172 Chapter 7 Length and Length-Related Parameters
surfaces, or fins as shown in Figure 7.7. If you look closely inside buildings around your cam-
pus, you will also see heat exchangers or radiators with extended surfaces under windows and
against some walls. As you know, these heat exchangers or radiators supply heat to rooms and
hallways during the winter. For another example, have you ever thought about why crushed ice
cools a drink faster than ice cubes? It is because given the same amount of ice, the crushed ice
has more surface exposed to the liquid. You may have also noticed that given the same amount
of meat, it takes longer for a roast of beef to cook than it takes stew. Again, it is because the stew
has more surface area exposed to the liquid in which it is being cooked. So next time you are
planning to make some mashed potatoes, make sure you first cut the potatoes into smaller
pieces. The smaller the pieces, the sooner they will cook. Of course, the reverse is also true.
That is, if you want to reduce the heat loss from something, one way of doing this would be to
reduce the exposed surface area. For example, when we feel cold we naturally try to curl up,
which reduces the surface area exposed to the cold surroundings. You can tell by observing
nature that trees take advantage of the effect and importance of surface area. Why do trees have
lots of leaves rather than one big leaf? It is because they can absorb more solar radiation that
way. Surface area is also important in engineering problems related to mass transfer. Your par-
ents or grandparents perhaps recall when they used to hang out clothes to dry. The clothes were
hung over the clothesline in such way that they had a maximum area exposed to the air. Bed-
sheets, for example, were stretched out fully across the clothesline.
Let us now investigate the relationship between a given volume and exposed surface area. Con-
sider a 1 m 1 m 1 m cube. What is the volume? 1 m
3. What is the exposed surface area of this
cube? 6 m
2
. If we divide each dimension of this cube by half, we get 8 smaller cubes with the
dimensions of 0.5 m 0.5 m 0.5 m, as shown in Figure 7.8. What is the total volume of the 8
smaller cubes? It is still 1 m
3
. What is the total exposed surface area of the cubes? Each cube now
has an exposed surface area of 1.5 m
2
, which amounts to a total exposed surface area of 12 m
2
.
Let us proceed with dividing the dimensions of our 1 m 1 m 1 m original cube into
even smaller cubes with the dimensions of 0.25 m 0.25 m 0.25 m. We will now have
64 smaller cubes, and we note that the total volume of the cubes is still 1 m
3
. However, the
surface area of each cube is 0.375 m
2
, leading to a total surface area of 24 m
2
. Thus, the same
cube divided into 64 smaller cubes now has an exposed surface area that is four times the origi-
nal surface area.
■Figure 7.7
The important role of area in the
design of various systems.Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀