Validation of thermal equilibrium assumption in free convection flow over a cylinder embedded in a packed bed

The validity of the local thermal equilibrium assumption in the free convective steady flow over a circular cylinder heated at constant temperature and embedded in a packed bed of spheres is investigated numerically. For this purpose, the Forchheimer–Brinkman-extended Darcy momentum model and the local thermal non-equilibrium energy model are solved numerically using a spectral element method. Numerical solutions obtained over broad ranges of representative dimensionless parameters, i.e. Rayleigh number (103 ≤ Ra ≤ 5 × 107), solid-to-fluid thermal conductivity ratio (0.1 ≤ kr ≤ 104), cylinder-to-particle diameter ratio (20 ≤ D/d ≤ 100), porosity (0.3 ≤ ε ≤ 0.7), are used to present conditions at which the local thermal equilibrium assumption can or cannot be employed. This study yields that the local thermal equilibrium LTE assumption is true at lower Rayleigh number, higher solid-to-fluid thermal conductivity ratio, higher cylinder-to-particle diameter ratio and lower porosity. In addition, it is found that the solid conductivity has the significant influence on satisfying the LTE, where it is completely satisfied in the system for all values of flow and structural parameters, i.e. Ra, D/d and ε, at higher kr, and vice versa, it cannot be satisfied at lower kr, for the whole ranges of other parameters.