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A spherical particle of radius ri experiences uniform thermal generation at a rate of q. The particle is encapsulated by a spherical shell of outside radius r, that is cooled by ambient air. The thermal conductivities of the particle and shell are k and ka, respectively, where kı = 2ka Chemical reaction Ambient air Th Control volume B Control volume A a. By applying the conservation of energy principle to spherical control volume A, which is placed at an arbitrary location within the sphere, determine a relationship between the temperature gradient dT/dr and the local radius r, for 0srs ri. b. By applying the conservation of energy principle to spherical control volume B, which is placed at an arbitrary location within the spherical shell, determine a relationship between the temperature gradient dT/dr and the local radius r, for ri s rsr2. c. On T-r coordinates, sketch the temperature distribution over the range Osrs2

A spherical particle of radius ri experiences uniform thermal generation at a rate of q. The particle is encapsulated by a spherical shell of outside radius r, that is cooled by ambient air. The thermal conductivities of the particle and shell are k and ka, respectively, where kı = 2ka Chemical reaction Ambient air Th Control volume B Control volume A a. By applying the conservation of energy principle to spherical control volume A, which is placed at an arbitrary location within the sphere, determine a relationship between the temperature gradient dT/dr and the local radius r, for 0srs ri. b. By applying the conservation of energy principle to spherical control volume B, which is placed at an arbitrary location within the spherical shell, determine a relationship between the temperature gradient dT/dr and the local radius r, for ri s rsr2. c. On T-r coordinates, sketch the temperature distribution over the range Osrs2

Elements Of Electromagnetics
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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A spherical particle of radius ri experiences uniform thermal generation at a rate of q. The particle is encapsulated by a spherical shell of outside radius r, that is cooled by ambient air. The thermal conductivities of the particle and shell are k and ka, respectively, where ki 2ka Chemical reaction Ambient air Control volume B Control volume A a. By applying the conservation of energy principle to spherical control volume A, which is placed at an arbitrary location within the sphere, determine a relationship between the temperature gradient dT/dr and the local radius r, for 0srs ri. b. By applying the conservation of energy principle to spherical control volume B, which is placed at an arbitrary location within the spherical shell, determine a relationship between the temperature gradient dT/dr and the local radius r, for ri srs r2. c. On T -r coordinates, sketch the temperature distribution over the range 0srsn The rear window of an automobile is defogged by passing warm air over its inner surface. (a) If the warm air is at T = 40°C and the corresponding convection coefficient is h = 30 W/m2 - K, what are the inner and outer surface temperatures of 4-mm-thick %3D
Transcribed Image Text:A spherical particle of radius ri experiences uniform thermal generation at a rate of q. The particle is encapsulated by a spherical shell of outside radius r, that is cooled by ambient air. The thermal conductivities of the particle and shell are k and ka, respectively, where ki 2ka Chemical reaction Ambient air Control volume B Control volume A a. By applying the conservation of energy principle to spherical control volume A, which is placed at an arbitrary location within the sphere, determine a relationship between the temperature gradient dT/dr and the local radius r, for 0srs ri. b. By applying the conservation of energy principle to spherical control volume B, which is placed at an arbitrary location within the spherical shell, determine a relationship between the temperature gradient dT/dr and the local radius r, for ri srs r2. c. On T -r coordinates, sketch the temperature distribution over the range 0srsn The rear window of an automobile is defogged by passing warm air over its inner surface. (a) If the warm air is at T = 40°C and the corresponding convection coefficient is h = 30 W/m2 - K, what are the inner and outer surface temperatures of 4-mm-thick %3D
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