25. Develop an algorithm, along with the program (in python), to find the temperature distribution in the Problem 5.102 NOTE: Use the explicit finite differences method 5.102 Consider the fuel element of Example 5.9. Initially, the element is at a uniform temperature of 250°C with no heat generation. Suddenly, the element is inserted into the reactor core causing a uniform volumetric heat generation rate of q = 108 W/m³. The surfaces are convectively cooled with T = 250°C and_h= 1100 W/m² K. Using the explicit method with a space increment of 2 mm, determine the temperature distribution 1.5 s after the element is inserted into the core. EXAMPLE 5.9 A fuel element of a nuclear reactor is in the shape of a plane wall of thickness 2L = 20 mm and is convectively cooled at both surfaces, with h = 1100 W/m². K and T=250°C. At normal operating power, heat is generated uniformly within the element at a volumetric rate of q₁ = 107 W/m³. A departure from the steady-state conditions associated with normal operation will occur if there is a change in the generation rate. Consider a sudden change to %2 = 2 × 107 W/m³, and use the explicit finite-difference method to determine the fuel element temperature distribu- tion after 1.5 s. The fuel element thermal properties are k=30 W/m • K and a = 5 × 10-6 m²/s. .

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Author:Sadiku, Matthew N. O.
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25. Develop an algorithm, along with the program (in python), to find the temperature
distribution in the Problem 5.102
NOTE: Use the explicit finite differences method
5.102 Consider the fuel element of Example 5.9. Initially,
the element is at a uniform temperature of 250°C with
no heat generation. Suddenly, the element is inserted
into the reactor core causing a uniform volumetric heat
generation rate of q = 108 W/m³. The surfaces are
convectively cooled with T = 250°C and_h=
1100 W/m² K. Using the explicit method with a
space increment of 2 mm, determine the temperature
distribution 1.5 s after the element is inserted into the
core.
EXAMPLE 5.9
A fuel element of a nuclear reactor is in the shape of a plane wall of thickness
2L = 20 mm and is convectively cooled at both surfaces, with h = 1100 W/m². K
and T=250°C. At normal operating power, heat is generated uniformly within the
element at a volumetric rate of q₁ = 107 W/m³. A departure from the steady-state
conditions associated with normal operation will occur if there is a change in the
generation rate. Consider a sudden change to %2 = 2 × 107 W/m³, and use the
explicit finite-difference method to determine the fuel element temperature distribu-
tion after 1.5 s. The fuel element thermal properties are k=30 W/m • K and a =
5 × 10-6 m²/s.
.
Transcribed Image Text:25. Develop an algorithm, along with the program (in python), to find the temperature distribution in the Problem 5.102 NOTE: Use the explicit finite differences method 5.102 Consider the fuel element of Example 5.9. Initially, the element is at a uniform temperature of 250°C with no heat generation. Suddenly, the element is inserted into the reactor core causing a uniform volumetric heat generation rate of q = 108 W/m³. The surfaces are convectively cooled with T = 250°C and_h= 1100 W/m² K. Using the explicit method with a space increment of 2 mm, determine the temperature distribution 1.5 s after the element is inserted into the core. EXAMPLE 5.9 A fuel element of a nuclear reactor is in the shape of a plane wall of thickness 2L = 20 mm and is convectively cooled at both surfaces, with h = 1100 W/m². K and T=250°C. At normal operating power, heat is generated uniformly within the element at a volumetric rate of q₁ = 107 W/m³. A departure from the steady-state conditions associated with normal operation will occur if there is a change in the generation rate. Consider a sudden change to %2 = 2 × 107 W/m³, and use the explicit finite-difference method to determine the fuel element temperature distribu- tion after 1.5 s. The fuel element thermal properties are k=30 W/m • K and a = 5 × 10-6 m²/s. .
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