1. Calculation Scope & Governing Equations
This rating sheet provides sizing and thermal-hydraulic verification for double-pipe and hairpin heat exchangers in accordance with TEMA (10th Edition, Section 9) and ASME Section VIII Division 1.
$$Q = \dot{m}_h C_{p,h} (T_{h,in} - T_{h,out}) = \dot{m}_c C_{p,c} (T_{c,out} - T_{c,in})$$
$$\text{LMTD} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}, \quad \Delta T_1 = T_{h,in} - T_{c,out}, \quad \Delta T_2 = T_{h,out} - T_{c,in}, \quad F_t = 1.000$$
$$A_{\text{req}} = \frac{Q}{U_o \cdot \text{LMTD}}, \quad N_{\text{hairpins}} = \left\lceil \frac{A_{\text{req}}}{A_{\text{hairpin}}} \right\rceil$$
$$\frac{1}{U_o} = \frac{1}{\eta_o h_{ann}} + R_{f,ann} + \frac{d_o \ln(d_o / d_i)}{2 k_w} + \left(R_{f,tube} + \frac{1}{h_{tube}}\right) \frac{A_o}{A_i}$$
$$m = \sqrt{\frac{2 h_{ann}}{k_f t_f}}, \quad \eta_f = \frac{\tanh(m H_f)}{m H_f}, \quad \eta_o = 1 - \frac{A_f}{A_o}(1 - \eta_f)$$
$$D_{h,hyd} = \frac{4 A_{ann}}{P_{w,hyd}} = \frac{4 A_{ann}}{\pi D_i + \pi d_o + 2 N_f H_f}, \quad D_{e,th} = \frac{4 A_{ann}}{\pi d_o + 2 N_f H_f}$$
$$\Delta P = \left(4 f \frac{L_{tot}}{D_h} + K_{bend} N_{bends}\right) \left(\frac{\rho v^2}{2}\right)$$
2. Standard Parameters & TEMA Design Criteria
| Service / Fluid Type | Typical Overall U ($W/m^2\cdot K$) | Recommended Fin & Velocity Limits |
|---|---|---|
| Heavy Fuel Oil (HFO) Preheater | $80 - 220\text{ W/m}^2\cdot\text{K}$ | Longitudinal fins ($N_f = 24 - 36$); $v_{ann} = 0.6 - 1.2\text{ m/s}$; prevents asphalt deposition. |
| High-Pressure Gas-Gas Interchanger | $150 - 350\text{ W/m}^2\cdot\text{K}$ | Deep temperature cross ($T_{c,out} > T_{h,out}$); bare or low fins; $v = 8 - 18\text{ m/s}$. |
| Reactor Jacket Booster (Water/Glycol) | $600 - 1,400\text{ W/m}^2\cdot\text{K}$ | Bare inner tube ($N_f = 0$); $v = 1.2 - 2.2\text{ m/s}$; low hydraulic pressure loss ($\le 0.35\text{ bar}$). |
| LMTD Correction Factor ($F_t$) | $1.000$ (Exact) | Pure counter-current flow eliminates temperature cross instability; no shell-series penalty. |
3. Engineering Assumptions & Boundary Limits
- Pure Counterflow Rigor: Assumes counter-current flow along all straight runs and 180° return bends, enforcing $F_t = 1.000$.
- Hydraulic vs Thermal Separation: Annular pressure drop is governed by total wetted perimeter ($D_{h,hyd}$), while convective heat transfer is evaluated using heat-transfer wetted perimeter ($D_{e,th}$) per Kern (1950).
- Fin Heat Transfer: Longitudinal fins are assumed to be continuous welded or integral with carbon or stainless steel inner tubes, with 100 percent bond conductance.
- Differential Thermal Expansion: Return bend floating hood allows independent expansion of the inner tube without requiring bellows or expansion joints.
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This specification sheet and its mathematical formulations adhere to internationally recognized process codes (TEMA Section 9, ASME Section VIII Division 1, and API 660). Sizing parameters and default design allowances are cross-referenced with empirical industry design practices.