Spatial and temporal evolution of three-dimensional thermovibrational convection in a cubic cavity with various thermal boundary conditions

Abstract

Thermovibrational flow in a differentially heated cubic cavity with vibrations applied in a direction parallel to the imposed temperature gradient is investigated by solving numerically the governing equations for mass, momentum, and energy in their original nonlinear form. A parametric analysis is conducted through the stepwise examination of the following degrees of freedom: magnitude of the Rayleigh number and the thermal behavior of the sidewalls. A complete characterization of the emerging time-varying convective structures is attempted in terms of spatial symmetries broken or retained, related temporal evolution, and global parameters, such as the Nusselt number. It is shown that the intrinsically three-dimensional nature of the problem and its sensitivity to the thermal boundary conditions can have a remarkable influence on the multiplicity of emerging solutions and the system temporal response.