🔧 Flow Across Banks of Tubes
Convective heat transfer and pressure drop across aligned (inline) and staggered tube bundles using Zukauskas correlations.
Heat Transfer
Parameters Setup
Results & Curves
Configure and run the calculator to see the computed results and velocity sweep curve.
Calculation Methodology
Mathematical Model & Theory
Heat transfer across tube bundles is modeled using the Zukauskas correlation:
$$\text{Nu}_D = C_1 C_2 \text{Re}_{max}^m \text{Pr}^{0.36} \left(\frac{\text{Pr}}{\text{Pr}_s}\right)^{0.25}$$
- $C_1$ and $m$ are constants determined from the Reynolds number range ($\text{Re}_{max} = \rho V_{max} D / \mu$).
- $C_2$ is a row correction factor for banks with fewer than 20 rows ($N_L < 20$).
For aligned arrangement, maximum velocity is:
$$V_{max} = V \frac{S_T}{S_T - D}$$
For staggered arrangement, if the diagonal flow area is smaller than the transverse area, then:
$$V_{max} = V \frac{S_T}{2(S_D - D)}$$
Aerodynamic pressure drop is calculated using friction factors:
$$\Delta P = N \chi f \frac{\rho V_{max}^2}{2}$$
Academic References:
- Incropera, F. P., & DeWitt, D. P. (2011). Fundamentals of Heat and Mass Transfer. 7th Edition, John Wiley & Sons.
- Zukauskas, A. (1972). Heat Transfer from Tubes in Crossflow. Advances in Heat Transfer.
Worked Engineering Example
Air at $25^\circ\text{C}$ flows at $5\text{ m/s}$ across an inline tube bank of 10 rows. Tubes of diameter $25\text{ mm}$ are arranged with pitches $S_T = S_L = 50\text{ mm}$. Surface temp is $100^\circ\text{C}$ ($T_f = 62.5^\circ\text{C}$). Find the convection coefficient $h$.
Step-by-step Solution:
1. Evaluate air properties at film temperature:
- $\rho = 1.177\text{ kg/m}^3, \mu = 1.85 \times 10^{-5}\text{ Pa·s}, k = 0.0263\text{ W/m·K}, Pr = 0.71$.
2. Calculate maximum velocity $V_{max}$:
$$V_{max} = V \frac{S_T}{S_T - D} = 5.0 \times \frac{0.05}{0.05 - 0.025} = 10.0\text{ m/s}$$ 3. Calculate maximum Reynolds number:
$$\text{Re}_{max} = \frac{\rho V_{max} D}{\mu} = \frac{1.177 \times 10.0 \times 0.025}{1.85 \times 10^{-5}} = 15,905$$ 4. From Zukauskas constants ($10^3 < \text{Re}_{max} < 2 \times 10^5$, inline):
- $C_1 = 0.27, m = 0.63$. For 10 rows, $C_2 = 0.97$.
$$\text{Nu}_D = 0.27 \times 0.97 \times (15,905)^{0.63} \times (0.71)^{0.36} \times 1.0 = 93.5$$ 5. Calculate convective coefficient $h$:
$$h = \frac{\text{Nu}_D k}{D} = \frac{93.5 \times 0.0263}{0.025} = 98.4\text{ W/m}^2\text{K}$$