Shell-and-Tube Heat Exchanger Design

📝 Configuration

Number of Shell Passes ($N$):

🔴 Hot Fluid (Tubes)

Inlet Temp ($T_{hi}$) [°C]:

Outlet Temp ($T_{ho}$) [°C]:

Flow Rate ($\dot{m}_h$) [kg/s]:

Specific Heat ($C_{p,h}$) [J/kg·K]:

🔵 Cold Fluid (Shell)

Inlet Temp ($T_{ci}$) [°C]:

Outlet Temp ($T_{co}$) [°C]:

Flow Rate ($\dot{m}_c$) [kg/s]:

Specific Heat ($C_{p,c}$) [J/kg·K]:

Heat Transfer Coefficient

Overall $U$ [W/m²·K]: Typical U values: Water-Water: 800-1500 · Steam Condenser: 1000-2500 · Gas-Gas: 10-50

Correction Factor sizing:
Q = U × A × F × LMTD_cf

LMTD_cf = LMTD counterflow baseline
F = correction factor for tube cross-parallel multi-passes

Temperature Cross limit:
If the temperature effectiveness P and capacity ratio R lead to invalid F bounds, it represents a temperature cross too severe for a single shell. An increase in shell passes (N) will be required.

📊 Results & Visualization

Configure inputs and click Sizing Shell-and-Tube to view results.

📘 Calculation Methodology

Mathematical Model & Theory

Shell-and-tube heat exchangers support high pressures and contain large surface areas in a compact shell. Sizing incorporates multi-pass log-mean temperature correction factors ($F$) and capacity rate considerations:

$$Q = U A F \Delta T_{lm, cf}$$ $$F = f(P, R, N_{shell}) \quad \text{(TEMA correlations for shell passes)}$$

Assumptions & Boundary Conditions:

Steady-state flow and thermal conditions.
Adiabatic shell outer boundaries (negligible heat loss to ambient environment).
Constant specific heats ($C_p$) and other thermophysical properties for shell-side and tube-side fluids.
Constant overall heat transfer coefficient ($U$) across all passes.
One-dimensional temperature change within the tubes and shell streams.
Uniform fluid distribution among parallel tubes.

Academic References:

TEMA (Tubular Exchanger Manufacturers Association). (2007). Standards of the Tubular Exchanger Manufacturers Association (9th ed.).
Kakaç, S., Liu, H., & Pramuanjaroenkij, A. (2012). Heat Exchangers: Selection, Rating, and Thermal Design (3rd ed.). CRC Press.
Incropera, F. P., Dewitt, D. P., Bergman, T. L., & Lavine, A. S. (2011). Fundamentals of Heat and Mass Transfer (7th ed.). John Wiley & Sons.

Worked Engineering Example

Problem Statement:
Size a 1-2 shell-and-tube heat exchanger ($U = 400$ W/m²·K) designed to cool water ($C_p = 4180$ J/kg·K, $\dot{m} = 2.5$ kg/s) from 90°C to 45°C using cold water entering at 20°C and exiting at 40°C. Check the correction factor $F$ and required area.

Step-by-step Solution:
1. Calculate heat duty $Q$:
$$Q = 2.5 \times 4180 \times (90 - 45) = 470,250 \text{ W}$$ 2. Calculate LMTD for counter-flow:
$$\Delta T_{lm, cf} = \frac{(90 - 40) - (45 - 20)}{\ln(50 / 25)} = 36.07 \text{ K}$$ 3. Calculate temperature effectiveness $P$ and capacity ratio $R$:
$$P = \frac{40 - 20}{90 - 20} = 0.286, \quad R = \frac{90 - 45}{40 - 20} = 2.25$$ 4. Determine correction factor $F$ (for 1 shell pass, 2 tube passes):
$$F \approx 0.88$$ 5. Calculate required area $A$:
$$A = \frac{Q}{U F \Delta T_{lm, cf}} = \frac{470,250}{400 \times 0.88 \times 36.07} = 37.0 \text{ m}^2$$
Final Result:
Required area is 37.0 m² with correction factor $F = 0.88$.

⚙️ Shell-and-Tube Heat Exchanger Design