Finned surfaces efficiency

The efficiency depends on the fin geometrical configuration, the fin thermal conductivity, and the heat transfer coefficient at the fin surface. 

These two may not be the same. In some instances, high-finned surface area but low bare tube surfece means that a lot of tall (sometimes less efficient) fins are crowded onto the tube. In this case, horsepower might be expected to be higher. 

The fin surface area will not be as effective as the bare tube surface, as the heat has to be conducted along the fin. This is allowed for in design by the use of a fin effectiveness, or fin efficiency, factor. The basic equations describing heat transfer from a fin are derived in Volume 1, Chapter 9 see also Kern (1950). The fin effectiveness is a function of the fin dimensions and the thermal conductivity of the fin material. Fins are therefore usually made from metals with a high thermal conductivity for copper and aluminium the effectiveness will typically be between 0.9 to 0.95. 

The total efficiency for a finned surface may be defined as the ratio of the total heat transfer of the combined area of the surface and fins to the heat which would be transferred if this total area were maintained at the base temperature T0. Show that this efficiency can be calculated from... 

C Two finned surfaces are identical, except that the convection heat transfer coefficient of one of them is twice that of the other. For which finned surface is the (a) fin effectiveness and (b) fin efficiency higher Explain. 

The effective area for heat transfer from a finned surface is the sum of the prime area (the tube surface between the fins) and the finned area multiplied by the fin efficiency ... 

In using the fin efficiency, the seemingly precise analytical solutions actually are premised upon several assumptions of unknown validity. Therefore, the resulting numerical values must be used cautiously and conservatively. And it must be remembered that, when using convective heat-transfer correlations for finned surfaces, the experimental data underlying these correlations were reduced using computed fin efficiencies. 

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 the fin cooling or heating situation. The fin temperature effectiveness or fin efficiency is defined as the ratio of the actual heat transfer rate through the fin base... 

In an extended surface heat exchanger, heat transfer takes place from both the fins (r /< 100 percent) and the primary surface (%= 100 percent). In that case, the total heat transfer rate is evaluated through a concept of total surface effectiveness or extended surface efficiency T 0 defined as... 

Subsequently, determine the fin efficiency r and the extended surface efficiency tip ... 

Equation (4.13-5) is only an approximation, since the temperature on the outside surface of the bare tube is not the same as that at the end of the fin because of the added resistance to heat flow by conduction from the fin tip to the base of the fin. Hence, a unit area of fin surface is not as efficient as a unit area of bare tube surface at the base of the fin. A fin efficiency r]y has been mathematically derived for various geometries of fins. 

The overall surface efficiency of the firmed surface can be calculated based on the fin efficiency... 

Where (rg - rn) is the fin height and yt, is the fin thickness. For the TRACE gas cooler design, the quantity x" is about 1.5, resulting in a fin efficiency of about 0.6. The actual fin efficiency would be determined with a more detailed equipment design and subsequent testing, The TRACE model uses cylindrical geometry hydraulics and heat structures. The heat structure is nodalized at 40 axial and 5 radial nodes. Axial conduction is enabled. The material properties applied are for Alloy 600. The TRACE heat structure has the same dimensions as an individual tube. A multiplier is used to produce the correct total heat transfer area. The fin surfaces are not explicitly modeled in TRACE. Instead, a gas (outside tube) heat transfer coefficient multiplier is used to account for the additional effective area. 

The subscripts / and o correspond to inner and outer surfaces of tube, respectively. In these equations, Pi is a reference area for which U is defined, and T[ is the total efficiency of a finned heat-transfer surface and is related to the fin efficiency, Tl by... 

Fin efficiency is defined as the ratio of the mean temperature difference from surface to fluid divided by the temperature difference from fin to fluid at the base or root of the fin. Graphs of fin efficiency for extended surfaces of various types are given by Gardner [Tmn.s. Am. Soc. Mech. Eng., 67,621 (1945)]. 

Fin efficiencies and fin dimensions are available from manufacturers. Ratios of finned to inside surface are usually available so that the terms Aj, A, and A may be obtained from these ratios rather than from the total surface areas of the heat exchangers. 

The area added by the fin is not as efficient for heat transfer as bare tube surface owing to resistance to conduction through the fin. The effective heat-transfer area is... 

The actual heat flow is calculated by multiplying the fin outer surface area by the fin efficiency. The outer surface area is easy to determine hence, if the fin efficiency is known, the heat transfer from the fin is easily calculated. 

This tube has a ratio of outside to inside surface of about 3.5 and is useful in exchangers when the outside coefficient is poorer than the inside tube coefficient. The fm efficiency factor, which is determined by fm shape and size, is important to final exchanger sizing. Likewise, the effect of the inside tube fouling factor is important to evaluate carefully. Economically, the outside coefficient should be about V5 or less than the inside coefficient to make the finned unit look attractive however, this break-even point varies with the market and designed-in features of the exchanger. 

The total surfece area, A, in the annulus is the sum of the extended surface area and the hare pipe surfeces not covered hy fins. See Table 10-40. The fm efficiency, rj, Cf or E, from Figure 10-154 is corrected for the percent surlace that is finned. The corrected value, is the effective surfece efficiency. 

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