![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
In this paper, numerical and experimental analyses of the heat transfer between an immersed heater and a cone bed of sand particles were carried out. A three-dimensional (3D) model using the Eulerian–Eulerian model coupled with the kinetic theory for granular flow was used to simulate heat transfer and the related bed flow characteristics. The effects of different inlet gas velocities, represented by the fluidizing number (the ratio between inlet gas velocity to minimum fluidizing velocity), and different particle-wall boundary conditions on heat transfer and hydrodynamics were investigated. Both the experiments and numerical simulation results showed that the heat transfer coefficient and the bed expansion ratio increased with increasing the inlet gas velocity. For the particle-wall boundary condition, applying the no-slip condition showed the best agreement in the heat transfer coefficient and the bed expansion ratio to the experimental results.
Nomenclature
| CD | = | drag coefficient |
| Cp | = | specific heat, J kg−1 K−1 |
| ds | = | diameter of the particles, m |
| e | = | coefficient of restitution |
| g | = | gravitational acceleration, m s−2 |
| go | = | radial distribution function |
| H | = | enthalpy, J |
| h | = | heat transfer coefficient, W m−2 K−1 |
| I | = | electrical current, A |
| k | = | thermal conductivity, W m−1 K−1 |
| N | = | fluidizing number |
| Nu | = | Nusselt number |
| p | = | pressure, Pa |
| Pr | = | Prandtl number |
| R | = | radius of the reactor, m, bed expansion ratio |
| R | = | lateral distance, m |
| Res | = | solid Reynolds number |
| T | = | temperature, K |
| V | = | voltage, V |
| v | = | velocity, ms−1 |
| Z | = | height above the air inlet, m |
| α | = | gas–solid drag exchange coefficient |
| β | = | interphase drag exchange coefficient |
| δ | = | interphase heat transfer coefficient, W m−1 K−1 |
| ε | = | volume fraction |
| μ | = | viscosity, N s m−1 |
| Θ | = | granular temperature, m2 s−2 |
| ρ | = | density, kg m−3 |
| = | stress tensor | |
| Subscripts | = | |
| b | = | bed |
| col | = | collision |
| eff | = | effective |
| g | = | gas |
| kin | = | kinetic |
| PF | = | particle fluctuation |
| s | = | solid |
| w | = | heater wall |
Nomenclature
| CD | = | drag coefficient |
| Cp | = | specific heat, J kg−1 K−1 |
| ds | = | diameter of the particles, m |
| e | = | coefficient of restitution |
| g | = | gravitational acceleration, m s−2 |
| go | = | radial distribution function |
| H | = | enthalpy, J |
| h | = | heat transfer coefficient, W m−2 K−1 |
| I | = | electrical current, A |
| k | = | thermal conductivity, W m−1 K−1 |
| N | = | fluidizing number |
| Nu | = | Nusselt number |
| p | = | pressure, Pa |
| Pr | = | Prandtl number |
| R | = | radius of the reactor, m, bed expansion ratio |
| R | = | lateral distance, m |
| Res | = | solid Reynolds number |
| T | = | temperature, K |
| V | = | voltage, V |
| v | = | velocity, ms−1 |
| Z | = | height above the air inlet, m |
| α | = | gas–solid drag exchange coefficient |
| β | = | interphase drag exchange coefficient |
| δ | = | interphase heat transfer coefficient, W m−1 K−1 |
| ε | = | volume fraction |
| μ | = | viscosity, N s m−1 |
| Θ | = | granular temperature, m2 s−2 |
| ρ | = | density, kg m−3 |
| = | stress tensor | |
| Subscripts | = | |
| b | = | bed |
| col | = | collision |
| eff | = | effective |
| g | = | gas |
| kin | = | kinetic |
| PF | = | particle fluctuation |
| s | = | solid |
| w | = | heater wall |