Heat exchangers are the workhorses of thermal energy management in any process plant. They heat, cool, condense, and evaporate fluids in applications ranging from HVAC chillers and boiler economizers to chemical reactor cooling and waste heat recovery. Understanding the fundamental heat transfer relationships allows engineers to size new exchangers, evaluate existing ones, and diagnose performance degradation before it becomes a production bottleneck.
The core equation is simple: Q = U x A x LMTD. The duty Q is the heat transfer rate, U is the overall heat transfer coefficient, A is the surface area, and LMTD is the log mean temperature difference. Everything in heat exchanger design comes back to this equation — selecting the right exchanger type, predicting fouling effects, and determining when an exchanger needs cleaning or replacement.
This guide covers the LMTD calculation, overall heat transfer coefficients, fouling, approach temperature, and the practical differences between common heat exchanger types used in industrial facilities.
Log Mean Temperature Difference (LMTD)
The LMTD accounts for the fact that the temperature difference between the hot and cold fluids changes along the length of the exchanger. For a counterflow arrangement: LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2), where ΔT1 is the temperature difference at one end and ΔT2 is the difference at the other end.
In counterflow, the hot fluid enters where the cold fluid exits, and vice versa. ΔT1 = T_hot_in - T_cold_out, and ΔT2 = T_hot_out - T_cold_in. Counterflow always produces a higher LMTD (and therefore requires less surface area) than parallel flow for the same inlet and outlet temperatures.
For a parallel flow arrangement, both fluids enter at the same end: ΔT1 = T_hot_in - T_cold_in (large difference at the inlet) and ΔT2 = T_hot_out - T_cold_out (small difference at the outlet). Parallel flow cannot achieve a cold outlet temperature higher than the hot outlet temperature, which limits its usefulness.
Multi-pass shell-and-tube exchangers and crossflow designs require a correction factor F applied to the counterflow LMTD: LMTD_corrected = F x LMTD_counterflow. The correction factor depends on the number of shell passes, tube passes, and the temperature effectiveness. F is always less than or equal to 1.0, and designs where F drops below 0.75 should be reconfigured (more shell passes or a different exchanger type) because the thermal efficiency is poor.
Overall Heat Transfer Coefficient (U)
The overall U value combines all the resistances to heat transfer in series: the hot-side film coefficient, the hot-side fouling resistance, the tube wall conduction, the cold-side fouling resistance, and the cold-side film coefficient. The formula is: 1/U = 1/h_hot + R_f_hot + t/k + R_f_cold + 1/h_cold, where h is the film coefficient, R_f is the fouling resistance, t is the wall thickness, and k is the wall thermal conductivity.
Typical U values vary widely depending on the fluids involved. Water-to-water exchangers run 150 to 300 BTU/hr·ft²·°F. Water-to-oil is 20 to 60. Gas-to-gas is 2 to 10. Steam condensing to water is 200 to 1000. These ranges assume clean surfaces; fouling reduces the effective U significantly over time.
The film coefficients depend on fluid properties (thermal conductivity, viscosity, specific heat, density) and flow conditions (velocity, turbulence). Turbulent flow produces film coefficients 5 to 10 times higher than laminar flow, which is why heat exchanger design always aims for turbulent conditions on both sides. Baffle spacing in shell-and-tube exchangers and plate corrugation patterns in plate exchangers are specifically designed to promote turbulence.
When evaluating an existing exchanger, you can back-calculate U from measured temperatures and flow rates: U = Q / (A x LMTD). Comparing this calculated U to the design U tells you how much the exchanger has fouled. If the operating U is 60 percent of the design U, the exchanger is significantly fouled and cleaning is overdue.
Fouling Factors and Their Impact
Fouling is the accumulation of deposits on heat transfer surfaces. It reduces the effective U value and increases pressure drop. The TEMA (Tubular Exchanger Manufacturers Association) standards provide recommended fouling factors for common services. River water: 0.002 to 0.003 hr·ft²·°F/BTU. Treated cooling tower water: 0.001 to 0.002. Clean steam condensate: 0.0005. Light hydrocarbons: 0.001. Heavy fuel oil: 0.005.
These fouling factors are added to the thermal resistance during the design stage to ensure the exchanger has enough surface area to maintain duty even when fouled. The result is that a new, clean exchanger is oversized and initially delivers more heat transfer than needed. As fouling accumulates, performance degrades toward the design point.
Over-specifying fouling factors wastes capital. An exchanger designed with excessive fouling allowance is much larger and more expensive than necessary. It also runs inefficiently when clean because the excess surface area leads to temperature overshooting that must be controlled with bypass valves.
Fouling types include scaling (mineral deposits from hard water), biological fouling (algae and biofilm in cooling water), corrosion fouling (oxide layers), and particulate fouling (suspended solids depositing in low-velocity zones). Each type responds to different mitigation strategies: chemical treatment, increased velocity, filtration, or periodic mechanical cleaning.
Approach Temperature and Pinch Analysis
Approach temperature is the smallest temperature difference between the hot and cold streams at any point in the exchanger. In a counterflow exchanger, this is typically at the hot outlet / cold inlet end: approach = T_hot_out - T_cold_in. A smaller approach means more heat is recovered but requires a larger (and more expensive) exchanger.
Typical minimum approach temperatures for liquid-to-liquid exchangers are 10 to 20°F. For condensing applications, approaches of 5 to 10°F are common. Going below 5°F is technically possible but the required surface area increases exponentially, making it economically unjustifiable for most industrial applications.
Pinch analysis extends the approach concept to entire process plants. The pinch point is the location in the overall heat balance where the available temperature driving force is smallest. Designing heat recovery systems around the pinch maximizes energy efficiency: heat should be transferred above the pinch from hot to cold streams, and utility heating and cooling should be applied only where process-to-process exchange is not thermodynamically possible.
In practice, every degree of approach temperature you specify costs money in exchanger surface area but saves money in energy. The optimum is found by plotting capital cost (exchanger surface) against operating cost (energy) and finding the minimum total annual cost. For most industrial applications, the optimum approach is between 10 and 25°F.
Common Heat Exchanger Types
Shell-and-tube exchangers are the most common type in process plants. They consist of a bundle of tubes inside a cylindrical shell. One fluid flows through the tubes and the other flows over the outside of the tubes within the shell. They handle high pressures, high temperatures, and virtually any fluid combination. TEMA designations (BEM, AES, AEL, etc.) describe the front end, shell type, and rear end configurations.
Plate-and-frame exchangers use thin corrugated metal plates stacked together with gaskets. They offer very high heat transfer coefficients (2 to 4 times shell-and-tube) in a compact footprint. They are ideal for liquid-to-liquid service at moderate pressures (up to 300 PSI) and temperatures (up to 350°F with standard gaskets). Plates can be added or removed to adjust capacity, and the unit opens for easy cleaning.
Air-cooled exchangers (fin-fan coolers) use ambient air blown across finned tubes by large fans. They eliminate the need for cooling water but require large footprints and are limited by ambient temperature. They are commonly used in refineries, gas plants, and any facility where cooling water is scarce or expensive to treat.
Double-pipe (hairpin) exchangers are the simplest type — one pipe inside another. They are used for small duties, high-pressure applications, or where true counterflow is needed for close temperature approaches. Multiple hairpins can be connected in series or parallel to increase capacity.