Page 167 - Design and Operation of Heat Exchangers and their Networks

Thermal design of evaporators and condensers 155

2. Gorenflo correlation
For R134a, the nucleate boiling heat transfer coefficient at the reference
point can be evaluated with Eq. (4.14):
0:6 5 6 0:6

α 0 ¼ 3580 dp=dTð Þ =σ p¼p 0 ¼ 3580 0:1363 10 =0:01013=10
sat
2
¼ 4277 W=m K
:
For R134a, we use Eqs. (4.15)–(4.17) to calculate F q and F p r
0:3 0:15
n ¼ 0:95 0:3p ¼ 0:9 0:3 0:1208 ¼ 0:7909
r
n 0:7909
F q ¼ q=q 0 Þ ¼ 12, 770=20, 000ð Þ ¼ 0:7013
ð
¼ 0:7p 0:2 +4p r + 1:4p r ¼ 0:7 0:1208 0:2 +4 0:1208 + 1:4 0:1208
F p r r
1 p r 1 0:1208
¼ 1:134
Because the tube material is copper and the surface roughness
R a ¼0.4μm, the correction factor F w ¼1.
F
Thus, the Gorenflo correlation α¼α 0 F q F p r w ¼4277 0.7013
2
1.134 1¼3402W/m K.
The detailed calculation procedure can be found in the MatLab code for
Example 4.1 in the appendix.

4.1.1.3 Critical heat flux
When the heat flux approaches to its critical value, vapor bubbles will grad-
ually cover the heating surface, and boiling heat transfer will reach its max-
imum and then depart from the nucleate boiling; meanwhile, the heat
transfer coefficient will decline. A further increase in the heat flux will cause
a sudden increase in the wall temperature, and the heating surface might be
burn out.
For a horizontal flat plate or a horizontal plain tube, the critical heat flux
can be approximated as (Zuber and Tribus, 1958)
1=4 1=2
σg ρ ρ Þ ρ l
ð
l
v
q cr ¼ C 1 Δh v ρ (4.26)
v
ρ 2 ρ + ρ
v l v
where π p 3 ffiffiffiffi 1 C 1 π p 3 ffiffiffiffi (0.119 C 1 0.157). A convenient average
24 2π 3 1=4 24 2π
value of C 1 for horizontal tubes, spheres, and finite heated surfaces was sug-
gested as C 1 ¼π/24¼0.131. For large horizontal plates, C 1 ¼0.149 (see
Bergman et al., 2011).