CHE-37

Exchanger duty Q=UA ΔTlm

Q = U A ΔTlm. Design equation of a two-stream exchanger.

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Heat exchangersTEMA

Governing equation

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

where

U: Overall coefficient (W/m²·K)
A: Area (m²)
\Delta T_{\mathrm{lm}}: LMTD (K)
Q: Duty (kW)

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-37 — Exchanger duty Q=UA ΔTlm) is the form associated with TEMA. Working symbols: $U$ , $A$ , $\Delta T_{\mathrm{lm}}$ $\rightarrow$ $Q$ . Newton's law of cooling integrated with the log-mean driving force. U lumps film, wall and fouling resistances.

Purpose

Purpose: compute

Q

from

U

A

\Delta T_{\mathrm{lm}}

in Chemical engineering via

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

Q = U A ΔTlm. Design equation of a two-stream exchanger. Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

U = 400.000\,\mathrm{W/m^{2}·K}

A = 12.000\,\mathrm{m^{2}}

\Delta T_{\mathrm{lm}} = 25.000\,\mathrm{K}

, the governing relation

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

yields

Q = 120.00\,\mathrm{kW}

. Two streams, an area A, a Q arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Overall coefficient U400 W/m²·KArea A12 m²LMTD \Delta T_{\mathrm{lm}}25 K

Outputs

Duty Q120.00 kW

Reading speed

Watch on YouTube

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Narration of this film

Two streams, an area A, a Q arrow.

Newton's law of cooling integrated with the log-mean driving force. U lumps film, wall and fouling resistances.

Reading speed

Watch on YouTube