Bubble Column Heat Transfer Coefficient (h_o)

Calculation Explanation

This calculator estimates the liquid-side film heat transfer coefficient (\(h_o\)) in bubble columns for Newtonian broths using two different empirical correlations.

Correlation 1 (Dimensional):
h_o = 9391 ⋅ U_G^0.25 ⋅ (μ_Lw / μ_L)^0.35
This correlation is dimensionally specific. The constant 9391 assumes inputs are in standard SI units (U_G in m/s, viscosities in kg/(m·s) or Pa·s) to yield h_o in W/(m²·K).
Validity Range (Newtonian broths):

• \(10^{-3} < \mu_L < 5 \times 10^{-2}\) kg m⁻¹ s⁻¹
• \(U_g \le 0.1\) m s⁻¹
• \(0.1 \le d_T \le 1\) m (Tank diameter, \(d_T\), is not an input but affects validity)

Correlation 2 (Dimensionless Groups):
St = h_o / (ρ_L C_p U_G) = 0.1 ⋅ [ (U_G³ ρ_L / (μ_L g)) ⋅ (μ_L C_p / k_T)² ]^1/4
This can be rewritten using the Prandtl number (\(Pr = \mu_L C_p / k_T\)):
St = 0.1 ⋅ [ (U_G³ ρ_L / (μ_L g)) ⋅ Pr² ]^1/4
The calculator computes the term in the square brackets, finds St (Stanton number), and then solves for h_o.
h_o = St ⋅ ρ_L ⋅ C_p ⋅ U_G
Acceleration due to gravity (g) is taken as 9.81 m/s².

Where:
- h_o: Liquid-side film heat transfer coefficient (W/(m²·K)). - U_G: Superficial gas velocity (m/s). - ρ_L: Liquid density (kg/m³). - μ_L: Liquid viscosity at bulk temperature (kg/(m·s)). - μ_Lw: Liquid viscosity at wall temperature (kg/(m·s)). - C_p: Liquid specific heat capacity (J/(kg·K)). - k_T: Liquid thermal conductivity (W/(m·K)). - g: Acceleration due to gravity (≈ 9.81 m/s²). - St: Stanton Number (dimensionless). - Pr: Prandtl Number (dimensionless).

Ensure all input units are consistent (SI units assumed as per labels). Results from the two correlations may differ.