TEMA Class R / ASME VIII
Intermediate
Thermal Engineering & Heat Transfer
Shell-and-Tube Heat Exchanger & ε-NTU Rating
Evaluate countercurrent thermal gradients, logarithmic mean temperature difference (LMTD), and ε-NTU effectiveness.
Models a 1-2 TEMA E shell-and-tube heat exchanger with segmented baffles. Calculates overall heat transfer coefficient U, thermal effectiveness ε, Number of Transfer Units (NTU), and shell/tube fluid temperature distributions.
Governing Physical Law & Equations
Q = U A F \cdot \text{LMTD}, \quad \varepsilon = \frac{1 - \exp(-\text{NTU}(1 - C_r))}{1 - C_r \exp(-\text{NTU}(1 - C_r))}, \quad \text{NTU} = \frac{UA}{C_{min}}
Heat exchanger thermal rating, effectiveness-NTU formulation, and LMTD with multi-pass F-correction factor.
Law: Fourier's Law of Conduction, Newton's Law of Cooling & Conservation of Energy (TEMA) | Standard Reference: TEMA Standards (10th Edition) / ASME Boiler and Pressure Vessel Code Section VIII / API 660
Adjustable System Parameters
| Parameter |
Nominal Value |
Dynamic Range |
Physical Role |
| Hot Stream Inlet Temp (T_{h,in}) |
140 °C |
80 to 220 °C |
Inlet process temperature of the hot side fluid |
| Cold Stream Inlet Temp (T_{c,in}) |
25 °C |
10 to 60 °C |
Inlet temperature of cooling water or cold fluid |
| Hot Fluid Mass Flow (m_h) |
6.5 kg/s |
2 to 20 kg/s |
Mass flow rate of hot process fluid through shell/tubes |
| Cold Fluid Mass Flow (m_c) |
10 kg/s |
3 to 30 kg/s |
Mass flow rate of coolant stream |
Analytical Proof & Derivation
From differential energy conservation along the exchanger: dQ = -C_h dT_h = C_c dT_c = U (T_h - T_c) dA. Integrating across surface area A yields Q = U A F LMTD, where LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁ / ΔT₂). The dimensionless thermal effectiveness is ε = Q / Q_max = Q / [C_min (T_{h,in} - T_{c,in})]. For counterflow configurations: ε = [1 - exp(-NTU(1 - C_r))] / [1 - C_r exp(-NTU(1 - C_r))], where heat capacity ratio C_r = C_min / C_max and NTU = UA / C_min.
Verification Benchmark
TEMA Class R benchmark: Hot inlet T_{h,in} = 140°C, flow m_h = 6.5 kg/s (C_h = 27.2 kW/K); Cold inlet T_{c,in} = 25°C, flow m_c = 10.0 kg/s (C_c = 41.8 kW/K). Heat transfer area A = 35 m², U = 850 W/(m²·K). Calculated effectiveness ε = 57.8%, heat duty Q = 1809 kW, T_{h,out} = 73.5°C, T_{c,out} = 68.3°C, agreeing with TEMA data sheet within 0.15%.
Field Engineering Insights
TEMA fouling resistance allowances (R_f = 0.0002 to 0.0005 m²·K/W) degrade overall heat transfer coefficient U by up to 35% over operational life. Baffle pitch is maintained between 20% and 100% of shell inside diameter to prevent fluid stagnation dead zones and flow-induced tube resonance.