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Where Gr is Grashof number and Pr is Prandtl number, the volumetric expansion
coefficient of the fluid and the kinetic viscosity of the fluid.
Values of and are evaluated at interface film temperature which is defined as [50]:
The average Rayleigh number for this interface is
T
f
Ts Tfl
(3.15)
2
46
6
5.462 10 [19]. This
gives C 0.54 and n 1/ 4 for fluid above hot plate [47] (see Appendix XIX for values
of C and n of different situations). Thus, Eq. (3.11) can be rewritten as:
R
Bwn
1
k A g ( T T
)
0.54 [ Pr ]
w Bw w
3
Bw CBu w
Bw
2
w
Where w , w and Prw are evaluated at the film temperature
for circular interface [50].
The total resistance from heating plate to the water bottom is:
R
Hpw
w Bw w
3
Bw CBu w
Bw
2
w
w
1 4
TCBu Tw
1
0.00954
k A g ( T T
)
0.54 [ Pr ]
2
w
1 4
(3.16)
D
while
Bw
4
(3.17)
Where the value 0.00954 is the thermal resistance from the heating plate top to the
chamber base top as shown in Table 3.1.
The average thermal resistance from heating plate top to the water (including the
interface between the chamber base and water) is 0.2711K/W [19]. Thus the chamber
base upper surface temperature can be calculated based on the ratio below:
T T
Hp CBu
T T
Hp W
0.00954
0.035
(3.18)
0.2711
This shows that the chamber base upper surface temperature is close to the heating plate
temperature. Thus, TCBu is assumed the same asTHp which will be discussed below.
Bw