A spherical container with an inner radius r1 = 1 m and an outer radius r2 = 1.05 m has its inner surface subjected to a uniform heat flux of q1=7kw/m^2. The outer surface of the container has a temperature T2 = 25°C, and the container wall thermal conductivity is k = 1.5 W/m·K. Show that the variation of temperature in the container wall can be expressed as and determine the temperature of the inner surface of the container at r = r1. = 1.05 m has its inner surface subjected to a uniform heat flux of q1=7 kW/m2. The outer surface of the container has a2-77 A spherical container with an inner radius n = 1 m and an outer radius25°C, and the container wall thermal conductivity is k 1.5 W/m K. Show that the variation of temperature in the container wall can be expressed as T(r)= (4,r^k(1r 1/r.) + T2 and determinetemperature T2the temperature of the inner surface of the container at r = ^FIGURE P2-77SphericalcontainerT2

Using differential equation for heat conduction,

= 1.05 m has its inner surface subjected to a uniform heat flux of q1=7 kW/m2. The outer surface of the container has a 2-77 A spherical container with an inner radius n = 1 m and an outer radius 25°C, and the container wall thermal conductivity is k 1.5 W/m K. Show that the variation of temperature in the container wall can be expressed as T(r)= (4,r^k(1r 1/r.) + T2 and determine temperature T2 the temperature of the inner surface of the container at r = ^ FIGURE P2-77 Spherical container T2

= 1.05 m has its inner surface subjected to a uniform heat flux of q1=7 kW/m2. The outer surface of the container has a 2-77 A spherical container with an inner radius n = 1 m and an outer radius 25°C, and the container wall thermal conductivity is k 1.5 W/m K. Show that the variation of temperature in the container wall can be expressed as T(r)= (4,r^k(1r 1/r.) + T2 and determine temperature T2 the temperature of the inner surface of the container at r = ^ FIGURE P2-77 Spherical container T2

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.54P

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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

A spherical container with an inner radius r₁ = 1 m and an outer radius r₂ = 1.05 m has its inner surface subjected to a uniform heat flux of q1=7kw/m^2. The outer surface of the container has a temperature T₂ = 25°C, and the container wall thermal conductivity is k = 1.5 W/m·K. Show that the variation of temperature in the container wall can be expressed as and determine the temperature of the inner surface of the container at r = r₁.

= 1.05 m has its inner surface subjected to a uniform heat flux of q1=7 kW/m2. The outer surface of the container has a
2-77 A spherical container with an inner radius n = 1 m and an outer radius
25°C, and the container wall thermal conductivity is k 1.5 W/m K. Show that the variation of temperature in the container wall can be expressed as T(r)= (4,r^k(1r 1/r.) + T2 and determine
temperature T2
the temperature of the inner surface of the container at r = ^
FIGURE P2-77
Spherical
container
T2

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