Number of transfer units

Physical key figure
Surname	Number of transfer units
Formula symbol	${\displaystyle {\mathit {NTU}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {NTU}}={\frac {k\cdot A}{{\dot {m}}\cdot c_{\mathrm {p} }}}}$
${\displaystyle k}$ Heat transfer coefficient ${\displaystyle A}$ Transfer area ${\displaystyle {\dot {m}}}$ Mass flow ${\displaystyle c_{\mathrm {p} }}$ specific heat capacity
scope of application	Heat transfer

The English term Number of Transfer Units (NTU, dt. For "number of transfer units ") describes a dimensionless number from the field of heat transfer .

The benefit of the NTU is to design a heat exchanger or to recalculate an existing device. The NTU method considerably simplifies the design or recalculation process, as it saves difficult calculations in the case of more complicated flow forms.

NTU can be derived by first using the formula for the fluid (with the mass flow , the specific heat capacity at constant pressure, the temperature difference ) and the formula for the transfer area (with the heat transfer coefficient , the area of the transfer area and the logarithmic temperature difference ), which both have to be the same because of energy conservation: ${\displaystyle {\dot {m}}}$ ${\displaystyle c_{\mathrm {p} }}$ ${\displaystyle \Delta T}$ ${\displaystyle k}$ ${\displaystyle A}$ ${\displaystyle \Delta \vartheta }$

${\displaystyle {\dot {Q}}={\dot {m}}\cdot c_{\mathrm {p} }\cdot \Delta T=k\cdot A\cdot \Delta \vartheta }$

Now this equation is converted into the ratio of the temperature difference and the logarithmic temperature difference, as the latter is difficult to determine in heat exchangers that do not follow the cocurrent or countercurrent principle:

${\displaystyle {\mathit {NTU}}={\frac {k\cdot A}{{\dot {m}}\cdot c_{\mathrm {p} }}}={\frac {\Delta T}{\Delta \vartheta }}}$

In the literature, the expression is also (often ) referred to as heat capacity flow . This term denotes the NTU for heat transfer. The NTU for the mass transfer is calculated as follows: ${\displaystyle {\dot {m}}\cdot c_{\mathrm {p} }}$ ${\displaystyle {\dot {W}}}$ ${\displaystyle {\dot {C}}}$

${\displaystyle {\mathit {NTU}}={\frac {\beta \cdot A}{\dot {V}}}}$

${\displaystyle \beta }$is here the mass transfer coefficient with as a unit and the volume flow. ${\displaystyle \mathrm {m \over s} }$ ${\displaystyle {\dot {V}}}$

To work with NTU you need so-called NTU diagrams, which are available in specialist literature for common types of flow. The NTU can be read off in the diagram using known mass flows and fluid temperatures. The heat transferring surface can be determined by estimating the heat transfer coefficient . ${\displaystyle k}$

literature

• Association of German Engineers, VDI Society for Process Technology and Chemical Engineering (GVC) (Ed.): VDI-Wärmeatlas. (Calculation documents for pressure loss, heat and mass transfer). 10th, revised and expanded edition. Springer, Berlin et al. 2006, ISBN 3-540-25504-4 .

Individual evidence

1. ^ Ramesh K. Shah, Dušan P. Sekulić: Fundamentals of heat exchanger design. Wiley, Hoboken NJ 2003, ISBN 0-471-32171-0 .