NTU method
Encyclopedia
The Number of Transfer Units (NTU) Method is used to calculate the rate of heat transfer in heat exchangers (especially counter current exchangers) when there is insufficient information to calculate the Log-Mean Temperature Difference (LMTD). In heat exchanger analysis, if the fluid inlet and outlet temperatures are specified or can be determined by simple energy balance, the LMTD method can be used; but when these temperatures are not available The NTU or The Effectiveness method is used.
To define the effectiveness of a heat exchanger we need to find the maximum possible heat transfer that can be hypothetically achieved in a counter-flow heat exchanger of infinite length. Therefore one fluid will experience the maximum possible temperature difference, which is the difference of
(The temperature difference between the inlet temperature of the hot stream and the inlet temperature of the cold stream). The method proceeds by calculating the heat capacity rate
s (i.e. mass flow rate multiplied by specific heat)
and 
for the hot and cold fluids respectively, and denoting the smaller one as 
. The reason for selecting smaller heat capacity rate is to include maximum feasible heat transfer among the working fluids during calculation.
A quantity
is then found,where
is the maximum heat that could be transferred between the fluids. According to the above equation, to experience the maximum heat transfer the heat capacity should be minimized since we are using the maximum possible temperature difference. This justifies the use of 
in the equation.
The effectiveness(E), is the ratio between the actual heat transfer rate and the maximum possible heat transfer rate:
where
Effectiveness is dimensionless quantity between 0 and 1. If we know E for a particular heat exchanger, and we know the inlet conditions of the two flow streams we can calculate the amount of heat being transferred between the fluids by
For any heat exchanger it can be shown that
For a given geometry,
can be calculated using correlations in terms of the 'heat capacity ratio'
and the number of transfer units,
where
is the overall heat transfer coefficient and 
is the heat transfer area.
For example, the effectiveness of a parallel flow heat exchanger is calculated with
Or the effectiveness of a counter-current flow heat exchanger is calculated with
Similar effectiveness relationships can be derived for concentric tube heat exchangers and shell and tube heat exchangers. These relationships are differentiated from one another depending on the type of the flow (counter-current, concurrent, or cross flow), the number of passes (in shell and tube exchangers) and whether a flow stream is mixed or unmixed.
Note that the
is a special case in which phase change condensation
or evaporation
is occurring in the heat exchanger. Hence in this special case the heat exchanger behavior is independent of the flow arrangement. Therefore the effectiveness is given by
To define the effectiveness of a heat exchanger we need to find the maximum possible heat transfer that can be hypothetically achieved in a counter-flow heat exchanger of infinite length. Therefore one fluid will experience the maximum possible temperature difference, which is the difference of
(The temperature difference between the inlet temperature of the hot stream and the inlet temperature of the cold stream). The method proceeds by calculating the heat capacity rateHeat capacity rate
The heat capacity rate is heat transfer terminology used in thermodynamics and different forms of engineering denoting the quantity of heat a flowing fluid of a certain mass flow rate is able to absorb or release per unit temperature change per unit time...
s (i.e. mass flow rate multiplied by specific heat)
and for the hot and cold fluids respectively, and denoting the smaller one as . The reason for selecting smaller heat capacity rate is to include maximum feasible heat transfer among the working fluids during calculation.A quantity
is then found,where
is the maximum heat that could be transferred between the fluids. According to the above equation, to experience the maximum heat transfer the heat capacity should be minimized since we are using the maximum possible temperature difference. This justifies the use of in the equation.The effectiveness(E), is the ratio between the actual heat transfer rate and the maximum possible heat transfer rate:
where
Effectiveness is dimensionless quantity between 0 and 1. If we know E for a particular heat exchanger, and we know the inlet conditions of the two flow streams we can calculate the amount of heat being transferred between the fluids by
For any heat exchanger it can be shown that
For a given geometry,
can be calculated using correlations in terms of the 'heat capacity ratio'and the number of transfer units,
where
is the overall heat transfer coefficient and is the heat transfer area.For example, the effectiveness of a parallel flow heat exchanger is calculated with
Or the effectiveness of a counter-current flow heat exchanger is calculated with
Similar effectiveness relationships can be derived for concentric tube heat exchangers and shell and tube heat exchangers. These relationships are differentiated from one another depending on the type of the flow (counter-current, concurrent, or cross flow), the number of passes (in shell and tube exchangers) and whether a flow stream is mixed or unmixed.
Note that the
is a special case in which phase change condensationCondensation
Condensation is the change of the physical state of matter from gaseous phase into liquid phase, and is the reverse of vaporization. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition....
or evaporation
Evaporation
Evaporation is a type of vaporization of a liquid that occurs only on the surface of a liquid. The other type of vaporization is boiling, which, instead, occurs on the entire mass of the liquid....
is occurring in the heat exchanger. Hence in this special case the heat exchanger behavior is independent of the flow arrangement. Therefore the effectiveness is given by