Classical thermodynamics, heat transfer Definition

NTU method

Builds on Heat exchanger theory Heat transfer coefficient

Definition

Consider the two-stream heat exchanger model with heat capacity rates $C_h$ and $C_c$ , overall heat transfer coefficient $U$ , area $A$ , and inlet temperatures $T_{h,i} > T_{c,i}$ . Let $C_{\min} = \min(C_h, C_c)$ , $C_{\max} = \max(C_h, C_c)$ and $C_r = C_{\min} / C_{\max}$ .

The largest possible heat rate is $q_{\max} = C_{\min} (T_{h,i} - T_{c,i})$ .
The effectiveness of the exchanger is $\varepsilon = q / q_{\max}$ , where $q$ is its actual heat rate.
The number of transfer units is $\mathrm{NTU} = U A / C_{\min}$ .

The NTU method computes $q = \varepsilon \, q_{\max}$ , where $\varepsilon = \varepsilon(\mathrm{NTU}, C_r)$ is the function obtained by solving the model for the given flow arrangement.

Remarks

The standard effectiveness relations are as follows. For parallel flow, $\varepsilon = \dfrac{1 - e^{-\mathrm{NTU}(1 + C_r)}}{1 + C_r}$ . For counterflow with $C_r < 1$ , $\varepsilon = \dfrac{1 - e^{-\mathrm{NTU}(1 - C_r)}}{1 - C_r \, e^{-\mathrm{NTU}(1 - C_r)}}$ , and for $C_r = 1$ , $\varepsilon = \mathrm{NTU}/(1 + \mathrm{NTU})$ . In the limit $C_r = 0$ , as for a stream that condenses or boils, $\varepsilon = 1 - e^{-\mathrm{NTU}}$ for every arrangement.

Example: counterflow with $C_r = 0.5$ and $\mathrm{NTU} = 2$ gives $\varepsilon = (1 - e^{-1})/(1 - 0.5 e^{-1}) \approx 0.632/0.816 \approx 0.77$ . So the exchanger transfers about $77$ percent of $q_{\max}$ .

Non-example: if $T_{h,i} = T_{c,i}$ , then $q_{\max} = 0$ and clause 2 does not define an effectiveness.

Always $0 \le \varepsilon \le 1$ , and $\varepsilon$ increases with $\mathrm{NTU}$ .

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Tag	`RA3XR6T2MB`
URI	`m2://RA3XR6T2MB`
Kind	definition
Writing	W0 stub
MSC	80A19, 80A20
Defines	NTU method
Uses	Heat exchanger theory, Heat transfer coefficient
Changed	3 November 2026

NTU method

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