Engineering task and calculation objective
The module calculates heat transfer in gas–solid fluidized beds according to chapter M5 of the VDI Wärmeatlas (VDI Heat Atlas, 12th edition 2019). It determines the heat transfer coefficient between the fluidized particle bed and heat transfer surfaces — the vessel wall or immersed internals such as tube bundles and coils — as a function of particle size and density, gas conditions and superficial velocity.
Fluidized beds combine intensive solids mixing with very high heat transfer coefficients and nearly isothermal behavior. The range of applications in plant engineering is correspondingly broad: fluidized bed dryers and coolers, fluidized bed combustion and gasification, catalytic reactors, granulation and coating processes. To calculate heat transfer in a fluidized bed, the operating point must be fixed between the minimum fluidization point and the entrainment point, and the contributions of particle convection, gas convection and radiation must be assessed separately.
The module follows the calculation concept of the VDI Wärmeatlas, which composes the total heat transfer from these mechanisms and also computes the fluidization limits of the bed.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define particle and gas data: Required are the mean particle diameter, particle density and bulk properties, as well as the physical properties of the fluidizing gas (density, viscosity, thermal conductivity, heat capacity) at operating temperature and pressure.
- Calculate the fluidization limits: From the force balance on the packed bed, the minimum fluidization velocity is determined; from the single-particle terminal velocity, the entrainment limit. The operating point of the superficial velocity must lie between both limits; this also documents the existence range of the fluidized bed.
- Characterize the state of the fluidized bed: Using dimensionless numbers (including the Archimedes number), the fluidization behavior, expansion and bubble formation of the bed are classified — from the homogeneously expanded bed of fine particles to the bubbling bed of coarse particles.
- Calculate the contributions to heat transfer: The heat transfer to the surface is composed of the particle-convective component (heat transport by particle packets sweeping the surface), the gas-convective component and, at high temperatures, the radiative component. The particle-convective component dominates for fine particles, the gas-convective one for coarse particles and high pressures.
- Determine the maximum and operating-point heat transfer: The heat transfer coefficient passes through a maximum as a function of superficial velocity. The module provides the curve or the value at the operating point as the basis for designing immersed heating or cooling surfaces.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Minimum fluidization velocity | ν | m/s |
| Fluid velocity | u0 | m/s |
| Density | ρF | kg/m³ |
| Inlet temperature of fluid | ϑf,ein | °C |
| Outlet temperature of fluid | ϑf,aus | °C |
| Mass flux | ṁ | kg/(m²·s) |
| Specific heac capacity | cp,f | J/(kg·K) |
| Thermal conductivity | λf | W/(m·K) |
| Kinematic viscosity | νF | m²/s |
| Particle diameter | d | m |
| Density | ρp | kg/m³ |
| Surface temperature of particle | ϑP | °C |
| Volume-specific particle surface | Av | m² |
| Mass of packed bed | MP | kg |
| Bed voidage at minimum fluidization | Ψmf | - |
| Archimedes number | Ar | - |
| Bed voidage under operating conditions | Ψ | - |
| Nusselt number turbulent | Nuturb | - |
| Number of Transfer Units | NTU | - |
| Reynolds number at terminal velocity | Remf | - |
| Prandtl number | Pr | - |
| Nusselt number laminar | Nulam | - |
| reynolds under operating conditions | Re0 | - |
| Reynolds number at minimum fluidization velocity | Reelu | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Heat transfer coefficient | α | W/(m²·K) |
| Heat flow rate | Q̇ | W |
| Optimum fluidization | Ψopt | - |
| Maximum heat transfer coefficient | αmax | W/(m²·K) |
| Heat transfer efficiency | ε | - |
| Maximum heat flow rate | Q̇max | W |
| Otimum superficial velocity | u0,opt | m/s |
Calculation options
Gas
Helium · Steam · Air · Other
Particle shape
sphere · Any
Heat transfer
Fluid particle · Wall gas · Wall liquid
Geldart particle class
Class A · Class B · Class D
Model
Model 1 · Model 2 · Modell 3 with Nu<sub>g</sub> · Modell 3 with Nu<sub>App</sub> · Model 4
Frequently asked questions
Why is heat transfer in fluidized beds so high?
Fresh particle packets — still at the cold or hot core temperature — are constantly swept against the transfer surface, release heat there across the thin gas gap within a short contact time, and are then mixed back into the bed. This particle-convective mechanism achieves heat transfer coefficients of several hundred W/(m²·K) — far beyond what pure gas convection could deliver at the same velocity.
What influence does the particle size have?
Fine particles (on the order of below a few hundred micrometers) deliver the highest particle-convective heat transfer, because many contact points with small gas-gap resistance are formed; however, powders that are too fine and cohesive fluidize poorly. For coarse particles in the millimeter range, the particle-convective component decreases, while the gas-convective contribution grows with the higher gas velocity required. The maximum of the total transfer shifts accordingly.
What does the maximum of the heat transfer versus gas velocity mean?
Above the minimum fluidization point, heat transfer first rises steeply because particle motion intensifies. At further increased velocity, the solids concentration at the surface decreases again through stronger expansion and larger bubbles, and the transfer drops. Design is usually carried out in the region of the flat maximum, with sufficient margin to the entrainment limit.
When must the radiative component be considered?
At bed temperatures from about 600 °C, as prevail in fluidized bed combustion and gasification, radiation between particles and surface contributes noticeably to the total transfer and must be included using the emissivities of bed and wall. For dryers and coolers in the low-temperature range, it is negligible.