Page 464 - Bird R.B. Transport phenomena

444 Chapter 14 Interphase Transport in Nonisothermal Systems

Table 14.6-1 The Factor d in Eq. 14.6-5, and the D in the Nusselt
Number, for Several Representative Shapes"
Vertical Horizontal Horizontal
Shape —» plate plate 0 cylinder Sphere
1.0 0.835 0.772 0.878

"D" in Nu Height H Width W Diameter D Diameter D
" For a hot upper surface and an insulated lower one, or the reverse for cold
surfaces.

Table 14.6-2 The Factor C 2 as a Function of the Prandtl Number
Hg Gases Water Oils
Pr 0.022 0.71 1.0 2.0 4.0 6.0 50 100 2000

Q 0.287 0.515 0.534 0.568 0.595 0.608 0.650 0.656 0.668

For the vertical plate with a constant-heat-flux boundary condition, the recommended
power on GrPr is also 1/5.
Laminar free-convection heat fluxes tend to be small, and a conduction correction
is often necessary for accurate predictions. The conduction limit is determined by
2
solving the equation V T = 0 for the given geometry, and this leads to the calculation
nd
of a "conduction Nusselt number/' Nu™ . Then the combined Nusselt number,
mb
Nu™ , is estimated by combining the two contributing Nusselt numbers by an equa-
tion of the form 1
mb
d
Nu™ = [(NUJT)" + Nur r] 1 / n (14.6-8)
(
Optimum values of n are shape-dependent, but 1.07 is a suggested rough estimate in the
absence of specific information.

Turbulent Boundary Layers

The effects of turbulence increase gradually, and it is common practice to combine the
laminar and turbulent contributions as follows: 1
rb
mb w
Nu£ ee = [(Nu™ ) + (Nu£ H 1/w (14.6-9)
Thus for the vertical isothermal flat plate, one writes 1

Nu;urb = C 3 ( G r P r ) 1 / 3
Nu ;
9
1 + (1.4 X 10 /Gr)
with
013Pr° 22
С з = . р о.в .
( 1 + о 61 г 1)О 42
and m = 6. The values of m in Eq. 14.6-9 are heavily geometry-dependent.