Fin Ratio, Fin Efficiency, and Selection of Fin Parameters

In the previous section, we discussed the principles of heat transfer and selection criteria for finned tubes. In this section, we will cover two important concepts related to finned tubes: the fin ratio and fin efficiency, along with considerations for selecting fin parameters.

However, first, we propose a method for labeling the structural parameters of finned tubes and fins themselves:

(1) Labeling Method for Finned Tubes and Fins

  • Labeling of Finned Tubes and Fins StructureWe use CPG to represent the abbreviation of “CHIPIAN GUAN” (finned tube). The structural characteristics, material, and manufacturing methods of the finned tube can be represented using the following series of numbers or symbols:

    CPG ( φDb×δ / Df / P / T – X / Y – A )

    Where:

    • CPG: Finned tube
    • φDb×δ: Outer diameter and thickness of the base tube
    • Df: Outer diameter of the fin, mm
    • P: Pitch of the fin, mm
    • T: Thickness of the fin, mm
    • X: Material of the base tube (Fe: iron, Al: aluminum, Cu: copper)
    • Y: Material of the fin
    • A: Manufacturing method (I: high-frequency welding; if not specified, it defaults to high-frequency welding)

    Example: CPG ( φ32×3.5 / 64 / 8 / 1 – Fe / Fe ) indicates that the finned tube has a base tube outer diameter of 32 mm, wall thickness of 3.5 mm, fin outer diameter of 64 mm (fin height of 16 mm), fin pitch of 8 mm, fin thickness of 1 mm, and both the base tube and fin are made of carbon steel and are high-frequency welded.

    Additionally, sometimes it is necessary to label the structural parameters of the fin itself separately. The labeling method is as follows:

    CP ( Db / Df / P / T – Y )

    Each symbol represents the same meaning as in the finned tube notation. For example:

    CP ( 32 / 62 / 8 / 1 – Fe ) indicates that the base tube outer diameter is 32 mm, fin outer diameter is 62 mm (fin height of 15 mm), fin pitch is 8 mm, fin thickness is 1 mm, and the material is carbon steel.

(2) Fin Ratio

The fin ratio refers to the multiple increase in surface area after adding fins to a bare tube. It is denoted by “β,” which is calculated as:

β = (Original outer surface area of the bare tube) / (Total outer surface area of the finned tube)

Calculation Example: For a finned tube, CPG ( φ25×2.5 / 50 / 4 / 1 – Fe / Fe ), calculate its fin ratio.

Number of fins per meter of tube length n = 1000 / 4 = 250

Area of fins per meter of tube length:

Af = 250 × [π/4 {(Df² – Db²) × 2 + π × Df × T}] = 0.775 m²

Bare tube area between fins per meter of tube length:

Ao = π × Db × 1 × (P – T) / P = 3.1416 × 0.025 × 1 × 3 / 4 = 0.0589 m²

Outer surface area of the bare tube per meter of tube length:

Ab = 3.1416 × 0.025 = 0.0785 m²

Fin ratio:

β = (Af + Ao) / Ab = (0.775 + 0.0589) / 0.0785 = 10.62

This means the heat transfer area after adding fins is 10.62 times that of the original bare tube.

For several commonly used finned tubes, the calculated fin ratios are listed in Table-1 for reference:

(3) Fin Efficiency

When fins are attached to the surface of a bare tube, the heat transfers from the base of the fins outward along their height, while continuously transferring heat to the surrounding fluid through convective heat transfer. This results in a gradual decrease in fin temperature along their height, as shown in the figure below.

The gradual decrease in fin temperature along their height indicates that the temperature difference between the fin and the surrounding fluid decreases, reducing the heat transfer rate per unit area. Consequently, the effectiveness of the fin area in enhancing heat transfer decreases. The taller the fins, the less contribution their increased area makes to heat transfer. Therefore, the concept of fin efficiency is introduced.

Fin efficiency η = (Actual heat dissipated from the fin surface) / (Heat dissipated assuming the fin surface temperature equals the base temperature)

Since fin efficiency is less than 1, doubling the fin surface area does not double the heat dissipation; rather, it increases by a factor of fin efficiency. The value of fin efficiency depends on the shape, height, thickness, material of the fins, and importantly, the convective heat transfer coefficient outside the tube. Calculations are complex and time-consuming. Below are some pre-calculated values for commonly used finned tubes in engineering practice, as shown in Table-1.

Table-1: Structural Characteristics of Fins

Fin Specifications Fin Ratio β Fin Efficiency η Effectiveness (β × η) Discussion
CP (25/50/6/1—Fe) 7.4 0.82 6.07 *
CP (25/55/6/1—Fe) 9.2 0.78 7.18 **
CP (25/55/6/1—Al) 9.2 0.92 8.46 **
CP (32/62/8/1—Fe) 6.62 0.78 5.16 *
CP (32/70/8/1—Fe) 8.71 0.71 6.18 **
CP (32/62/6/1—Fe) 8.49 0.78 6.62 **
CP (38/68/8/1—Fe) 6.32 0.79 4.99 *
CP (38/76/8/1—Fe) 8.25 0.72 5.94 **
CP (38/68/6/1—Fe) 8.10 0.79 6.40 **
CP (51/81/8/1—Fe) 5.92 0.81 4.80 *
CP (51/89/8/1—Fe) 7.60 0.73 5.55 **

The effectiveness of fins is the final indicator of the product of fin ratio (β) and fin efficiency (η).

(4) Effectiveness of Fins

Effectiveness of fins refers to the increase in convective heat transfer coefficient based on the outer surface area of the base tube after adding fins. The formula derived is:

ho = h × [( Ao + Af × η ) / Ab]

Here,

  • ho: Convective heat transfer coefficient based on the outer surface area of the bare tube, representing the overall effect after adding fins.
  • h: Convective heat transfer coefficient of the fin surface.
  • Ao, Af, Ab: Bare tube area in the fin gap, fin area, and original bare tube area.

Since Ao << Af, the formula can be simplified to:

ho = h × η × [( Ao + Af ) / Ab] = h × η × β

Thus, the product of fin ratio and fin efficiency (η × β) becomes the final indicator of fin effectiveness. For the group of finned tubes listed in Table-1, their effectiveness (η × β) values are also included. For example, for CP (38/68/8/1—Fe), assuming the convective heat transfer coefficient of the fin surface is h = 50 W/(m²·°C), the fin effectiveness is 5.94, leading to the convective heat transfer coefficient based on the outer surface area of the bare tube ho = 50 × 5.94 = 297 W/(m²·°C).

(5) Considerations for Selecting Fin Parameters

  • Selection of Fin Height: From the calculations in the table above, it is evident that for commonly used high-frequency welded finned tubes, when the fin height is 15 mm, the fin efficiency is around 0.8. When the fin height reaches 20 mm, the fin efficiency drops to around 0.7. This suggests that choosing a fin height of 15 mm is appropriate. If a fin height over 20 mm is selected, caution is advised due to the low fin efficiency, which is generally not recommended. For aluminum fins used in air coolers, since aluminum has a much higher thermal conductivity than carbon steel, a fin efficiency of around 0.8 can be achieved even with fin heights of 22-25 mm.
  • Selection of Fin Pitch: Choosing a smaller pitch can effectively increase the fin ratio. However, caution is needed when selecting the pitch. Factors to consider include:
    • Properties of the fluid and the likelihood of fouling. There are three scenarios:
      1. Severe fouling conditions, such as exhaust gases from electric furnaces in steel plants, converter furnaces, and certain industrial kilns. High fin pitches should be used, e.g., 10 mm or more, supplemented with reasonable designs for ash removal and the use of soot blowers.
      2. Conditions where fouling is not severe but still significant, such as exhaust gases from power plant boilers and industrial boilers. A fin pitch of around 8 mm is suitable, supplemented with designs that have self-cleaning capabilities.
      3. Conditions with minimal fouling or no fouling, such as exhaust gases from natural gas combustion equipment or air coolers. A fin pitch of 4-6 mm is acceptable. For aluminum air coolers, the fin pitch is often around 3 mm.
    • Processing technology and cost of the fins should also be considered when selecting the fin pitch.

  • Selection of Fin Thickness: Primarily consider the corrosive and abrasive nature of the fluid. For severely corrosive and abrasive conditions, thicker fins can be selected.