For preliminary evaluation, use a separate overall heat-transfer coefficient for each thermal zone rather than one coefficient for the entire exchanger. Common shell-and-tube heuristics are 850 W/(m²·°C) for water-to-liquid service and condensers, 280 W/(m²·°C) for liquid-to-liquid service, 60 W/(m²·°C) for liquid-to-gas service, 30 W/(m²·°C) for gas-to-gas service, and approximately 1,140 W/(m²·°C) for reboilers. These are starting values for preliminary calculations; measured pilot-plant data or detailed resistance calculations should replace them when available.

In a multi-zone exchanger, assign a distinct (U) value to each region, such as sensible liquid heating, boiling, condensation, or gas heating. The appropriate value depends primarily on the phases, flow regime, fouling condition, exchanger geometry, and whether the coefficient is based on the inside or outside tube area.

Why Multi-Zone Evaluation Is Necessary

Different zones have different thermal resistances

A process stream may pass through several heat-transfer regimes in one exchanger. For example, it may undergo sensible liquid heating, boil in a separate region, and then experience superheated-vapor heating.

The controlling resistance changes between these regions. A boiling zone may have a much higher heat-transfer coefficient than a gas-heating zone, so applying one average (U) value can misrepresent the required area in each section.

Each zone has its own heat duty

For each zone, calculate the duty from the relevant mass flow rate, heat capacity, and temperature or phase change:

[ Q_z = U_z A_z \Delta T_{\mathrm{lm},z} ]

Here, (Q_z), (U_z), (A_z), and (\Delta T_{\mathrm{lm},z}) are the heat duty, overall coefficient, area, and log mean temperature difference for zone (z).

The total exchanger duty is the sum of the zone duties, but the area should be evaluated zone by zone.

Standard Preliminary (U) Values

Water-to-liquid service

A commonly used heuristic for water-to-liquid service is:

[ U \approx 850\ \mathrm{W/(m^2\cdot{}^\circ C)} ]

This value is suitable as a general preliminary estimate when both streams are liquid and at least one stream is water.

For water-to-water service, broader pilot-plant and design references may use approximately 800-1,500 W/(m²·°C), while some empirical references cite 850-1,700 W/(m²·°C). The selected value should reflect flow velocity, tube dimensions, fouling allowance, and the area basis.

Condensers

For a general condenser heuristic:

[ U \approx 850\ \mathrm{W/(m^2\cdot{}^\circ C)} ]

This is a broad starting point. Water-to-steam condensation can support substantially higher values, with supplementary design ranges of approximately 1,420-4,250 W/(m²·°C) or, for steam-to-water heating service, 1,500-4,000 W/(m²·°C).

The higher range should not be applied automatically to every condenser. Condensate drainage, non-condensable gases, vapor-side resistance, and fouling can reduce the actual coefficient significantly.

Liquid-to-liquid service

For generic liquid-to-liquid exchange:

[ U \approx 280\ \mathrm{W/(m^2\cdot{}^\circ C)} ]

This is a conservative heuristic for preliminary work. Water-to-water systems commonly achieve higher values because water has favorable thermal properties and often operates at relatively high flow velocity.

Organic-solvent service is commonly represented by a broader range of approximately 100-300 W/(m²·°C). Light-oil service may fall near 100-400 W/(m²·°C), while heavy-oil service is often lower, around 50-300 W/(m²·°C).

Liquid-to-gas service

For liquid-to-gas exchange:

[ U \approx 60\ \mathrm{W/(m^2\cdot{}^\circ C)} ]

Gas-side convection is frequently the dominant resistance, so these coefficients are much lower than those for liquid-to-liquid service.

References for water-to-gas systems span approximately 17-280 W/(m²·°C), reflecting the large variation in gas velocity, pressure, density, geometry, and whether the gas is undergoing phase change.

Gas-to-gas service

For gas-to-gas service:

[ U \approx 30\ \mathrm{W/(m^2\cdot{}^\circ C)} ]

A broader practical range is approximately 10-50 W/(m²·°C). The lower end is more representative of low-velocity or poorly mixed gas streams, while higher values require stronger convection and favorable equipment geometry.

Reboilers

For preliminary reboiler calculations:

[ U \approx 1{,}140\ \mathrm{W/(m^2\cdot{}^\circ C)} ]

Reboiler performance must also be checked against allowable heat flux. A cited maximum heat flux limit is approximately 31.5 kW/m², although the applicable limit depends on fluid properties, pressure, boiling regime, surface condition, and equipment design.

Steam heating of viscous liquids

Steam-to-heavy-oil heating may have an overall coefficient in the approximate range of 60-450 W/(m²·°C).

The wide range reflects the strong influence of oil viscosity, temperature, flow pattern, and fouling. A single high steam-side coefficient does not guarantee a high overall (U), because the viscous liquid-side resistance may dominate.

How to Apply the Values by Zone

Sensible liquid-heating zone

For a liquid being heated without phase change, select a liquid-to-liquid value if both sides are liquid. A preliminary value near 280 W/(m²·°C) is a generic choice, while water-to-water service may justify a value in the 800-1,500 W/(m²·°C) range when operating conditions support it.

Boiling or reboiling zone

For a boiling region, use a reboiler or boiling-service estimate rather than the coefficient for sensible liquid heating. A starting value near 1,140 W/(m²·°C) may be used for a reboiler, subject to heat-flux and boiling-regime checks.

Condensation zone

For vapor condensation, begin with the condenser heuristic of 850 W/(m²·°C) unless the service is specifically comparable to clean steam-to-water condensation. Steam-condensation references may support values in the 1,420-4,250 W/(m²·°C) range, but the lower end or a measured value may be more appropriate for pilot equipment.

Gas-heating or gas-cooling zone

For a gas region, use approximately 60 W/(m²·°C) for liquid-to-gas service or 30 W/(m²·°C) for gas-to-gas service. These zones often require disproportionate area because the gas-side film coefficient is relatively low.

How (U) Is Determined

Experimental determination

The most reliable coefficient for a particular pilot exchanger is obtained under the actual operating conditions. Measure both streams' flow rates and inlet and outlet temperatures, calculate the heat duty, determine the zone-specific LMTD, and solve:

[ U = \frac{Q}{A\Delta T_{\mathrm{lm}}} ]

An experimentally determined value is specific to the tested fluid properties, flow rates, exchanger geometry, fouling state, and operating configuration. It should not be transferred uncritically to another zone or operating condition.

Thermal-resistance calculation

The overall coefficient combines the two fluid-film resistances, tube-wall conduction, and fouling resistances. Based on the outside tube area, a representative expression is:

[ \frac{1}{U_o}

\frac{1}{h_o} + \frac{1}{h_{od}} + \frac{d_o\ln(d_o/d_i)}{2k_w} + \frac{d_o}{d_i}\frac{1}{h_{id}} + \frac{d_o}{d_i}\frac{1}{h_i} ]

The exact form depends on the selected area basis and resistance definitions, but the governing principle is that thermal resistances add in series.

This method makes the controlling resistance visible. For example, a low gas-side film coefficient or a high-viscosity liquid film may dominate the total resistance even when the opposite-side coefficient is large.

Empirical estimation

Empirical tables are appropriate for preliminary sizing, training exercises, and comparison with pilot-plant measurements. They are not a substitute for detailed design when the exchanger operates near boiling limits, has significant fouling, or contains multiple phase-change regions.

Understanding the Trade-offs

A high (U) reduces area but increases design sensitivity

Selecting a higher coefficient reduces the calculated heat-transfer area:

[ A = \frac{Q}{U\Delta T_{\mathrm{lm}}} ]

However, a high assumed (U) may require high flow velocities, strong mixing, clean surfaces, or favorable phase-change behavior that the pilot plant cannot consistently maintain.

A low (U) increases area but provides margin

A lower design value produces a larger calculated area and therefore may increase initial equipment cost and physical size. It can nevertheless provide greater tolerance for fouling, property variation, declining performance, and uncertain operating conditions.

Do not mix coefficient ranges without checking service definitions

Values reported for water-to-water, water-to-steam, steam-to-heavy-oil, and generic liquid-to-gas service are not interchangeable. The phase combination and service description must match the zone being evaluated.

Keep the area basis consistent

(U_i) based on inside tube area and (U_o) based on outside tube area have different numerical values. The area used in (Q=UA\Delta T_{\mathrm{lm}}) must correspond to the selected coefficient.

Flow-rate changes affect the coefficient

For turbulent tube-side flow, a common preliminary scaling is:

[ \frac{U_2}{U_1}\approx \left(\frac{\dot m_2}{\dot m_1}\right)^{0.8} ]

This is an approximation, not a universal law. It should be used only when the flow regime and fluid properties remain sufficiently comparable.

How to Apply This to Your Project

For a multi-zone pilot-plant exchanger, establish the phase and heat-transfer regime in each zone before selecting (U).

If your primary focus is preliminary sizing: Use approximately 850 W/(m²·°C) for water-to-liquid service or condensers, 280 W/(m²·°C) for generic liquid-to-liquid service, 60 W/(m²·°C) for liquid-to-gas service, 30 W/(m²·°C) for gas-to-gas service, and 1,140 W/(m²·°C) for reboiler service.
If your primary focus is phase-change design: Evaluate boiling and condensing zones separately, use the applicable phase-change range, and check heat-flux limitations in boiling regions.
If your primary focus is pilot-plant data analysis: Determine (U_z=Q_z/(A_z\Delta T_{\mathrm{lm},z})) from measured temperatures and flow rates for each zone.
If your primary focus is conservative equipment selection: Choose a lower credible coefficient within the applicable range and include fouling and operating variability in the design assessment.

The defensible standard is not one universal heat-transfer coefficient, but a zone-specific (U) selected from the correct service category and verified against the pilot plant's actual operating data.

Summary Table:

Service or zone	Preliminary overall heat-transfer coefficient, U	Key design consideration
Water-to-liquid	850 W/(m²·°C)	Water-to-water systems may reach 800-1,500 W/(m²·°C).
Condenser	850 W/(m²·°C)	Clean steam-to-water service may support 1,420-4,250 W/(m²·°C).
Liquid-to-liquid	280 W/(m²·°C)	Organic and oil services vary with viscosity, flow, and fouling.
Liquid-to-gas	60 W/(m²·°C)	Gas-side resistance commonly controls performance.
Gas-to-gas	30 W/(m²·°C)	Typical practical range is 10-50 W/(m²·°C).
Reboiler or boiling zone	1,140 W/(m²·°C)	Check boiling regime and allowable heat flux, approximately 31.5 kW/m² in one cited case.
Steam-to-viscous liquid	60-450 W/(m²·°C)	Liquid viscosity and fouling can dominate the overall resistance.

Use a separate U value for each thermal zone and keep the coefficient's inside- or outside-area basis consistent with the area used in Q = UAΔTₗₘ.

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What standard heat transfer coefficients are used when evaluating multi-zone shell-and-tube heat exchangers in unit operations pilot plants?