Page 163 - Design and Operation of Heat Exchangers and their Networks

Thermal design of evaporators and condensers 151

data were given by Farber and Scorah (1948) for water boiling on horizontal
chromel wires with diameter of 1mm at the atmospheric pressure (0.5m
below the water level). They divided the whole boiling curve into six
regions:
I. Single-phase natural convective heat transfer from the metal surface
and evaporation at the liquid-vapor interface.
II. Nucleate boiling on the metal surface with bubbles condensed in the
superheated liquid and evaporation at the liquid-vapor interface.
III. Nucleate boiling with bubbles rising to the liquid-vapor interface.
IV. Partial nucleate boiling and unstable film boiling.
V. Stable film boiling.
VI. Radiation dominated film boiling.

4.1.1.1 Natural convection boiling
For natural convection above horizontal hot surfaces of circular, square,
rectangular, and right triangular planforms, Lloyd and Moran (1974) pro-
posed the following correlations:

1=4 4 6
Nu l ¼ 0:54Ra 2:2 10 Ra l < 8 10 (4.1)
l
1=3 6 9
Nu l ¼ 0:15Ra 8 10 Ra l 1:6 10 (4.2)
l
where Ra l is the Rayleigh number
3
gβ l Δt
l
Ra l ¼ ¼ Gr l Pr l (4.3)
ν l a l
Gr l is the Grashof number
3
gβ l Δt
l
Gr l ¼ (4.4)
ν 2
l
Δt is the temperature difference between the temperature of the heating sur-
face and the fluid temperature far from the surface, Δt¼t w t ∞ , and β is the
volumetric thermal expansion coefficient, β¼ (∂ρ/∂T ) p /ρ. The charac-
teristic length l¼A/P, where A is the surface area and P is the surface
perimeter.
For natural convection heat transfer, the properties are evaluated at the
average of the bulk and surface temperatures of the liquid:
t m ¼ t w + t ∞ Þ=2 (4.5)
ð