Consider a large plane wall of thickness 2L=20mm. Both surfaces of the wall are convectively cooled by the surrounding coolant at Too = 250°C with a heat transfer coefficient of h= 1100 W/m³.K. A fuel element of a nuclear reactor is considered in the shape of this large plane wall with given constant thermal properties as thermal conductivity k = 30 W/m.K and a = 5 x 10-6m²/s. It is known that heat is generated uniformly within the element at a volumetric rate of q = 1x 107W/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 d2 = 2 × 107W /m³. Assuming steady one-dimensional heat transfer along the wall, use the explicit finite- difference method to show how to calculate temperature To at 1.2 sec and temperature Ts at 1.5 sec. (show which equation to use and the calculations in details)

Consider a large plane wall of thickness 2L=20mm. Both surfaces of the wall are convectively cooled by the surrounding coolant at Too = 250°C with a heat transfer coefficient of h= 1100 W/m³.K. A fuel element of a nuclear reactor is considered in the shape of this large plane wall with given constant thermal properties as thermal conductivity k = 30 W/m.K and a = 5 x 10-6m²/s. It is known that heat is generated uniformly within the element at a volumetric rate of q = 1x 107W/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 d2 = 2 × 107W /m³. Assuming steady one-dimensional heat transfer along the wall, use the explicit finite- difference method to show how to calculate temperature To at 1.2 sec and temperature Ts at 1.5 sec. (show which equation to use and the calculations in details)

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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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

Consider a large plane wall of thickness 2L=20mm. Both surfaces of the wall are
convectively cooled by the surrounding coolant at To = 250°C with a heat transfer
coefficient of h= 1100 W/m².K. A fuel element of a nuclear reactor is considered in the
shape of this large plane wall with given constant thermal properties as thermal
conductivity k = 30 W/m.K and a = 5 x 10-6m²/s. It is known that heat is generated
uniformly within the element at a volumetric rate of q = 1x 107W /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 q2 = 2 x 107W/m³.
Assuming steady one-dimensional heat transfer along the wall, use the explicit finite-
difference method to show how to calculate temperature To at 1.2 sec and temperature
Ts at 1.5 sec. (show which equation to use and the calculations in details)

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