There is sniffer test done for identifying heat exchanger tube rupture. Basically a hydrocarbon detector is used in the cooling water return line to detect if any hydrocarbon is coming in return water.
In case of heat exchange between 2 different med, it can be predicted by temperatures of shell and tube side. However for single tube leak or leaks from few tubes it may be difficult to identify, except if there is some reactivity defined.
A cooling tower uses evaporative cooling for creating cooling media to be used for heat exchange.
Cooling towers also have a lot of water conditioning operations viz. Blowdown, chlorination, water makeup etc
A heat exchanger is of various types with a single purpose of energy exchange in terms of heat. It may have both latent and sensible or just sensible heat exchange.
Both equipment is based on phase change phenomenon .
In heat exchanger use fast and stabilised the liquid to its general temperature but cooling tower use large section to exposed to liquid to gas phase phenomenon.
In cooling tower the heat transfer through convection and in HX heat trasfer through conduction