Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Heat can be transferred in three different ways:conduction, convection,and

radiation.We will give a brief description of each mode to familiarize the

reader with the basic mechanisms of heat transfer. All modes of heat transfer

require the existence of a temperature difference, and all modes of heat

transfer are from the high-temperature medium to a lower temperature one.

Conductionis the transfer of energy from the more energetic particles of

a substance to the adjacent less energetic ones as a result of interactions

between the particles. Conduction can take place in solids, liquids, or gases.

In gases and liquids, conduction is due to the collisions of the molecules

during their random motion. In solids, it is due to the combination of vibra-

tions of molecules in a lattice and the energy transport by free electrons. A

cold canned drink in a warm room, for example, eventually warms up to the

room temperature as a result of heat transfer from the room to the drink

through the aluminum can by conduction (Fig. 2–69).

It is observed that the rate of heat conduction through a layer of con-

stant thickness xis proportional to the temperature difference Tacross the

layer and the area Anormal to the direction of heat transfer, and is inversely

proportional to the thickness of the layer. Therefore,

(2–51)

where the constant of proportionality ktis the thermal conductivityof the

material, which is a measure of the ability of a material to conduct heat

(Table 2–3). Materials such as copper and silver, which are good electric

conductors, are also good heat conductors, and therefore have high ktvalues.

Materials such as rubber, wood, and styrofoam are poor conductors of heat,

and therefore have low ktvalues.

In the limiting case of x→0, the equation above reduces to the differen-

tial form

(2–52)

which is known as Fourier’s lawof heat conduction. It indicates that the

rate of heat conduction in a direction is proportional to the temperature gra-

dientin that direction. Heat is conducted in the direction of decreasing tem-

perature, and the temperature gradient becomes negative when temperature

decreases with increasing x. Therefore, a negative sign is added in Eq. 2–52

to make heat transfer in the positive xdirection a positive quantity.

Temperature is a measure of the kinetic energies of the molecules. In a liq-

uid or gas, the kinetic energy of the molecules is due to the random motion

of the molecules as well as the vibrational and rotational motions. When two

molecules possessing different kinetic energies collide, part of the kinetic

energy of the more energetic (higher temperature) molecule is transferred to

the less energetic (lower temperature) particle, in much the same way as

when two elastic balls of the same mass at different velocities collide, part of

the kinetic energy of the faster ball is transferred to the slower one.

Q

#

cond¬¬
kt A¬

dT

dx

¬¬ 1 W 2

Q

#

cond
kt A¬

¢T

¢x

¬¬ 1 W 2

Q

#

cond

92 | Thermodynamics

TOPIC OF SPECIAL INTEREST* Mechanisms of Heat Transfer

*This section can be skipped without a loss in continuity.

COLA

T 1

Heat

Wall of

aluminum

can

∆x

AIR

T 2

COLA

Heat

AIR

∆T

FIGURE 2–69

Heat conduction from warm air to a
cold canned drink through the wall of
the aluminum can.

SEE TUTORIAL CH. 2, SEC. 9 ON THE DVD.

INTERACTIVE

TUTORIAL