Heat Transfer: Heat Exchangers

Heat exchangers are the workhorses of thermal engineering. They recover waste heat in power plants, chill process streams in chemical facilities, maintain temperatures in HVAC systems, and manage thermal loads in engines, electronics, and renewable energy systems. Despite their variety in shape and application, most heat exchangers are governed by the same ideas: energy conservation, heat transfer driving forces, and flow arrangement.

A strong design starts with two questions. How much heat must be transferred, and what temperature changes are acceptable on each side? From there, engineers select an exchanger type and size it using either the Log Mean Temperature Difference (LMTD) method or the effectiveness-NTU method, then refine the design around pressure drop, fouling, materials, and operability.

What a Heat Exchanger Does

A heat exchanger transfers thermal energy between two fluids at different temperatures. The fluids may be separated by a solid wall (typical in shell-and-tube or plate exchangers), or they may be in direct contact (as in some cooling towers and mixing devices). In most industrial equipment, the streams remain separated for safety, cleanliness, or process reasons.

For steady operation with negligible heat loss to the environment, an overall energy balance gives:

$$Q={\dot{m}}_h{c}_{p,h}(T_{h,in}-T_{h,out})={\dot{m}}_c{c}_{p,c}(T_{c,out}-T_{c,in})$$

where $Q$ is the heat transfer rate, $\dot{m}$ is mass flow rate, and $c_p$ is specific heat. Subscripts $h$ and $c$ denote hot and cold streams.

The thermal driving force is the temperature difference between the two streams, but because that difference varies along the exchanger, sizing requires a method that accounts for the changing temperature profile.

Flow Arrangements: Parallel, Counter, and Crossflow

The arrangement of the two flow paths shapes both performance and feasibility.

Parallel Flow

In parallel (co-current) flow, both fluids enter the exchanger at the same end and move in the same direction. The temperature difference is highest at the inlet and drops quickly, which limits how close the cold outlet can approach the hot inlet temperature. Parallel flow can be attractive for simplicity, but it is usually thermally less efficient than counterflow for the same area.

Counterflow

In counterflow, fluids enter from opposite ends and move in opposite directions. This maintains a higher average temperature difference along the length, often allowing a smaller exchanger for the same duty. Counterflow also enables a closer temperature approach, and in some cases the cold outlet temperature can exceed the hot outlet temperature, which is not possible in parallel flow.

Crossflow

In crossflow, streams move roughly perpendicular to each other. This is common in finned-tube air coolers, radiators, and many HVAC coils where one side is a gas with a large flow area. Crossflow performance depends on whether each stream is mixed or unmixed in the transverse direction, which affects the temperature distribution and therefore the sizing correction factors used with LMTD.

The LMTD Method: Sizing When Outlet Temperatures Are Known

The LMTD method is widely used for rating and design when inlet and outlet temperatures are specified or can be determined from the duty and flow rates.

The basic heat transfer relation is:

$$Q=UA\Delta T_{lm}$$

• $U$ is the overall heat transfer coefficient (accounts for convection on both sides, conduction through the wall, and fouling resistances)
• $A$ is the heat transfer area
• $\Delta T_{lm}$ is the log mean temperature difference

For many common configurations, $\Delta T_{lm}$ is computed from the temperature differences at the two ends:

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

For example, in a counterflow exchanger, one may define:

• $\Delta T_1=T_{h,in}-T_{c,out}$
• $\Delta T_2=T_{h,out}-T_{c,in}$

For parallel flow:

• $\Delta T_1=T_{h,in}-T_{c,in}$
• $\Delta T_2=T_{h,out}-T_{c,out}$

LMTD Correction Factor for Real Exchangers

Many practical exchangers are not pure parallel or pure counterflow. Shell-and-tube units with multiple passes, and crossflow coils, require a correction factor $F$:

$$Q=UAF\Delta T_{lm}$$

The factor $F$ depends on the flow arrangement and on temperature ratios derived from the four terminal temperatures. An $F$ close to 1 indicates behavior similar to ideal counterflow. A low $F$ suggests the chosen configuration may be thermally inefficient or may require excessive area.

The Effectiveness-NTU Method: When Outlet Temperatures Are Unknown

When one or both outlet temperatures are not specified, the effectiveness-NTU method is often more practical. It expresses performance in terms of how much heat is transferred relative to the maximum possible.

Define heat capacity rates:

$$C_h={\dot{m}}_h{c}_{p,h},C_c={\dot{m}}_c{c}_{p,c}$$

Then:

$$C_{min}=\min (C_h,C_c),C_{max}=\max (C_h,C_c),C_r=\frac{C_{min}}{C_{max}}$$

The maximum possible heat transfer is:

$$Q_{max}=C_{min}(T_{h,in}-T_{c,in})$$

Effectiveness is:

$$\epsilon =\frac{Q}{Q_{max}}$$

The number of transfer units (NTU) is:

$$NTU=\frac{UA}{C_{min}}$$

For each exchanger type (parallel, counter, crossflow with mixed/unmixed assumptions), correlations relate $\epsilon$ to $NTU$ and $C_r$. Once $\epsilon$ is found, you compute $Q=\epsilon Q_{max}$ and then determine outlet temperatures from the energy balance.

This method is especially useful in selecting or rating compact exchangers, HVAC coils, and situations where the exchanger area is known but the resulting outlet temperatures must be predicted.

Design Considerations That Matter in Practice

Thermal sizing is necessary, but it is rarely sufficient. Successful heat exchanger design balances performance, reliability, and cost.

Overall Heat Transfer Coefficient and Thermal Resistances

The overall coefficient $U$ bundles multiple resistances in series: convection on the hot side, conduction through the wall, convection on the cold side, plus fouling. A typical resistance form is:

$$\frac{1}{U}=\frac{1}{h_h}+R_{f,h}+R_w+R_{f,c}+\frac{1}{h_c}$$

where $h$ values are film coefficients and $R_f$ are fouling resistances. Even a thin fouling layer can dominate thermal resistance, so conservative fouling allowances are common in design standards.

Pressure Drop and Pumping Power

Higher velocities improve convection and reduce the required area, but they increase pressure drop. Pressure drop limits are often set by available pump head, compressor power, or process constraints. In gas-side heat transfer, pressure drop can be a dominant cost driver because moving large gas volumes is expensive.

Temperature Approach and Pinch Constraints

Designs are often constrained by minimum temperature difference requirements, sometimes called the approach temperature. Very tight approaches demand large areas because the driving force becomes small near the “pinch” region. Counterflow typically handles small approaches better than parallel flow.

Materials, Corrosion, and Mechanical Constraints

Fluid chemistry, operating temperature, and pressure determine materials selection. Stainless steels, titanium, and nickel alloys may be needed for corrosive service, while carbon steel may be adequate for benign fluids. Mechanical design must also address thermal expansion, vibration risk (especially in shell-and-tube exchangers), gasket compatibility in plate exchangers, and allowable stresses.

Fouling, Cleaning, and Maintainability

Cooling water, oils, and many process fluids foul over time. Designs should anticipate cleaning methods:

• Shell-and-tube exchangers can be mechanically cleaned on the tube side when removable bundles are used.
• Plate heat exchangers offer high heat transfer coefficients but require cleanable plate packs and careful gasket selection.
• Air-side finned coils can foul with dust and require access for washing or filtration.

Configuration Selection in Brief

• Shell-and-tube: robust, wide pressure and temperature capability, easier to design for high pressure, often larger footprint.
• Plate: compact, high $U$, good for liquid-to-liquid duties, limited by gasket materials unless welded/brazed.
• Finned-tube air coolers/radiators: suited for gas-side heat transfer where surface area must be increased with fins.

A Practical Design Workflow

A typical engineering workflow looks like this:

1. Define duty and constraints: required $Q$, inlet temperatures, allowable outlet temperatures, pressure drop limits, fouling expectations, materials constraints.
2. Choose a preliminary configuration: based on fluids, pressures, cleanliness, and maintenance.
3. Thermal sizing:

• Use LMTD when terminal temperatures are known