Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

11.3 Temperature Difference and Heat Transfer 319

Note, as we explained before, a 15C temperature difference is equal to a 15 K temperature

difference. Substituting for the values ofk,A, (T 1 T 2 ), andLin Equation (11.12),

we have

(Be careful with lowercasek, denoting thermal conductivity, and the capital K, representing

Kelvin, an absolute temperature scale.)

Thermal Resistance

In this section, we will explain what theR-values of insulating materials mean. Most of you

understand the importance of having a well-insulated house because the better insulated a house

is, the less the heating or cooling cost of the house. For example, you may have heard that in

order to reduce heat loss through the attic, some people add enough insulation to their attic so

that theR-value of insulation is 40. But what does theR-value of 40 mean, and what does the

R-value of an insulating material mean in general? Let us start by rearranging Equation (11.12)

in the following manner. Starting with Equation (11.12),

(11.12)

and rearranging it, we have

(11.13)

and thermal resistance L/kA.

Figure 11.9 depicts the idea of thermal resistance and how it is related to the material’s

thickness, area, and thermal conductivity. When examining Equation (11.13), you should note

the following: (1) The heat transfer (flow) rate is directly proportional to the temperature dif-

ference; (2) the heat flow rate is inversely proportional to the thermal resistance — the higher

the value of thermal resistance, the lower the heat transfer rate will be.

When expressing Fourier’s law in the form of Equation (11.13), we are making an analogy

between the flow of heat and the flow of electricity in a wire. Ohm’s law, which relates the volt-

ageVto currentIand the electrical resistanceRe, is analogous to heat flow. Ohm’s law is

expressed as

VRe I (11.14)

q

T 1 T 2

L

kA



temperature difference

thermal resistance

qkA

T 1 T 2

L

qkA

T 1 T 2

L

 1 1.42a

W

m#K

b11.8 m

2

2a

15 K

0.008 m

b4725 W

T 1 T 2 20°C5°C15°C15 K

A 1 1 m 2 1 1.8 m 2 1.8 m

2

1.8 m

1 m

8 mm

Glass

5C

20C

■Figure 11.8

The single-pane window of

Example 11.5.

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