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Goodness Factor Comparisons
DOI 10.1615/hedhme.a.000302
3.9.7 Goodness factor comparisons
Surface geometries must be selected for each fluid stream before the heat exchanger design can be undertaken. This selection will depend on mechanical design and thermal performance considerations. On a thermal performance basis alone, one desires a surface geometry that meets the required cost, size, and friction power limitations. Several “goodness factors” have been proposed to allow comparison of surface performance characteristics in this regard (LaHaye et al., 1974; Kays and London, 1951; Cox and Jallouk, 1973; Bergles et al., 1974; Soland et al., 1976). These methods compare the thermal performance of two surfaces on a friction power basis. By writing the heat transfer coefficient (α) and the friction power (P) as functions of j, f, ReDh, and Dh, one obtains
\[\label{eq1} \alpha=\frac{c_{p}\eta}\,{\mbox{Pr}^{2/3}}\frac{j\mbox{Re}_{D_{h}}}{D_{h}} \tag{1}\]
\[\label{eq2} \frac{P}{A}=\frac{\eta^{3}}{2\rho^{2}}\frac{f\,\mbox{Re}^{3}_{D_{h}}}{D^{3}_{h}} \tag{2}\]
The thermal performance of two surfaces may be compared by plotting j ReDh Dh versus f (ReDh /Dh)3, which compares the heat transfer coefficients for equal friction power per unit surface area. For equal P /A, or f (ReDh /Dh)3, the surface having the largest value of j ReDh /Dh will require the least heat transfer surface area for equal thermal effectiveness. Alternatively, one may modify Equation 1 and Equation 2 to allow comparison on a volume basis. Multiplying each equation by (β = A /V = 4σ /Dh) allows comparison of α A /V versus P /V. Thus, for equal friction power per unit volume (P /V), one compares the heat exchanger volumes for equal thermal effectiveness.
The application of Equation 1 and Equation 2 are illustrated in Figure 1. This figure shows the performance of the surfaces of Figure 299.1 and Figure 299.2 on a surface area goodness factor basis. The graph is prepared for the case of equal hydraulic diameter. Figure 1 shows that the offset-strip fin yields significantly higher heat transfer coefficients for equal P /A. As the Reynolds number is reduced to small values, associated with laminar flow, the offset fin loses some of its advantage.
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