Effect of inclination angle on heat transport properties in two-dimensional Rayleigh-Bénard convection with smooth and rough boundaries

Using direct numerical simulations, two-dimensional tilted Rayleigh-Bénard convection is studied in both smooth and roughness facilitated convection cell of double-aspect-ratio for air as a working fluid. We investigate the effect of inclination angle (0^○ ≤ Φ ≤ 90^○) on heat flux (Nu), Reynolds number (Re), and flow structures. In a Rayleigh number range 10⁶ ≤ Ra ≤ 10⁹, we address the Ra dependence of Nu(Φ) trend. In the smooth case, while greater tilt results in highest heat flux below Ra=10⁸, Nu drops with Φ monotonically above it. For the smooth case, we identify the control parameters (Φ=75^○ and Ra=10⁷) which yield maximum heat flux (an increment of 18% with respect to the level case). On the other hand, among the three roughness setups, the tallest roughness configuration yields the maximum increment in heat flux (25%) in vertical convection (Φ=90^○) at Ra=10⁶. With increase in Ra, Re changes with Φ marginally in the smooth case, whereas it shows notable changes in its roughness counterpart. We find that the weakening of thermal stratification is directly related to the height of roughness peaks. While Ra delays the onset of thermal stratification (in terms of Φ) in the smooth case, an increase in roughness height plays the same role in roughness facilitated convection cells.