Thermal systems / Field guide 02

A first-pass heat exchanger check

Before estimating area, make the proposed inlet and outlet states agree with conservation of energy. Then check the temperature driving force. A plausible UA from inconsistent temperatures is still a bad design input.

1. Close both sides of the energy balance

For a single-phase stream with approximately constant heat capacity, use Q = ṁ c_p ΔT. For a refrigerant changing phase or a fluid with strongly varying properties, use measured or modeled enthalpies: Q = ṁ(h_out − h_in), with the sign chosen consistently for each stream.

Compare hot-side heat loss with cold-side heat gain. A mismatch can come from sensors, property data, heat loss to ambient, or a wrong flow measurement. Do not silently average a large mismatch away.

2. Compute the counterflow driving force

For counterflow, define ΔT₁ = T_h,in − T_c,out and ΔT₂ = T_h,out − T_c,in. Both must be positive for this simple sensible-heat example. Calculate ΔT_lm = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂); if they are equal, use their common value. The first-pass conductance is UA = Q/ΔT_lm. Crossflow and multipass layouts need an appropriate correction or another exchanger method.

Worked example

Consider hot water at 0.20 kg/s cooling from 60 to 45 °C and cold water at 0.25 kg/s warming from 20 to 32 °C. Using c_p = 4,180 J/(kg·K) on both sides gives 12.54 kW from each energy balance. The counterflow end differences are 28 and 25 K, so ΔT_lm ≈ 26.47 K and UA ≈ 474 W/K. These are illustrative inputs, not a component rating.

3. Test the limits before selecting hardware

Check minimum approach temperature, pressure drop at both flow rates, fouling allowance, flow regime, and off-design states. A very small approach can demand much more area or become impossible once control and property variation are included. Record which side defines the area basis when converting UA into U and A.

Download the review worksheet

Try the heat exchanger tool for a quick calculation and carry the assumptions into your worksheet.

Compare two measured operating cases with the exchanger comparison tool.

Further reading

U.S. Department of Energy, Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2 covers LMTD and exchanger temperature profiles.

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