Many additional analytical results for fully developed laminar flow (Re ≤ 2,000) are presented in Shah and London (1978) and in Shah and Bhatti (1987). In this case, it can be shown that Δp ∞ u m Reducing the hydraulic diameter is an obvious way to increase exchanger compactness and heat transfer, or D h can be optimized using well-known heat transfer correlations based on design problem specifications. Here, H1 denotes constant axial wall heat flux with constant peripheral wall temperature, H2 denotes constant axial and peripheral wall heat flux and T denotes constant wall temperature.Īs Nu = αD h/λ, a constant Nu implies the convective heat transfer coefficient α is independent of the flow velocity and fluid Prandtl Number.Īn increase in α can best be achieved either by reducing D h or by selecting a geometry with a low aspect ratio, rectangular flow passage. Three thermal boundary conditions (denoted by the subscripts H1, H2, and T) have a strong influence on the Nusselt numbers. Rectangular passages approaching a small aspect ratio exhibit the highest Nu and fRe. There is a strong influence of flow passage geometry on Nu and fRe. In this case, the total heat transfer rate is evaluated through a concept of total surface effectiveness or surface efficiency η o defined as: In an extended surface heat exchanger, heat transfer takes place from both the fins (η f < 100%) and the primary surface (η f = 100%). These results are not valid when the fin is thick or is subject to variable heat transfer coefficients or variable ambient fluid temperature, nor for fins with temperature depression at the base. Fin efficiency formulas for some common plate-fin and tube-fin geometries of uniform fin thickness are presented in Table 1. This 1-D fin efficiency is a function of fin geometry, fin material thermal conductivity, heat transfer coefficient at the fin surface and fin tip boundary condition it is not a function of the fin base or fin tip temperature, ambient temperature or heat flux at the fin base or fin tip. Since most real fins are “thin,” they are treated as one-dimensional (1-D), with standard idealizations used for analysis. The fin temperature effectiveness or fin efficiency is defined as the ratio of the actual heat transfer rate through the fin base divided by the maximum possible heat transfer rate through the fin base, which can be obtained if the entire fin is at base temperature (i.e., its material thermal conductivity is infinite). The concept of fin efficiency accounts for the reduction in temperature potential between the fin and the ambient fluid due to conduction along the fin and convection from or to the fin surface, depending on fin cooling or heating situation. įin efficiency and extended surface efficiency Note that shell-and-tube exchangers sometimes employ individually finned tubes-low finned tubing (similar to Figure 2a but with low height fins). Major categories of extended surface heat exchangers are Tube-fin Tube-fin ( Figure 1), and Tube-fin ( Figure 2, individually finned tubes – Figure 2a and flat fins on an array of tubes – Figure 2b) exchangers. Fins are attached to the primary surface by brazing, soldering, welding, adhesive bonding or mechanical expansion, or extruded or integrally connected to tubes. Fins may also be used on the high heat transfer coefficient fluid side in a heat exchanger primarily for structural strength (for example, for high pressure water flow through a flat tube) or to provide a thorough mixing of a highly-viscous liquid (such as for laminar oil flow in a flat or a round tube). In addition, enhanced fin geometries also increase the heat transfer coefficient compared to that for a plain fin. Pins are primarily used to increase the surface area (when the heat transfer coefficient on that fluid side is relatively low) and consequently to increase the total rate of heat transfer. Fins can be of a variety of geometry-plain, wavy or interrupted-and can be attached to the inside, outside or to both sides of circular, flat or oval tubes, or parting sheets. Extended surfaces have fins attached to the primary surface on one side of a two-fluid or a multifluid heat exchanger.
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