The LMTD method needs all four terminal temperatures. Very often you know only the two inlets and the hardware — and then the effectiveness–NTU method is the one that works.

It runs on capacity rates. Multiply a stream's mass flow by its specific heat, $C = \dot{m} c_p$, and you have how many kilowatts that stream carries for every kelvin it changes, in $\mathrm{kW/K}$. Of the two streams, $C_{min}$ is the SMALLER and $C_{max}$ the larger — the subscripts name size, not hot and cold, and either stream may be either. The smaller one always changes temperature more, and it is the one everything is measured against.

Three groups follow. $C_r = \dfrac{C_{min}}{C_{max}}$, the capacity rate ratio, between 0 and 1 — 1 means perfectly balanced streams, 0 means one side is condensing or boiling and never changes temperature. $\mathrm{NTU} = \dfrac{UA}{C_{min}}$, the number of transfer units, a bare number that is the exchanger's SIZE: conductance measured in units of the smaller stream. And $\dot{Q}_{max} = C_{min}(T_{h,in} - T_{c,in})$, the ceiling — the smaller stream taken all the way to the other stream's inlet, which no exchanger of any size ever beats.

Effectiveness is then simply how much of that ceiling you reach: $\varepsilon = \dfrac{\dot{Q}}{\dot{Q}_{max}}$, between 0 and 1 always. An $\varepsilon$ above 1 is not a very good exchanger; it is an arithmetic error, usually C_max used where C_min belonged.

And the two roads meet: for counterflow, $\varepsilon = \dfrac{1 - e^{-\mathrm{NTU}(1 - C_r)}}{1 - C_r \, e^{-\mathrm{NTU}(1 - C_r)}}$ — performance predicted from hardware alone, no outlet temperatures anywhere. When the streams are balanced ($C_r = 1$) that expression is indeterminate and collapses to the much friendlier $\varepsilon = \dfrac{\mathrm{NTU}}{1 + \mathrm{NTU}}$, which is worth memorising on its own.