Explanation Given information: The inner radius of the spherical container is 50 cm , thickness of walls is 5 cm , thermal conductivity of the container is 15 W / m ⋅ K , andthe heat flux is 60 kW / m 2 . Write the expression for one dimensional steady state conduction of heat through the sphere. d d r ( r 2 d T d r ) = 0 ...... (I) Here, the temperature is T and distance is x . Write the expression for the Fourier’s law of heat conduction in the radial direction. q s = − k d T d r ...... (II) Here, thermal conductivity of material is k and the temperature gradient is d T d r . Write the expression for the heat equation for the container. − h [ T s − T ( r ) ] = − k d T d r ...... (III) Here, the heat transfer coefficient at a distance x is h x , temperature of the surrounding medium on left side is T ∞ 1 and the temperature of the surrounding medium on right side is T ∞ 2 and the thermal conductivity of the material is k . Write the expression for the outer radius of pipe. r 2 = r 1 + t ......(IV) Here, thickness of the pipe is t . Calculation: Integrate both sides on Equation (I). ∫ d d r ( r 2 d T d r ) = ∫ 0 d T d r = C 1 r 2 ...... (V) Integrate both sides on Equation (V). ∫ d T d r = ∫ C 1 r 2 T ( r ) = − C 1 r + C 2 ...... (VI) Substitute T ( r 2 ) for T ( r ) and r 2 for r in Equation (VI). T ( r 2 ) = − C 1 r 2 + C 2 ...... (VII) Substitute C 1 r 2 for d T d r , r 1 for r , 60 kW / m 2 for q s , 50 cm for r 1 and 15 W / m ⋅ K for k in Equation (II). 60 kW / m 2 = − 15 W / m ⋅ K ( C 1 ( 50 cm ) 2 ) 60 kW / m 2 ( 1000 W / m 2 1 kW / m 2 ) = − 15 W / m ⋅ K ( C 1 ( 50 cm ( 10 − 2 m 1 cm ) ) 2 ) C 1 = − 1000 Substitute C 1 r 2 for d T d r and r 2 for r in Equation (III)

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ISBN: 9780073398198

Author: CENGEL

Publisher: RENT MCG

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Chapter 2, Problem 80P

To determine

The variation of temperature in the container wall.

The temperatures on the inner and the outer surfaces of the container.

Whether the outer surface temperature is safe to prevent thermal burn.

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Chapter 2, Problem 79P

Chapter 2, Problem 81P

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The variation of temperature in the container wall. The temperatures on the inner and the outer surfaces of the container. Whether the outer surface temperature is safe to prevent thermal burn.

The variation of temperature in the container wall. The temperatures on the inner and the outer surfaces of the container. Whether the outer surface temperature is safe to prevent thermal burn.

Want to see the full answer?

Chapter 2 Solutions

The variation of temperature in the container wall.

The temperatures on the inner and the outer surfaces of the container.

Whether the outer surface temperature is safe to prevent thermal burn.