Natural convection in an enclosure with disconnected and conducting solid blocks

Natural convection through a rectangular enclosure filled with a fluid bathing several discrete, conducting and disconnected solid objects is common in many applications, such as environmental control (e.g., indoor buildings, storage), materials processing (e.g., drying), food processing (e.g., baking), and electronics (e.g., cabinets). The case of an enclosure heated from the side and containing equally spaced, conducting solid square blocks is investigated here by using a continuum model, which treats the fluid and solid constituents individually. The dispersive effect of the solid constituent is isolated by increasing the number of solid blocks (N) while reducing their size as to maintain their relative total volume constant. Results obtained for a wide Rayleigh number (Ra) range and several values of solid-to-fluid conductivity ratio (κ) show the strong hindrance effect of the blocks on the convection process to be dependent on a minimum number of blocks, Nmin, for every Ra. An analytical expression predicting Nmin is proposed and validated by the numerical results.