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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 to , 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 and hysteresis for . For a relatively small tilt angle β, the large-scale circulation can either orient along one of the the vertical diagonal planes (denoted by mode) or orient parallel to the front wall (denoted by mode). Which of the two modes transports heat more efficiently is not definitive, and it depends on the Rayleigh number Ra. For and , the time-averaged flow field contains four rolls in the upper half and lower half of the cell, respectively, and modes only developing in tilted cells. By investigating NOB effects in tilted convection for fixed , it is found that the NOB effects on the Nusselt number Nu, the Reynolds number Re and the central temperature for different β ranges are different. NOB effects can either increase or decrease Nu, Re and when β is varied.

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