Heat exchanger capacity

In a heat exchanger, two fluids flow past each other. In the process, heat flows from the hotter to the colder fluid. The heat exchanger capacity, i.e. the heat flow transferred in watts, depends on several factors:

Flow type: counter or direct current

Input temperature difference

Volumetric flow rates of the two fluids

Size of the heat transferring surface

Heat transfer coefficient

If both fluids flow in the same direction, it is called a co-current heat exchanger; if they flow in the opposite direction, it is called a countercurrent heat exchanger.

In principle, countercurrent flow is the most thermodynamically efficient form of flow. All other factors being equal, more heat is transferred in counterflow than in co-current flow due to better utilization of the temperature curves.

Calculating heat exchanger

Most heat exchangers transfer heat indirectly. This means that the material flows are spatially separated from each other by heat-conducting material (usually metal) and cannot mix.

The heat is first transferred from the hot fluid to the partition wall (convective heat transfer), then heat conduction takes place through the wall and on the other side there is again convective heat transfer to the colder fluid. Only the resulting total heat transfer is decisive for the performance and calculation of the heat exchanger. This can best be imagined analogous to electrical engineering as a series connection of 3 resistors:
$$\frac{1}{kA} = R = R_{\rm fl1} + R_{\rm w} + R_{\rm fl2}$$
Instead of thermal resistance, the product of heat transfer coefficient \(k\) and heat transfer area \(A\) is more commonly used.

The driving potential for a heat flow \(\dot{Q}\) is a temperature difference \(\Delta T\) (analogous to electric current and voltage difference). However, in the heat exchanger the temperature difference between the two fluids is not constant but changes as it flows through. The temperature of the cold fluid increases and that of the warm fluid decreases. These effects must be taken into account in the heat exchanger calculation. For simple flow forms (co-current and counter-current) this is possible with the logarithmic temperature difference:
$$\dot{Q}=kA \frac{\Delta T_{\rm a} - \Delta T_{\rm b}}{\ln \frac{\Delta T_{\rm a}}{\Delta T_{\rm b}}}$$