Stirred Tank Heat Transfer Coefficient (ho)

Select the type of heat transfer surface.
Inner diameter of the stirred tank. Consistent length units required.
Thermal conductivity of the bulk liquid (broth). Consistent units required.
Diameter of the impeller. Must use same length unit as dT.
Rotational speed of the impeller. Units must be revolutions per time (e.g., rps or rpm converted to rps).
Density of the bulk liquid (broth). Consistent units required.
Dynamic viscosity of the bulk liquid (broth) at bulk temperature. Consistent units required.
Specific heat capacity of the bulk liquid (broth). Consistent units required.
Dynamic viscosity of the liquid (broth) evaluated at the heat transfer surface (wall) temperature. Same units as μL.

Calculation Explanation

This calculator estimates the broth-side film heat transfer coefficient (\(h_o\)) in agitated Newtonian fluids within stirred tank bioreactors, using empirical correlations (Table 7.1). The correlations depend on the heat transfer configuration (cooling coils or jacketed vessel).

The correlations relate the Nusselt number (\(Nu\)) to the Reynolds number (\(Re\)), Prandtl number (\(Pr\)), and a viscosity correction factor:
Nu = C ⋅ Rea ⋅ Pr1/3 ⋅ (μLw / μL)0.14

Where:
- Nu = ho dT / kT (Nusselt Number - dimensionless heat transfer) - Re = di² N ρL / μL (Reynolds Number - ratio of inertial to viscous forces) - Pr = Cp μL / kT (Prandtl Number - ratio of momentum diffusivity to thermal diffusivity) - ho: Broth-side film heat transfer coefficient (target value, e.g., W/(m²·K)). - dT: Tank diameter (e.g., m). - kT: Liquid thermal conductivity (e.g., W/(m·K)). - di: Impeller diameter (e.g., m). - N: Agitation speed (e.g., rev/s). - ρL: Liquid density (e.g., kg/m³). - μL: Liquid viscosity at bulk temperature (e.g., Pa·s). - Cp: Liquid specific heat capacity (e.g., J/(kg·K)). - μLw: Liquid viscosity at wall temperature (e.g., Pa·s).

The constants C and a depend on the configuration:

The calculator first computes Re and Pr, then selects the appropriate C and a based on your choice, calculates Nu, and finally solves for \(h_o\).
Ensure all input units are consistent (e.g., use SI units throughout).