plane wall of thickness L = 0.2 m experiences uniform volumetric heating at a rate q. One surface of the wall (x = 0) is insulated, and the other surface is exposed to a fluid at T = 25°C, with convection heat transfer characterized by h = 1200 Initially, the temperature distribution in the wall is T(x, 0) = a + bx², where a = 300 °C, b = -1.0 × 10-4, and x is in meters. W m2.K Suddenly, the volumetric heat generation is deactivated (q=0 for t≥0), while convection heat transfer continues to occur at x = L. The properties of the wall are = 5000 kg/m3, cp=500, and k = 100- kg.K' W m.K ,k,p, cp, q(t≤ 0)
1. Figure.1 depicts a plane wall of thickness L = 0.2 m experiences uniform volumetric heating at a rate q. One surface of the wall (x = 0) is insulated, and the other surface is exposed to a fluid at T = 25°C, with convection heat transfer characterized by h = 1200 Initially, the temperature distribution in the wall is T(x, 0) = a + bx², where a = 300 °C, b = -1.0 × 10-4, and x is in meters. W m2.K Suddenly, the volumetric heat generation is deactivated (q=0 for t≥0), while convection heat transfer continues to occur at x = L. The properties of the wall are = 5000 kg/m3, cp=500, and k = 100- kg.K' W m.K ,k,p, cp, q(t≤ 0)
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![1. Figure.1 depicts a plane wall of thickness L = 0.2 m experiences uniform volumetric
heating at a rate q. One surface of the wall (x = 0) is insulated, and the other surface
is exposed to a fluid at T = 25°C, with convection heat transfer characterized by h =
Initially, the temperature distribution in the wall is T(x,0) = a + bx²,
where a = 300 °C, b = -1.0 × 10-4, and x is in meters.
W
1200
m².K
Suddenly, the volumetric heat generation is deactivated (à = 0 for t≥ 0), while
convection heat transfer continues to occur at x = L. The properties of the wall are =
5000 kg/m3, cp = 500 and k = 100-
kg.K'
m.K
L
L
k,p, cp,q(t ≤ 0)
Too, h
111
Fig.1. A heat transfer of a plane wall
(a) Determine the magnitude of the volumetric energy generation rate à associated
with the initial condition (t < 0)
(b) On 7 -x coordinates, sketch the temperature distribution for the following
conditions: initial condition (t < 0), steady-state condition (t → ∞), and two
intermediate conditions.
(c) On q" - t coordinates, sketch the variation with time of the heat flux at the
boundary exposed to the convection process (q" (L, t)). Calculate the corresponding
value of the heat flux at t = 0,q" (L, t).
(d) Calculate the amount of energy removed from the wall per unit area (J/m2) by the
fluid stream as the wall cools from its initial to steady-state condition.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ecfbd04-9453-4891-92a0-8c48cc184af7%2Fbf7e1b57-cec0-4c00-8779-cc4a453589f6%2F84toc6_processed.png&w=3840&q=75)
Transcribed Image Text:1. Figure.1 depicts a plane wall of thickness L = 0.2 m experiences uniform volumetric
heating at a rate q. One surface of the wall (x = 0) is insulated, and the other surface
is exposed to a fluid at T = 25°C, with convection heat transfer characterized by h =
Initially, the temperature distribution in the wall is T(x,0) = a + bx²,
where a = 300 °C, b = -1.0 × 10-4, and x is in meters.
W
1200
m².K
Suddenly, the volumetric heat generation is deactivated (à = 0 for t≥ 0), while
convection heat transfer continues to occur at x = L. The properties of the wall are =
5000 kg/m3, cp = 500 and k = 100-
kg.K'
m.K
L
L
k,p, cp,q(t ≤ 0)
Too, h
111
Fig.1. A heat transfer of a plane wall
(a) Determine the magnitude of the volumetric energy generation rate à associated
with the initial condition (t < 0)
(b) On 7 -x coordinates, sketch the temperature distribution for the following
conditions: initial condition (t < 0), steady-state condition (t → ∞), and two
intermediate conditions.
(c) On q" - t coordinates, sketch the variation with time of the heat flux at the
boundary exposed to the convection process (q" (L, t)). Calculate the corresponding
value of the heat flux at t = 0,q" (L, t).
(d) Calculate the amount of energy removed from the wall per unit area (J/m2) by the
fluid stream as the wall cools from its initial to steady-state condition.
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