The design basis for choosing the spacing among the geometricadvantages of a group of fixed size (such as, area or volume) likethis that the overall thermal behavior between the tube array andfluid flow. Experimental investigation of heat exchangers withfinned elliptical tubes, as carried out by [50,109,110], shows arelative pressure drop reduction of up to 30% with the relative heattransfer gain observed in the elliptical arrangements whenweighed with the circular ones. A hybrid mathematical modelfor finned circular and elliptic tubes arrangements was formulatedby Rocha et al. [111]. This model is based on energy conservationand heat transfer coefficients achieved from an experiment ofnaphthalene sublimation through a heat and mass transfer analogy[112,113]. Fin temperature and fin efficiency in one and tworow elliptic tube and plate fin heat exchangers are obtainednumerically. A relative fin efficiency gain of up to 18% was detectedwith the elliptical arrangement when fin efficiency results forplate fin and circular tube heat exchangers were compared withthe outcomes of Rosman et al. [114]. The optimal plate-to-platespacing and maximum overall heat conductance for laminarforced convection were studied by Bejan and Sciubba [115]. Theyused two boundary conditions applied on the surfaces of the plate:both uniform heat flux and uniform temperature. The Prandtlnumber was in the range of 0.71rPrr1000. They found that theoptimized space between the plates is proportional to the pressurehead (Δp) the upped to the power (0.25), plate length L0.5, andproperty set (μα)0.25. The maximum overall thermal conductance isproportional to (Δp)0.5. Cooling was performed by the use offorced convection, the previous studies containing the results ofoptimum spacing between parallel plates [116] and plates withcylinders [42,60]. Jubran et al. [117] carried out an experimentalinvestigation of the influence of shroud clearance, wasting pins,and fin pitch on the heat transfer coefficient with circular pin finsin both in-line and staggered configurations. The researchersfound a small and a powerful influence of the wasting pins inthe in-line and staggered arrangements, respectively.
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