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

(Steven Felgate) #1

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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