Thermal Convection in a Tilted Rectangular Cell with Aspect Ratio 0.5

Thermal convection in a three-dimensional tilted rectangular cell with aspect ratio 0.5 is studied using direct numerical simulations within both Oberbeck–Boussinesq (OB) approximation and strong non-Oberbeck–Boussinesq (NOB) effects. The considered Rayleigh numbers Ra range from 10^5 to 10^7, the working fluid is air at 300 K, and the corresponding Prandtl number Pr is 0.71. Within the OB approximation, it is found that there exist multiple states for Ra=10^5 and hysteresis for Ra=10^6. For a relatively small tilt angle \beta, the large-scale circulation can either orient along one of the vertical diagonal planes (denoted by M_\rm d mode) or orient parallel to the front wall (denoted by M_\rm p mode). Which of the two modes transports heat more efficiently is not definitive, and it depends on the Rayleigh number Ra. For Ra=10^7 and \beta=0^\circ, the time-averaged flow field contains four rolls in the upper half and lower half of the cell, respectively, M_\rm d and M_\rm p modes only developing in tilted cells. By investigating NOB effects in tilted convection for fixed Ra=10^6, it is found that the NOB effects on the Nusselt number Nu, the Reynolds number Re and the central temperature T_\rm c for different \beta ranges are different. NOB effects can either increase or decrease Nu, Re and T_\rm c when \beta is varied.