The Rayleigh Number Effect on the Periodic Heating of an Enclosure Filled With a Fluid and Discrete Solid Blocks

The steady-periodic natural convection phenomenon inside a heated enclosure filled with disconnected, discrete solid blocks, and under horizontal, time-periodic heating is investigated numerically. This configuration is akin to several practical engineering applications, such as oven baking in food processing, heat treating of metal parts in materials processing, and storage and transportation of discrete solid goods in containerization. Because of the relative large size, and limited number of solid bodies placed inside the enclosure, the solid and fluid constituents are viewed separately and the process modeled using continuum balance equations for each with suitable compatibility conditions imposed at their interfaces. The periodic heating is driven by a sinusoidal in time hot-wall temperature, while maintaining the cold wall temperature constant, with top and bottom surfaces adiabatic. Results are presented in terms of hot and cold wall-averaged Nusselt numbers, time-varying energy capacity of the enclosure, and periodic isotherms and streamlines, for Ra varying from 10³ to 10⁷, Pr equal to 1, and 36 uniformly distributed, conducting and disconnected solid square blocks. The results explain why and how the effect of varying Ra on the convection process is significantly affected by the presence of the solid blocks. An analytical equation, valid for time-periodic heating, is proposed for anticipating the block interference effect with great accuracy, substantiating the distinct features of Nusselt versus Rayleigh observed when the blocks are present inside the enclosure.