Overall Heat Transfer Coefficient U – Practical Design Guide

A Practical Guide to Overall Heat Transfer Coefficient (U) and Heat Exchanger Design Rules of Thumb

The thermal design of heat exchangers in chemical, petrochemical, and power plants revolves around one central parameter: the overall heat transfer coefficient, $U$.

The fundamental design equation remains:

$$Q = U \, A \, \Delta T_m \qquad [\text{W}]$$

where:

• $Q$ = heat duty
• $U$ = overall heat transfer coefficient (W/m²·K)
• $A$ = heat transfer area (usually based on tube outside surface)
• $\Delta T_m$ = corrected mean temperature difference (typically $F \times \Delta T_{\text{LMTD}}$)

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1. What the Overall Heat Transfer Coefficient Really Includes

For a tubular exchanger, the exact resistance equation (with $U$ based on outside area) is:

$$\frac{1}{U_o} = \underbrace{\frac{1}{h_o}}_{\text{shell-side film}} + \underbrace{R_{f,o}}_{\text{shell-side fouling}} + \underbrace{\frac{d_o \ln(d_o/d_i)}{2 k_w}}_{\text{wall conduction}} + \underbrace{\frac{d_o}{d_i} \left( \frac{1}{h_i} + R_{f,i} \right)}_{\text{tube-side film \& fouling, area-corrected}}$$

Where:

• $h_o$, $h_i$ = shell-side and tube-side film coefficients (W/m²·K)
• $R_{f,o}$, $R_{f,i}$ = shell-side and tube-side fouling resistances (m²·K/W)
• $k_w$ = tube wall thermal conductivity (W/m·K)
• $d_o$, $d_i$ = tube outside and inside diameters (m)

In preliminary design, the wall and area-correction terms are relatively small (≈3–8 %) for common carbon/stainless tubes. Many engineers use a simplified resistance sum and then verify details later in rating.

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2. Fouling Factors – Current Best Practice

TEMA 10th edition (2019) and most modern company standards have reduced recommended fouling factors. Over-specifying fouling is one of the most common causes of oversized, expensive exchangers.

Table 1 – Typical Fouling Resistances and Equivalent $h_f$

Service	Typical Fouling Resistance $R_f$ (m²·K/W)	Equivalent $h_f$ (W/m²·K)	Notes
Cooling water (clean, treated)	0.00009 – 0.00018	5,500 – 11,000	Good treatment, $v > 1.8$ m/s
Cooling water (brackish/seawater)	0.00018 – 0.00035	2,850 – 5,500	Check for scaling, biofouling
Treated boiler feedwater	0.00002 – 0.00009	>10,000	Essentially clean
Steam (clean, non-oil-bearing)	0.00001 – 0.00005	>20,000	Often taken as ~0 in prelim design
Light hydrocarbons	0.00010 – 0.00020	5,000 – 10,000	Deposits depend on composition
Heavy oils, crude fractions	0.00040 – 0.00080	1,250 – 2,500	Coking / asphaltene risk
Gases (dry)	~0.00010	~10,000	Dust can increase fouling

Rule of thumb :

Avoid using more than 0.00035 m²·K/W total fouling unless plant history proves it is needed.

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3. Realistic Overall Heat Transfer Coefficients

These values reflect typical clean vs design (with fouling) $U$ for shell-and-tube exchangers.

Table 2 – Typical Overall $U$ Values by Service

Service	Typical Clean $U$ (W/m²·K)	Typical Design $U$ (incl. fouling)	Notes
Water – Water	1,400 – 2,500	800 – 1,500	Plate exchangers can exceed 4,000
Water – Light oil ($\mu < 5$ cP)	800 – 1,400	350 – 900
Water – Medium oil (5–50 cP)	400 – 800	200 – 500
Water – Heavy oil ($\mu > 100$ cP)	100 – 400	60 – 250	Strongly viscosity-limited
Steam – Water (condensing steam)	4,000 – 8,000	1,500 – 4,000	Condensing on shell
Steam – Heavy oil (condensing)	800 – 2,000	400 – 1,200	Oil-side limits $U$
Organic – Organic liquids	500 – 1,200	250 – 800
Gas – Gas (1–10 bar)	50 – 250	25 – 150	Low $U$ is normal
Gas – Liquid (process gas cooler)	100 – 700	50 – 400	Depends heavily on gas side
Refrigerant evaporating – Water	1,500 – 3,500	800 – 2,000	Chillers, evaporators
Air-cooled exchangers (process liquid)	400 – 800	300 – 600	Based on bare tube area

Sanity check: If your calculated $U$ is < 50 % or > 200 % of these ranges, revisit:

• Correlation choice
• Velocity and flow regime
• Fouling assumptions
• Geometry (very short or very long tubes, unusual layouts)

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4. Golden Rules of Thumb – Fluid Allocation

Where to put each fluid (shell vs tube) has a big impact on cost, performance, and maintainability.

Table 3 – Fluid Allocation Guidance

Condition	Preferred Side	Reason
Corrosive fluid	Tube side	Cheaper to build tubes & channel in alloy than entire shell
High-pressure fluid (> 70 barg)	Tube side	Tubes and channel withstand pressure more economically
Fouling / scaling fluid	Tube side	Easier mechanical cleaning, higher allowable velocity
Very viscous fluid	Shell side	Cross-flow over baffles improves turbulence & $h$
Condensing vapor	Shell side	Gravity drainage, better condensate handling, easier subcooling
Boiling fluid	Often shell side (kettle) or tube side (thermosiphon)	Depends on configuration & control
Low allowable pressure drop	Shell side	Larger flow area, lower velocity

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5. Velocity & Pressure-Drop Rules of Thumb

Velocities must balance heat transfer performance, erosion risk, and pumping power.

Table 4 – Typical Velocities and $\Delta P$ Targets

Fluid / Side	Recommended Velocity	Typical $\Delta P$ Allowance
Cooling water (tube side)	1.5 – 2.5 m/s	0.5 – 1.0 bar
Process water (tube side)	1.2 – 2.0 m/s
Light hydrocarbons (tubes)	1.5 – 3.0 m/s
Viscous liquids (> 50 cP)	< 1.0 m/s	Keep shear & $\Delta P$ manageable
Shell-side liquids	0.5 – 1.0 m/s (crossflow zone)	0.3 – 0.7 bar
Saturated vapor	Limit $\rho v^2 \lesssim 4{,}000\ \text{kg/m·s}^2$	Erosion / noise control

Higher velocities → higher $h$, but also:

• Higher pressure drop
• More erosion risk (especially with solids or flashing)
• Possible vibration issues in tubes

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6. Temperature Approach & LMTD Correction Factor

For countercurrent flow, the Log Mean Temperature Difference is:

$$\Delta T_{\text{LMTD}} = \frac{\Delta T_1 - \Delta T_2}{\ln \left( \dfrac{\Delta T_1}{\Delta T_2} \right)}$$

Where:

• $\Delta T_1 = T_{H,\text{in}} - T_{C,\text{out}}$
• $\Delta T_2 = T_{H,\text{out}} - T_{C,\text{in}}$

In shell-and-tube exchangers with multiple passes, a correction factor $F$ is applied:

$$\Delta T_m = F \cdot \Delta T_{\text{LMTD}}$$

Practical Targets

• Minimum economic approach (process–process): typically 15–25 °C
• Water coolers: approach (hot in – water out) often 8–12 °C
• Refrigeration chillers: 3–6 °C (tighter for energy efficiency)

LMTD correction factor $F$:

• Aim for $F \ge 0.85$ for most shell-and-tube designs
• For simple 1–2 or 2–4 exchangers, $F$ is often 0.90–0.95
• If $F < 0.75$, consider:
  • Additional shells in series
  • Different pass arrangement
  • Plate heat exchanger or other configuration

Temperature cross (when $T_{C,\text{out}} > T_{H,\text{out}}$):

• Can be feasible in multi-shell arrangements
• Requires careful LMTD + $F$ evaluation; not recommended in a single simple S&T without a detailed check

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7. Quick Preliminary Sizing Example (Updated)

Objective: Cool 250 t/h of lube oil from 80 °C → 50 °C using cooling water 32 °C → 42 °C.

Assume:

• $Q \approx 3.5$ MW (from detailed enthalpy balance; not shown here)

Step 1 – Temperature Differences

• $\Delta T_1 = 80 - 42 = 38^\circ\text{C}$
• $\Delta T_2 = 50 - 32 = 18^\circ\text{C}$

LMTD:

$$\Delta T_{\text{LMTD}} = \frac{38 - 18}{\ln(38/18)} \approx 26.8^\circ\text{C}$$

Assume a 1-shell, 2-tube-pass exchanger:

• From standard LMTD correction charts → $F \approx 0.96$

So:

$$\Delta T_m = F \cdot \Delta T_{\text{LMTD}} \approx 0.96 \times 26.8 \approx 25.7^\circ\text{C}$$

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Step 2 – Choose Trial $U$

From Table 2, for oil–water service:

• Design $U$ in the range 350–900 W/m²·K

Take a conservative $U = 450\ \text{W/m}^2\cdot\text{K}$.

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Step 3 – Area Estimate

$$A_{\text{req}} = \frac{Q}{U \cdot \Delta T_m} = \frac{3.5 \times 10^6}{450 \times 25.7} \approx 300\ \text{m}^2$$

This is a realistic first-pass result:

• You would then pick tube size (e.g. 19 mm OD, 6–8 m length), count, passes, and shell size
• Next step: compute detailed $h_i$, $h_o$, fouling effects and compare the calculated $U$ with this trial value (450 W/m²·K)
• Adjust layout or velocities as needed and iterate

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8. Final Sanity-Check Checklist

Use this list before accepting any heat exchanger design (in-house or vendor):

• Is design $U$ within ±50 % of typical values for the service?
• Tube-side liquid velocities in the 1.2–2.5 m/s range (unless special case)?
• Total fouling resistance ≤ 0.00035 m²·K/W unless plant data justifies more?
• LMTD correction factor $F \ge 0.85$?
• No problematic temperature cross in a single-shell unit?
• Pressure drops compatible with pump/compressor head and control valves?
• Fluid allocation consistent with corrosion, fouling, and pressure guidelines?

Mastering these numbers and rules means you will:

• Avoid chronic under-performing exchangers
• Avoid over-designed, unnecessarily expensive units
• Speak the same language as vendors, licensors, and operations teams

The rest is refinement with HTRI, Aspen EDR, or vendor software — but good engineering judgement starts with a solid feel for $U$, fouling, and these rules of thumb.