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exchanger con?gurations: (i) circular tubes with ?at ?ns (., Kays and London’s surface ), whose thermalhydraulic characteristics are j 188。 $ ,tubes and ?ns (Kays and London’s surface ), whose thermalhydraulic characteristics are j 188。 $ f 188。 $, s 188。 and Dh 188。 mm. Also note that Pr z for air. Fig. 4 pares the performance characteristics ( j and f curves) of surfaces 188。 rucDh/m. Fig. 5 pares the dimensionless entropy generation Observed for both surfaces as a function of NTU. A curve ofε 188。 ε(NTU), which the same for both surfaces, is also plotted to be used as a reference. It can be clearly seen that the (ε, NTU) design which minimizes the rate of entropy generation is (, ) for surface (, ) for surface . It can also be noted that the circular?n surface showed a higher rate of entropy generation for all NTU span,which is mostly due to the viscous ?uid ?ow effect assurface has a higher friction factor than surface 3/8T for the same Reynolds number (see Fig. 4). For low NTU values, where the entropy generation is ruled by NS,DT, both surfaces showed similar NS values as their jcurves are close (see Fig. 4).Fig. 6 pares three different condenser designs consid ering surface under the same working conditions. The heat exchanger length was also varied in order to acmodate the heat transfer surface area for different face areas. For a vertical, constant NTU line (. same heat transfer area), it can be clearly observed that a heat exchanger design with high aspect ratio (higher face area, smaller length in the ?ow direction) produces a signi?cantly lower amount of entropy in parison to a low aspect ratio design (lower face area, larger length). It can be additionally observed that the NS curves converge for low NTU values. This is so as the pressure drop effects, which rule the entropy generation for the low aspect ratio designs, are attenuated for low NTU values where the entropy generation due to ?nite temperature difference is Dominant. Now consider an airsupplied evaporator for household refrigeration appliances, prised of 10 tube rows in the ?ow 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。 As/AfL, do also have optimum values (see Fig. 9) since both are strongly dependent on Ntu: 4L/Dh 188。 NTU/St (see Fig. 9a) and b 188。 4s/Dh (see Fig. 9b) where St 188。 j/Pr 2/3 is the Stanton number. In both cases, the optimum ?ow path and heat exchanger surface area density are calculated as follows: ( 9) ( 10) Fig. 9 illustrates Eqs. (9) and (10). Unlike Fig. 8, the curves in Fig. 9a do not converge for low NTU values as lower s values imp