Heat exchangers are devices that facilitate the exchange of heat between two fluids that are at different temperatures while keeping them from mixing with each other. Heat exchangers are commonly used in practice in a wide range of applications, from heating and air-conditioning systems in a household, to chemical processing and power production in large plants. Heat exchangers differ from mixing chambers in that they do not allow the two fluids involved to mix. In a car radiator, for example, heat is transferred from the hot water flowing through the radiator tubes to the air flowing through the closely spaced thin plates outside attached to the tubes.

Heat transfer effectiveness ε, defined as ratio of actual heat transfer rate to the maximum possible heat transfer rate ε=$\frac{Q}{Q_max}$ =(Actual heat transfer rate)/(Maximum possible heat transfer rate) The actual heat transfer rate in a heat exchanger can be determined from an energy balance on the hot or cold fluids and can be expressed as

Q = $C_c(T_c,out -T_c,in) = C_h(T_h,in - T_h,out)$

To determine the maximum possible heat transfer rate in a heat exchanger, we first recognize that the maximum temperature difference in a heat exchanger is the difference between the inlet temperatures of the hot and cold fluids. That is, $∆T_max$=$T_(h,in)-T_(c,in)$