CHE-37

Exchanger duty Q=UA ΔTlm

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

Reading speed

Heat exchangersTEMA

Governing equation

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

$A \in \left[0.2, 200\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

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

$A \in \left[0.2, 200\right]$

$A = 0.2$ $Q = 2$

Along the curve

②

Domain of the variable — blue

A_{\min} = 0.2,\quad A_{\max} = 200

$A \in \left[0.2, 200\right]$

$A = 0.2$ $A = 0.2$

Along the curve

③

Response curve — green

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

$A \in \left[0.2, 200\right]$

$A = 0.2$ $Q = 2$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Q}{\mathrm{d}A}

$A \in \left[0.2, 200\right]$

$A = 1.457$ $Q^{\prime} = 10$

Along the curve

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

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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