Page 185 - Mechanical Engineers' Handbook (Volume 4)

174 Heat-Transfer Fundamentals

Nu CRe 0.5 Pr ( / ) 0.25
0.4
0

D
D
where C 0.95 for cylinders and 1.28 for spheres; is the free stream gas density and 0

is the stagnation density of stream behind the bow shock. The heat-transfer rate for this case,
is given by q A(T T ).h s 0
2.3 Free Convection
In free convection the fluid motion is caused by the buoyant force resulting from the density
difference near the body surface, which is at a temperature different from that of the free
fluid far removed from the surface where velocity is zero. In all free convection correlations,
except for the enclosed cavities, the fluid properties are usually evaluated at the mean film
temperature T (T T )/2. The thermal expansion coefficient , however, is evaluated
ƒ 1
at the free fluid temperature T . The convection heat-transfer coefficient h is based on the

temperature difference between the surface and the free fluid.
Free Convection from Flat Plates and Cylinders
For free convection from flat plates and cylinders, the average Nusselt number Nu L can be
expressed as 4
Nu C(Gr Pr) m
L
L
where the constants C and m are given as shown in Table 15. The Grashof Prandtl number
product, (Gr Pr) is called the Rayleigh number (Ra ) and for certain ranges of this value,
L L
Figs. 13 and 14 are used instead of the above equation. Reasonable approximations for other
types of three-dimensional shapes, such as short cylinders and blocks, can be made for 10 4
1
9
Ra 10 , by using this expression and C 0.6 , m ⁄4, provided that the characteristic
L
length, L, is determined from 1/L 1/L 1/ L , where L is the height and L is
hor ver ver hor
the horizontal dimension of the object in question.
For unsymmetrical horizontal square, rectangular, or circular surfaces, the characteristic
length L can be calculated from the expression L A/P, where A is the area and P is the
wetted perimeter of the surface.
Table 15 Constants for Free Convection from Flat Plates and Cylinders
Geometry Gr K Pr C m L
Vertical flat plates and 10 –10 4 Use Fig. 12 Use Fig. 12 Height of plates and cylinders;
1
cylinders 10 –10 9 0.59 1 restricted to D/L 35/Gr L 1/4
4
⁄4
10 –10 13 0.10 for cylinders
9
1
⁄3
Horizontal cylinders 0–10 5 0.4 0 Diameter D
10 –10 4 Use Fig. 13 Use Fig. 13
5
4
10 –10 9 0.53 1
⁄4
9
10 –10 13 0.13
1
⁄3
4
Upper surface of heated 2 10 –8 10 6 0.54 1 Length of a side for square plates,
⁄4
plates or lower surface 8 10 –10 11 0.15 the average length of the two
6
1
of cooled plates ⁄3 sides for rectangular plates
5
Lower surface of heated 10 –10 11 0.58 1 0.9D for circular disks
⁄5
plates or upper surface
of cooled plates