Engineering guide
The module calculates heat transfer in stirred vessels according to chapter N3.2 of the VDI Wärmeatlas (VDI Heat Atlas, 12th edition 2019). It determines the heat transfer coefficient between the agitated vessel contents and the heat exchange surfaces — the vessel wall with a jacket or double jacket, internal coils or other internals — as a function of impeller type, rotational speed and the physical properties of the medium.
In practice, this calculation is needed for every temperature-controlled stirred vessel in apparatus and plant engineering: reactors with exothermic reactions, crystallizers, batching and storage vessels with heating or cooling jackets. To calculate heat transfer in a stirred tank, the Nusselt number of the respective exchange surface is determined from the impeller Reynolds number and the Prandtl number, and from it the heating or cooling times and the required exchange area.
The correlations of the VDI Wärmeatlas cover the common impeller types such as paddle, anchor, propeller, disc (Rushton) and helical ribbon impellers, and also account for viscous and shear-thinning (non-Newtonian) media via a representative viscosity.
Scope
- Heat transfer and Power consumption in stirred vessels: Heat transfer
Typical workflow
Define geometry and agitation system
The vessel diameter, filling height, impeller type and impeller diameter, rotational speed and the type of heat exchange surface (jacket, half-pipe coil, internal coil) are specified. The correlation constants depend on this combination.
Provide the physical properties of the vessel contents
Density, dynamic viscosity, thermal conductivity and specific heat capacity are determined at the mean product temperature; the viscosity additionally at wall temperature for the viscosity correction term. For non-Newtonian media, a representative apparent viscosity is formed from the flow law and the impeller-specific shear rate.
Form the dimensionless numbers
The impeller Reynolds number and the Prandtl number are calculated from rotational speed, impeller diameter and the physical properties. They characterize the flow regime in the vessel from laminar to fully turbulent.
Evaluate the Nusselt correlation
For the chosen combination of impeller and exchange surface, the Nusselt relationship of the VDI Wärmeatlas is evaluated with its equipment-specific constants and exponents, including the correction factor for the viscosity ratio between bulk flow and wall.
Determine heat transfer coefficient and overall heat transfer
The inner heat transfer coefficient follows from the Nusselt number. Together with wall conduction, the outer heat transfer in the jacket and any fouling resistances, the overall heat transfer coefficient is obtained, from which heating/cooling duty and tempering times are calculated.
Frequently asked questions
Which impeller provides the best heat transfer at the vessel wall?
Close-clearance impellers such as anchor or helical ribbon impellers renew the boundary layer at the wall directly and have the advantage with highly viscous media. With low-viscosity media, high-speed impellers (propeller, disc impellers) achieve comparable or better values at lower torque through high turbulence. What matters is always the combination of medium, Reynolds range and exchange surface — exactly what the equipment-specific constants of the correlations represent.
How are non-Newtonian media taken into account?
For shear-thinning media, following the Metzner-Otto concept, an effective shear rate proportional to the rotational speed is assumed and a representative apparent viscosity is calculated from it using the flow law. Reynolds and Prandtl numbers are formed with this viscosity and the Newtonian correlations are approximately retained. For media with a pronounced yield stress or viscoelastic behavior, this approach reaches its limits.
Why does the real overall heat transfer often deviate from the calculated value?
The inside heat transfer is only one partial resistance. In practice, the outer transfer in the jacket often dominates (particularly with unguided jacket flow), along with deposits and fouling on the product side and cake buildup on the wall. Partially filled vessels, baffles and internals also change the flow pattern compared with the experimental conditions of the correlations. Safety margins on the exchange area are therefore common.
Do the correlations also apply in the laminar regime?
The correlations of the VDI Wärmeatlas cover wide Reynolds ranges depending on the impeller type, but the constants and exponents differ between the laminar, transition and turbulent regimes. At very small Reynolds numbers with creeping flow, heat transfer is increasingly co-determined by natural convection and transient conduction; the results are then to be understood as approximations.
Technical content source: LV-Solved-Problems-Content 628d313247e7