Numerical prediction of heat transfer between a bubbling fluidized bed and an immersed tube bundle

In this paper a numerical analysis of the heat transfer between a bubbling fluidized bed of mono-dispersed glass beads of Geldart type B and an immersed heated tube bundle is investigated. The numerical procedure is based on a solution of the mass, momentum and energy equations of both phases with an Eulerian approach. Different physical models for the thermal transport coefficient of the solid phase were used. The results are compared with new experimental data. The numerical and the experimental results show a strong correlation between fluid dynamics and heat transfer similar to the packet theory of Mickley and Fairbanks (1955). B Defined in equation (15) – - c _p Specific heat J/kg/K - d _s Particle diameter m - d _Tube Diameter of the heat transfer tube m - g, Gravitational constant m/s² - g ₀ Radial distribution function – - h Specific enthalpy J/kg - k Solids fluctuating energy diffusion coefficient Pa s - Nu Nusselt number – - p Pressure N/m² - p _s Solid pressure N/m² - Heat flux W - Heat flux W - Re Reynolds number – - T Temperature K - T(t) Measured foil temperature K - t Time s - tr Trace of a tensor (sum of main-diagonal elements) m/s - v Velocity, v-direction m/s - Velocity vector m/s - x x-coordinate m - y y-coordinate m - Volumetric interphase heat transfer coefficient W/m³/K - Bed-to-wall heat transfer coefficient W/m²/K - _gs Fluid-particle heat transfer coefficient W/m²/K - _T Heat transfer coefficient at tube surface W/m²/K - Interphase drag coefficient kg/m³/s - Thickness of CuNi foil m - Dissipation of fluctuating energy Pa/s - Volume fraction – - Angle ° - Thermal conductivity W/m/K - _cyl Defined in equation (13) – - Fluctuating energy exchange Pa/s - Volumetric heat generation rate W/m³ - Density kg/m³ - Granular temperature m²/s² - Viscous stress tensor N/m² - Defined in equation (14) – - Bulk Bulk properties - g Gas phase - gas Gas - i i = g, s (gas or solid) - m Mixture - pen Penetration theory - pm Particle material - s Solid phase - T Tube - Tube Tube - t total - W Wall - * Parameter multiplied by the volume fraction of its phase