# NTU method - maximum heat transfer rate (q_max)

## Description

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 T_h,i – T_c,i (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 rates (i.e. mass flow rate multiplied by specific heat) C_h and C_c for the hot and cold fluids respectively, and denoting the smaller one as C_min.

Then the maximum possible heat transfer rate (q_max) is calculated by the shown formula.

The effectiveness can be calculated by the formula:

Related formulas## Variables

q_{max} | Maximum heat transfer rate (W) |

C_{min} | The smaller heat capacity rate between the hot and cold fluids (W/K) |

T_{hi} | Inlet temperature of the hot stream (K) |

T_{ci} | Inlet temperature of the cold stream (K) |