Heat exchanger sizing

Start from the duty

Q = ṁₕ cₚₕ (Tₕᵢ − Tₕₒ) = ṁₗ cₚₗ (Tₗₒ − Tₗᵢ)

Both sides must give the same number. The tool takes the hot side as given and solves the cold outlet from it, which is why the cold outlet is a result here rather than an input.

LMTD

ΔTₜₘ = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂)

A = Q / (U · F · ΔTₜₘ)

F is the correction that accounts for an arrangement not being true counter-flow. For a 1 shell / 2 tube pass exchanger this tool evaluates the Bowman expression rather than reading a chart. If F drops below about 0.8 the arrangement is fighting a temperature cross, and the fix is another shell pass — not more tubes.

Effectiveness–NTU

ε = Q / Qₘₐₓ ,  Qₘₐₓ = Cₘᵢₙ(Tₕᵢ − Tₗᵢ)
NTU = U·A / Cₘᵢₙ ,  Cₕ = ṁₕcₚₕ ,  Cₗ = ṁₗcₚₗ

LMTD is the right tool when you know all four temperatures and want an area. ε–NTU is the right tool when you have an exchanger and want to know what it will do. Showing both on one screen makes it obvious when an inconsistent set of temperatures has been assumed.

Watch the pinch

Required area is inversely proportional to the effective ΔT, so as the pinch closes the area curve goes vertical. At a 3 K approach a one-degree instrument error moves the required surface by a third. Buying approach is usually cheaper than buying the last of the recovery.

Fouling

The fouling resistance adds in series: 1/U₌ = 1/U + R₌. It is small in absolute terms and enormous in consequence — on a high-U water-to-water duty a resistance of 0.0002 m²K/W can take fifteen per cent off the clean coefficient.