Heat Transfer and Flow Resistance of Finned Tube Bundles

In the first and second lectures, the concept of convective heat transfer coefficient $h$ on the outer surface of finned tubes was introduced, particularly emphasizing the need for finned tubes due to low heat transfer coefficients on the air or flue gas side. This lecture will explain how to calculate the heat transfer coefficient. Additionally, when fluid flows through a finned tube bundle, it encounters flow resistance, leading to a pressure drop $Δ P$ . Larger pressure drops indicate greater power consumption. Therefore, calculating the pressure drop is also essential, and this lecture will introduce methods for doing so.

1. Convective Heat Transfer Coefficient Around Finned Tube Bundles

First, let’s revisit the definition of heat transfer coefficient $h$ : it is the amount of heat transferred per unit time, per unit area, and per unit temperature difference when fluid flows over a solid surface. Note that the temperature difference here refers to that between the solid surface and the fluid. In this lecture, $h$ is represented in units of W/(m²·°C).

As previously mentioned, finned tubes can be arranged in either inline or staggered configurations, as shown below. Since the flow states differ between inline and staggered arrangements, their heat transfer coefficients are calculated differently.

For inline and staggered flow arrangements:

All formulas for calculating the convective heat transfer coefficient around finned tube bundles are derived experimentally. Many factors influence these experiments, leading to empirical correlations. Different researchers may derive slightly different empirical correlations, but results under similar conditions should be close. Our task is to select reliable correlations for calculations. Here, we recommend the empirical correlation developed by Briggs and Young, who studied over ten types of staggered annular finned tube bundles with triangular pitch spacing. Their standard error was around 5%. Below is their experimental result for high finned tube bundles:

When $(d_{f} / d_{b}) = 1.7 2.4$ , $d_{b} = 1241$ mm, $h = 0.1378 (d ^{b} λ) (μ d ^{b} G ^{max})^{0.718} (P r)^{0.333} (H Y)^{0.296}$ where $d_{f}$ and $d_{b}$ are the fin outer diameter and base tube diameter, respectively; $Y$ and $H$ are the fin gap and height; $λ$ , $μ$ , and $P r$ are the fluid’s thermal conductivity, viscosity, and Prandtl number, respectively; $G_{max}$ is the mass flow rate at the narrowest cross-section, in units of kg/(m²·s).

The narrowest cross-section refers to the space between adjacent finned tubes. From the equation, the primary factor influencing $h$ is the flow velocity, proportional to $G_{max 0.718}$ .

2. Flow Resistance Around Finned Tube Bundles

Robinson and Briggs conducted isothermal flow resistance tests on over ten types of staggered annular finned tube bundles. The test range was: $R e = (μ d ^{b} G ^{max}) = 200050000$ $P_{t} / d_{b} = 1.8 4.6$ $d_{b} = 1241$ mm

The pressure drop expression is: $Δ P = f \times (2 ρ N G ^{max 2})$ where $N$ is the number of longitudinal tube rows, and $f$ is the friction factor, a dimensionless number. For bundles arranged in triangular pitch, the friction factor is calculated as: $f = 37.86 (μ d ^{b} G ^{max})^{-0.316} (d ^{b} P ^{t})^{-0.927}$

From the equations, the primary factors affecting the pressure drop $Δ P$ are the flow velocity, proportional to $G_{max 1.684}$ , and the tube spacing, inversely proportional to $P_{t}$ .

3. Calculation Example

Consider a finned tube bundle arranged in an equilateral triangular staggered pattern with a frontal area of 2m × 2m. The airflow rate through the bundle is 32,000 kg/h, and the geometric structure of the finned tube is: CPG (φ38×3.5/70/6/1)

Tube spacing: 92 mm, number of longitudinal rows: 10. Air inlet temperature: 20°C, outlet temperature: 100°C.

Calculate the convective heat transfer coefficient and pressure drop when air flows through the bundle.

3-1 Determine Fluid Properties at Average Temperature

Average temperature = (20 + 100) / 2 = 60°C At this temperature, the properties of air are: Density $ρ = 1.06$ kg/m³ Viscosity $μ = 20.1 \times 1 0^{-6}$ kg/(m·s) Thermal conductivity $λ = 0.029$ W/(m·°C) Prandtl number $P r = 0.696$

3-2 Calculate Flow Velocity

Mass flow rate of air at the frontal area: $G_{f} = 32000/3600/ (2 \times 2) = 2.22$ kg/m²·s Ratio of narrowest cross-sectional area to frontal area: $( P ^{t} \times 1000 ) ( P ^{t} \times 1000 ) - ( 2 \times d ^{b} /2 ) \times 1000 - ( 1000/6 ) \times T \times H \times 2 = ( 92 \times 1000 ) ( 92 \times 1000 ) - ( 38 \times 1000 ) - ( 166.6 \times 1 \times 16 \times 2 ) = 0.529$ Mass flow rate at the narrowest cross-section:

By admin|2024-12-10T08:24:04+00:00November 27th, 2024|Categories: BLOG|0 Comments

Heat Transfer and Flow Resistance of Finned Tube Bundles