**5. Conclusion**

76 Heat Exchangers – Basics Design Applications

transfer which is possible in case of the parallel flow heat exchanger.

Fig. 7. Outlet Temperature of Both Fluids for Parallel, Counter and Cross Flow Heat

 ( ,, *NTU flow arrangement*) . It is logical that the outlet temperature of the fluid 1 is a discontinued function. After the step unit increase of the temperature of the fluid 1 at z = 0, the temperature of the fluid 1 falls due to heating of the wall of the heat exchanger and then heating of the fluid 2. However, in the case of the parallel flow heat exchanger, in the beginning after perturbation, the outlet temperature of the fluid 1 grows even before the perturbation reaches the outlet of the exchanger. This means that at one time of the nonsteady state part of the process, the fluid 2 heats up the flow of the fluid 1, as well as the wall instead of vice versa. Namely, ahead of the front, there is the fluid flow 2 heated up by the fluid flow 1. Since the velocity of the fluid flow 2 is higher than the velocity of the fluid flow 1 therefore, it heats up later non-perturbed part of the flow 1 which is ahead of the moving front of the perturbation. By all means, this indicates that before the occurrence of the perturbation all non-dimensionless temperatures are equal to zero (initial condition). After the time z = 5.33, the perturbation of the fluid 1 has reached the outlet edge of the exchanger which is registered by the step change of the outlet temperature. In case of the cross and counter flow heat exchangers, there is not heating up of the fluid flow 1 ahead of the perturbation front (Fig. 7). The fluid flow 1 cools down in the beginning by heating up the wall of the heat exchanger and the part of the fluid flow 2 in case of the cross flow heat exchanger and the whole fluid flow 1 in the case of counter flow but, it cannot happen that the fluid flow 2 gets ahead of the perturbation front and causes a reversal process of the heat

 

Exchangers.

 

> A method providing exact analytical solutions for transient response of parallel, counter and cross flow heat exchangers with finite wall capacitance is presented. Solutions are valid in the case where velocities are different or equal. These solutions procedure provides necessary basis for the study of parameters estimated, model discriminations and control of all analyzed heat exchangers.

> Generally speaking, the analytical method is superior to numerical techniques because the final solution also preserves physical essence of the problem. Testing of solutions given in this paper indicates that they can be used in practice efficiently when designing and managing processes with heat exchangers.
