Page 276 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 22] HEAT TRANSFER 261

SOLVED PROBLEM 22.4
An icebox 3 ft by 3 ft by 2 ft is built of R–0.3 plywood on the inside and outside, with R–10 plastic foam
insulation between the plywood layers. If the box is filled with ice at 32 F and the outside temperature
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is 85 F, how much ice melts per hour?
The thermal resistance of the box walls is
R = R 1 + R 2 + R 3 = 0.3 + 10 + 0.3 = 10.6
The area of the box walls is
A = (2)(3ft)(3ft) + (4)(3ft)(2ft) = 42 ft 2

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and the temperature difference is T = 85 F − 32 F = 53 F. Hence the heat flow is
2
Q A T (42 ft )(53 F)
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= = = 210 Btu/h
t R 10.6ft · F/(Btu/h)
2 ◦
The heat of fusion of water is 144 Btu/lb, so the rate at which ice in the box melts is
m Q/t 210 Btu/h
= = = 1.5 lb/h
t L f 144 Btu/h
CONVECTION
In convection, heat is transferred from one place to another by the actual motion of a hot fluid. Convection is
usually the chief mechanism of heat transfer in fluids.
In natural convection, the buoyancy of a heated fluid leads to its motion. When a pan of water is heated on
a stove, for instance, the hot water at the bottom expands slightly so that its density decreases. The buoyancy of
this water causes it to rise to the surface while colder, denser water sinks to the bottom. In forced convection,
a pump or blower is responsible for the motion of the heated fluid. An example is the cooling system of a car,
in which water is circulated between the hot engine block and the radiator. In the radiator the convected heat is
conducted through thin-walled metal tubes to the atmosphere.
The rate Q/t at which a hot object transfers heat to a surrounding fluid by convection is approximately pro-
portional to the area A of the object in contact with the fluid and to the temperature difference T between them:
Q
= h A T
t
The convection coefficient h depends on the shape and orientation of the object and on the properties and state
of motion of the fluid. For instance, h is greater for the upper surface of a horizontal plate than for its lower
surface, and increases with the speed of the fluid in forced convection.

SOLVED PROBLEM 22.5
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A spotlight has a 50-W bulb in a metal hood whose temperature is 60 C when the room temperature is
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20 C. If the 50-W bulb is replaced by a 75-W bulb, what is the new temperature of the hood?
Because h and A are the same in both cases,

(Q/t) 1 T 1
=
(Q/t) 2 T 2
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When (Q/t) 1 = 50 W, the temperature difference between the hood and the surrounding air is T 1 = 60 C−20 C =
40 C. When (Q/t) 2 = 75 W,
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(Q/t) 2 75 W
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T 2 = T 1 = (40 C) = 60 C
(Q/t) 1 50 W
Hence the new hood temperature is 20 C + 60 C = 80 C
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