Concurrent Flow - In this exchange system, the two fluids flow in the same direction. As the diagram shows, a concurrent exchange system has a variable gradient over the length of the exchanger. With equal flows in the two tubes, this method of exchange is only capable of moving half of the property from one flow to the other, no matter how long the exchanger is. If each stream changes its property to be 50% closer to that of the opposite stream's inlet condition, exchange will stop because at that point equilibrium is reached, and the gradient has declined to zero. In the case of unequal flows, the equilibrium condition will occur somewhat closer to the conditions of the stream with the higher flow.
Countercurrent Flow - By contrast, when the two flows move in opposite directions, the system can maintain a nearly constant gradient between the two flows over their entire length. With a sufficiently long length and a sufficiently low flow rate this can result in almost all of the property being transferred. However, note that nearly complete transfer is only possible if the two flows are, in some sense, "equal". If we are talking about mass transfer, then this means equal flowrates of solvent or solution, depending on how the concentrations are expressed. For heat transfer, then the product of the average specific heat capacity (on a mass basis, averaged over the temperature range involved) and the mass flow rate must be the same for each stream. If the two flows are not equal (for example if heat is being transferred from water to air or vice-versa), then conservation of mass or energy requires that the streams leave with concentrations or temperatures that differ from those indicated in the diagram.
Countercurrent exchange is much more efficient due to the fact that you have two currents flowing in opposite directions. This allows for faster fluid exchange. This occurs in the kidneys for example. It can be a much more efficient way of fluid/gas/nutrient exchange as opposed to concurrent exchange.
This link should help:
http://www.stolaf.edu/people/mckelvey/envision.dir/exchange.dir/exchange.html
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