Manual calculation of heat exchangers

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Now, the calculations related to heat exchangers are all done using computers; I merely hope that through these calculations, people can gain an intuitive understanding of how such calculations are carried out! Optimal Design of Tubular Heat Exchangers Xie Tao Abstract: An overall optimization approach and simplified calculation procedures for designing tubular heat exchangers are proposed, thereby facilitating designers in carrying out calculations to obtain appropriate or optimal designs. Keywords: Tubular heat exchangers ； Overall design ； Optimize ； Simplified classification number: O6-04 Document code: A The Optimal Design of the Shell and Tube Heat Exchanger *E Tao (Department of Chemistry and Chemical Engineering, Guangxi University for Nationalities, Nanning, Guangxi, 530006, China) Abstract: The author presents a method for optimizing and simplifying the overall design of shell and tube heat exchangers, in order to simplify calculations and achieve a suitable or optimal design. Keywords: Shell and tube heat exchanger ； Entire design ； Optimization ； **Simplicity 0 – Introduction**
Shell-and-tube heat exchangers are heat exchangers with a robust structure, high reliability, strong adaptability, and a wide range of applicable materials. Therefore, they serve as the main structural form for large-scale heat exchangers used in petroleum and chemical industries, especially under conditions of high temperature and pressure. Currently, research on heat exchangers mainly focuses on aspects such as the heat transfer performance of non-standard heat transfer tubes; there are few reports regarding the overall optimization and simplified design of heat exchangers.

**1 Design Steps and Calculations for Shell-and-Tube Heat Exchangers**
**1.1 Process Calculations**
In designing a shell-and-tube heat exchanger, it is first necessary to determine the required heat transfer area based on process requirements through chemical engineering calculations. Subsequently, the tube diameter, tube length, number of tubes, number of tube passes, and number of shell passes must be selected.

**1.1.1 Preliminary Design of the Heat Exchanger**
① Heat transfer rate:
  Q = W·Cp·(T1–T2)
② Effective temperature difference ΔT and logarithmic mean temperature difference Δtm:
Assuming there is only one shell pass and NB tube passes, calculate and look up the temperature difference correction factor Ft; then:
  ΔT = Ft·Δtm
③ Based on the properties of the heat transfer media and process conditions, assume an overall heat transfer coefficient K′ and calculate the required heat transfer area A.

**1.1.2 Heat Transfer Tubes**
Since heat transfer occurs via the surfaces formed by the heat transfer tubes, their dimensions and shape have a significant impact on heat transfer efficiency. Additionally, tube size and arrangement are crucial for preventing fouling.
① Smooth tubes or low-finned tubes are typically used; common specifications include Φ19×2 and Φ25×2.5.
② Determine the total number of heat transfer tubes.
③ Decide on the tube arrangement pattern and tube pitch a.
④ The tube material is determined based on fluid chemistry and process conditions such as pressure and temperature.

**1.2 Mechanical Design of the Heat Exchanger**
**1.2.1 Calculation of Shell Diameter Di and Thickness S**
**1.2.2 Shell Material Selection**
The shell material can be chosen based on material properties, operating pressure, and temperature.
**1.2.3 Selection of Head**
Standard heads should be used, selected according to JB1154–73.
**1.2.4 Selection of Vessel Flanges**
Flanges must be selected according to JB1160–82 standards.
**1.2.5 Tube Sheet Dimensions**
These are calculated and determined using the *Structural Design Manual for Steel Shell-and-Tube Fixed Tube Sheet Heat Exchangers*.
**1.2.6 Calculation of Tube Pull-Out Force**
For expanded joints, both fluid pressure and thermal stress caused by temperature differences between the tube and shell generate a pull-out force q tending to separate the tubes from the tube sheet. For welded joints, no verification of pull-out force is required.
**1.2.7 Calculation of Thermal Stress**
For fixed tube sheet heat exchangers, thermal stresses tend to be relatively large; therefore, these stresses must be calculated and verified to determine whether expansion joints are needed.
① Axial thermal force
② Thermal stress:
  σt = F/At; σs = F/As

**1.2.8 Baffles**
Installing baffles inside a heat exchanger increases fluid velocity and turbulence within the shell side, thereby enhancing heat transfer efficiency; this is a common method for intensifying heat transfer. Rounded segmental baffles are commonly used.
Empirically, the spacing between baffles should not exceed the shell inner diameter; the minimum spacing equals the shell inner diameter. Excessive spacing reduces turbulence intensity, while too little spacing increases flow resistance.

**1.3 Calculation of Pressure Drops in Tube and Shell Passes**
Based on the preliminary design, calculate the pressure drops in both tube and shell passes; verify if these values are reasonable. If not, adjust the number of tube passes and baffle spacing accordingly.
**1.3.1 Shell-side Pressure Drop ΔPo**
**1.3.2 Tube-side Pressure Drop ΔPi**

**1.4 Overall Heat Transfer Coefficient**
After determining the basic structure and dimensions, calculate the overall heat transfer coefficient K and compare it to the initially assumed value K′. If K/K′ falls between 1.5 and 1.25, the preliminary design is acceptable; otherwise, redesign is required.
① Tube-side convective heat transfer coefficient αi: Choose an appropriate calculation formula based on the flow regime inside the tubes: αi = f(Re, Pr).
② Shell-side convective heat transfer coefficient αo: Use the Donohue method.
③ Overall heat transfer coefficient: Considering that the thermal resistances due to the wall and fouling layers account for roughly 5% of K’s value...

**2 Example Design**
**2.1 Scenario**
Water is used to cool benzene flowing at 60 m³/h from 80°C down to 35°C; water inlet temperature is 25°C. Design suitable heat exchangers for three different outlet temperatures: 30°C, 35°C, and 40°C respectively (benzene flows through the shell side; water flows through the tube side).

Material Properties:
| Substance | ρ (kg/m³) | Cp (kJ/kg·°C) | μ (mPa·s) | λ (kJ/m²·°C) |
|-----------|-----------|----------------|------------|----------------|
| Benzene | 880 | 1.60 | 1.15 | 0.148 |
| Water | 994 | 4.187 | 0.727 | 0.626 |

**Design Results:**
All designs employ fixed tube sheet heat exchangers (no expansion joints required).

| Outlet Temp (°C) | Dg (mm) | S (mm) | A (m²) | L (m) | N (tubes) | NB (baffles) | Baffle Spacing (m) | Tube Spec (mm) | Tube Layout | Tube Center Distance (mm) | Overall K (W/m²·°C) | Shell ΔP (Pa) | Tube ΔP (Pa) |
|------------------|---------|--------|--------|-------|-----------|--------------|--------------------|----------------|-------------|--------------------------|----------------------|---------------|--------------|
| 30 | 700 | 7 | 133.6 | 6 | 284 | 12 | 0.5 | Φ25×2.5 | Triangular | 32 | 421 | 4.43×10³ | 1.55×10³ |
| 35 | 800 | 8 | 160 | 6 | 340 | 17 | 0.35 | Φ25×2.5 | Triangular | 32 | 423 | 2.07×10³ | 8.45×10³ |
| 40 | 900 | 9 | 217.9 | 6 | 463 | 24 | 0.25 | Φ25×2.5 | Triangular | 32 | 404 | 1.2×10⁴ | 0.41×10³ |

**2.2 Discussion**
From the design results, it is evident that as the water outlet temperature rises, to maintain the same overall heat transfer coefficient, more heat transfer tubes, more baffles, and a larger shell diameter are required. This is because higher water outlet temperatures reduce the overall temperature difference driving heat transfer; consequently, a larger heat transfer area is needed to ensure consistent Q and K values. As a result, larger heat exchangers require greater consumption of metal materials. This example demonstrates how critical proper selection of design parameters is for maximizing heat transfer efficiency while minimizing economic costs.

**3 Conclusions**
The design methodology proposed herein takes into account factors like heat transfer coefficients and pressure drops in both tube and shell sides during process design; certain simplified mechanical calculations are also performed. Although numerous formulas are involved, computer programming can render these calculations straightforward, thus meeting all design requirements