11B.4. Heat conduction in a spherical shell (Fig. 11B.4). A spherical shell has inner and outer radiiR₁ and R₂. A hole is made in the shell at the north pole by cutting out the conical segment inthe region 0 ≤ 0 ≤ 0₁. A similar hole is made at the south pole by removing the portion (™-0₁) ≤ 0 ≤7. The surface 0 = 0, is kept at temperature T = T₁, and the surface at 0= 7 - 0₁ isheld at T = T₂. Find the steady-state temperature distribution, using the heat conductionequation.364 Chapter 11 The Equations of Change for Nonisothermal Systems0₁ 0₁(a)R₂SolidInsulatedsurfacesHole at top(at "north pole")Similar holeat "south pole"(b)Fig. 11B.4. Heat conduction in a spherical shell: (a) cross sectioncontaining the z-axis; (b) view of the sphere from above.

Answered: Image /qna-images/answer/320da7fb-660b-4435-881b-0027f1451c7a.jpg

11B.4. Heat conduction in a spherical shell (Fig. 11B.4). A spherical shell has inner and outer radii R₁ and R₂. A hole is made in the shell at the north pole by cutting out the conical segment in the region 0 ≤00₁. A similar hole is made at the south pole by removing the portion (7- 0₁) ≤0. The surface 0 = 0, is kept at temperature T = T₁, and the surface at 0 = - 0, is held at T = T₂. Find the steady-state temperature distribution, using the heat conduction equation. 364 Chapter 11 The Equations of Change for Nonisothermal Systems R₁ Solid Insulated surfaces Hole at top (at "north pole") Similar hole at "south pole" (a) (b) Fig. 11B.4. Heat conduction in a spherical shell: (a) cross section containing the z-axis; (b) view of the sphere from above. -

11B.4. Heat conduction in a spherical shell (Fig. 11B.4). A spherical shell has inner and outer radii R₁ and R₂. A hole is made in the shell at the north pole by cutting out the conical segment in the region 0 ≤00₁. A similar hole is made at the south pole by removing the portion (7- 0₁) ≤0. The surface 0 = 0, is kept at temperature T = T₁, and the surface at 0 = - 0, is held at T = T₂. Find the steady-state temperature distribution, using the heat conduction equation. 364 Chapter 11 The Equations of Change for Nonisothermal Systems R₁ Solid Insulated surfaces Hole at top (at "north pole") Similar hole at "south pole" (a) (b) Fig. 11B.4. Heat conduction in a spherical shell: (a) cross section containing the z-axis; (b) view of the sphere from above. -

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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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

11B.4. Heat conduction in a spherical shell (Fig. 11B.4). A spherical shell has inner and outer radii
R₁ and R₂. A hole is made in the shell at the north pole by cutting out the conical segment in
the region 0 ≤ 0 ≤ 0₁. A similar hole is made at the south pole by removing the portion (™-
0₁) ≤ 0 ≤7. The surface 0 = 0, is kept at temperature T = T₁, and the surface at 0= 7 - 0₁ is
held at T = T₂. Find the steady-state temperature distribution, using the heat conduction
equation.
364 Chapter 11 The Equations of Change for Nonisothermal Systems
0₁ 0₁
(a)
R₂
Solid
Insulated
surfaces
Hole at top
(at "north pole")
Similar hole
at "south pole"
(b)
Fig. 11B.4. Heat conduction in a spherical shell: (a) cross section
containing the z-axis; (b) view of the sphere from above.

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