【正文】 direction and 2 rows in the transversal direction, whose performance characteristics are as follows f z is the ?nning factor, L m is the heat exchanger Fig. 7 shows the rate of entropy generation as a function of NTU for the nofrost evaporator. It can be clearly seen that the length, Dt z 8 mm is the tube ., Af z m is the face area, and s z . The working conditions are:Tiz260K. In the following analysis, the mass transfer and the related frost accretion phenomena have not been taken into entropy generation takes place for NTU w and ε/1, thus indicating that, in this type of evaporator, the pressure drop effects are negligible in parison with the heat transfer with ?nite temperature difference. Noheless, these ?gures may change dramatically in presence of frost, which increases not only the pressure drop but also the thermal conduction resistance. also noted that the minimum dimensionless entropy generation rate not only increases as s decreases, but also that the optima move towards the left, Indicating that the pressure drop effects bee dominant for lower NTU values as s decreases. It can also be noted that the curves for different s converge for low NTU values as mainly affects the pressure drop rather than the temperature difference, being the former attenuated for low NTU values. In addition to the optima found for the number of transfer units and, consequently, for the heat exchanger effectiveness, two other important design parameters, the ?ow path, 4L/Dh, and the heat exchanger surface area density, b 188。 mm. Also note that Pr z for air. Fig. 4 pares the performance characteristics ( j and f curves) of surfaces 188。 $, s 188。 $ ,tubes and ?ns (Kays and London’s surface ), whose thermalhydraulic characteristics are j 188。 300 K (Waltrich et al., 2021。 1kW, _ V 188。 j(Re) and f 188。 (ToeTi)/(TseTi) as the coil surface temperature, Ts,must be free to vary thus ensuring that Q (andso _Q and _ m) is constrained. However, the solution is Ts, thus requiring an iterative calculation procedure:a guessed Ts value is needed to calculate the effectiveness and NTU 188。 （ 6） where NS is the dimensionless rate of entropy generation. The errors associated to the approximation used in Eq. (4) are marginal: noting that DTm 20 K in most smallcapacity refrigeration applications, it follows that the difference between the exact and approximated mean temperature never exceeds 1 K, which in turn affects the dimensionless entropy generation by less than 1%. Now noting that both condensers and evaporators are designed to provide a heat transfer duty subjected to ?ow rate and face area constraints Eq. (6) can be rewritten as follows (Hermes, 2021): （ 7） And Q188。 hAs/mcp is the number of transfer units. The pressure drop, on the other hand, can be calculated from(Kays and London, 1984): （ 3） where f is the friction factor, uc is the velocity in the minimum ?ow passage, Ac, and the subscripts “i” and “o” refer to the heat exchanger inlet and outlet ports, respectively. One should note that Eqs. (1) and (3) can be linked to each other through the following approximation for the Gibbs relation, （ 4） where Tmz(Ti 254。 Hermes et al., 2021). However, the models adopted in those studies do not provide a straightforward indication of howthe design parameters (geometry, ?uid properties, working conditions) affect the rate of entropy generation. They also require plex numerical solutions,being therefore not suitable for backoftheenvelope calculations in the industrial a recent publication, Hermes (2021) advanced an explicit, algebraic formulation which expresses the dimensionless rate of entropy generation as a function of the number of transfer units, the ?uid properties, the thermal hydraulic characteristics ( j and f curves), and the operating. conditions (heat transfer duty, core velocity, and coil surface temperature) for heat exchangers with uniform wall temperature. An expression for the optimum heat exchanger effectiveness, based on the working condi