# Final Project ```Artoza, Christian Jelo R.
2019-01811
BSCHE 3-1
Computer Applications in ChE
Final Project
Sizing of a Plate-Fin Heat Exchanger
Operating Conditions and Geometrical Variables
The goal is to Design a direct-transfer regenerator for an open-cycle gas-turbine plant
operating at an effectiveness of 0.75355 with the following operating conditions and heat
transfer surfaces.
A. Mean Temperature Calculations and Fluid Properties
Since the exchanger effectiveness was specified in the design problem, the definition of
effectiveness was used to calculate the outlet temperature on both fluid sides.
𝜖=
𝐶ℎ 𝑇ℎ,𝑖 − 𝑇ℎ,𝑜
𝐶𝑚𝑖𝑛 𝑇ℎ,𝑖 − 𝑇𝑐,𝑖
=
𝐶𝑐 𝑇𝑐,𝑜 − 𝑇𝑐,𝑖
𝐶𝑚𝑖𝑛 𝑇ℎ,𝑖 − 𝑇𝑐,𝑖
𝐶
For the first iteration, the same heat capacities for both fluid sides were assumed so that 𝐶ℎ =
𝑚ℎ
.
𝑚𝑐
𝑐
The resulting outlet temperatures for the first iteration were then used to calculate the
mean temperature, and the heat capacity on both fluid sides. With the obtained heat
capacity, a number of iterations were carried out to determine the outlet temperatures, and
subsequently, the mean temperatures and the fluid properties were refined accordingly.
B. NTU Calculations
Both fluids were assumed to be unmixed, and the flow arrangement was set to be crossflow.
Hence, the following effectiveness-NTU relationship was used:
𝜖 = 1 − exp
1
𝐶∗
𝑁𝑇𝑈
0.22
{exp −𝐶 ∗ 𝑁𝑇𝑈
0.78
− 1}
Where 𝐶 ∗ is the capacity rate ratio. The number of transfer units for the gas and air fluid
sides, which are needed in the estimation of the mass velocities, were then estimated as
𝑁𝑇𝑈𝑎𝑖𝑟 = 𝑁𝑇𝑈𝑔𝑎𝑠 = 2𝑁𝑇𝑈.
C. Surface Basic Heat Transfer and Flow Friction Characteristics
Heat transfer and flow friction data were retrieved from Kays and London (2018). With these
data, j and f versus Re plots were constructed and appropriate curve fit models were
obtained. Since Re is unknown in the first iteration, an approximate average of the ratio of
the Colburn factor j to the friction factor f over the complete range of Re was obtained.
Subsequently, mass velocities on the two fluid sides were obtained using the core mass
velocity equation provided by Kays and London (2018):
𝐺=
𝑗
𝑓
Δ𝑃
𝑔𝑐
NTU𝑠𝑖𝑑𝑒 𝑣𝑚 Pr 2/3
Re, j and f on both fluid sides were then calculated with the mass velocities and the heat
transfer data; and heat transfer coefficients were obtained using :
ℎ = 𝑗𝐺𝑐𝑝 Pr −2/3
D. Efficiencies and Overall Coefficient
The fin efficiency and the extended surface efficiency on both fluid sides were obtained as
follows, assuming that no heat transfer occurs at the tip of each fin:
𝜂𝑓 =
tanh 𝑚𝑙
,
𝑚𝑙
𝑚=
2ℎ
,
𝑘𝑓𝛿
𝜂𝑜 = 1 − 1 − 𝜂𝑓
𝐴𝑓
𝐴
Where
𝑙=
𝑏
−𝛿
2
Assuming no fouling resistances, the gas side overall heat transfer coefficient for the first
iteration was obtained by:
1
1
=
𝑈𝑔
𝜂𝑜 ℎ
+
𝑔
𝛼𝑔 Τ𝛼𝑎
𝜂𝑜 ℎ 𝑎
The air side overall coefficient was obtained similarly.
E. Areas and Flow Lengths
F. Pressure Drops
```