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Thermodynamics HW Solutions 53
Course: PHY 4803, Fall 2010School: UNF
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1 Chapter Basics of Heat Transfer 1-104E A spherical ball whose surface is maintained at a temperature of 170F is suspended in the middle of a room at 70F. The total rate of heat transfer from the ball is to be determined. Assumptions 1 Steady operating conditions exist since the ball surface and the surrounding air and surfaces remain at constant temperatures. 2 The thermal properties of the ball and the...
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1 Chapter Basics of Heat Transfer
1-104E A spherical ball whose surface is maintained at a temperature of 170F is suspended in the middle
of a room at 70F. The total rate of heat transfer from the ball is to be determined.
Assumptions 1 Steady operating conditions exist since the ball surface and the surrounding air and surfaces
remain at constant temperatures. 2 The thermal properties of the ball and the convection heat transfer
coefficient are constant and uniform.
Properties The emissivity of the ball surface is given to be = 0.8.
Analysis The heat transfer surface area is
Air
70F
170F
As = D = ft) (2/12 = 0.08727 ft
Under steady conditions, the rates of convection and radiation heat transfer are
D = 2 in
Q
&
Qconv = hAs T = (12Btu/h.ft 2 o F)(0.08727ft 2 )(170 70) o F = 104.7 Btu/h
&
Q rad = As (Ts4 To4 )
= 0.8(0.08727ft 2 )(0.1714 10 8 Btu/h.ft 2 R 4 )[(170 + 460R) 4 (70 + 460R) 4 ]
= 9.4 Btu/h
Therefore,
&
&
&
Qtotal = Qconv + Qrad = 104.7 + 9.4 = 114.1 Btu / h
Discussion Note that heat loss by convection is several times that of heat loss by radiation. The radiation
heat loss can further be reduced by coating the ball with a low-emissivity material.
1-53
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