Before the tube leak, name W the flow of the hot fluid through the shell with higher pressure than the cold fluid that flows with the flow rate Q inside the tubes.

After the leak, part of W, for example W´, goes into the tube and as the hot fluid has an additional path, the total shell flow will be higher, but the new tube flow Q´ will be lower than Q.

The tube outlet temperature will be higher because the cold fluid is mixed with a part of the hot fluid and the final shell outlet temperature depends on the tube leak size and its location.

In order to obtain a practical design, if one of the streams is corrosive, it must flow inside the tubes rather than the shell. In a shell-and-tube design, the shell has many more objects and surfaces requiring special fabrication (stamping, welding, cutting, etc.), while the tubes are more simple and bending is comparatively easy. Corrosion-resistant materials are always more expensive, often less ductile, and more difficult to weld. This is the motivation for alternative designs, such as the one pictured. These are often designed to be dismantled, cleaned, and repaired.

Looks like someone trying to get ResearchGate members to do a homework problem.

The leakage will certainly affect the performance of the heat exchanger. The extent depends on the design parameters which are not given. One can write generalised equations for the situation based on simple classical heat exchanger design, but it is better to focus on the actual situation to reduce the time wasted in over generalising. The most critical factors are obviously pressure differences and temperature differences. How is the size of the leak known?

The only reason why anyone would want to "quantify" the impact of a leak (or other failure) would be to perform a cost/benefit analysis of how long to wait before taking a component out of service (possibly forcing a shut-down) in order to effect repairs. You might also want to weigh repair vs. change of design, because this will likely occur again. We don't care how well something works that's obviously broken—unless this is a hypothetical problem such as homework, as Brian suggests. This is why you don't see John Doe's Famous Leak Correction Factor in the literature. Leaks also result in mixing (cross contamination) of the fluids, which may be far more expensive to remedy.

Hi Muhammad and all.

It looks very much like a clasroom quiz. By the way, as a rule, high pressure fluid goes to the tubes. There is no simple or straightforward answer to the question. Initially, the shell fluid (high pressure and hot) will flow into the damaged tube (low pressure and cold), possibly in both directions. This depends on various factors including, mainly, the pressure difference between pipelines carrying each fluid. Due to the mixture, the hot fluid in the damaged pipe will lose its identity: it is a third fluid in the system (new density, viscosity and temperature). The pressure will build up in the heat exchanger head, where corrosive fluid from all tubes met. The incomimg high pressure and hot fluid would be split in two streams. One would go through the line for the would be heated corrosive fluid. The other would push the remaining corrosive fluid back upstream, possibly through the pump driving it. The process would be mostly unsteady/transient. Eventually, the heat exchanger will work as a passage/lung vessel, flooded with the high-pressure fluid.