Numerical analysis and optimization of natural convection heat transfer in inclined square cavities with sinusoidal heating elements

Abstract This study presents a numerical analysis of natural convection heat transfer within inclined square cavities featuring sinusoidal heating elements. The analysis, conducted using a finite volume approach implemented in ANSYS 16.0, aims to estimate flow and heat regimes under steady-state conditions. Grid-independent analyses were performed to ensure numerical accuracy. The vertical walls of the enclosure were maintained at a cold temperature, while the other two walls were perfectly insulated. Key parameters investigated include Rayleigh numbers (10 4 , 10 5 , 10 6 ), corrugation numbers (3, 5, and 7), amplitude values (0.1, 0.3 and 0.5), and enclosure inclination angles (δ = 0°, 15°, 30°, 45°, 60°, 75°). The sinusoidal element’s diameter to enclosure length ratio was set at 0.4, and fluid properties were assumed constant with a Prandtl number of 7.0. Results were illustrated using isothermal and flow lines, with heat transfer discussed in terms of local and average Nusselt numbers. Findings indicate that at Ra = 10 6 , local Nusselt numbers exhibited a sinusoidal distribution influenced by corrugation and amplitude, with a 50% increase in local Nusselt number as amplitude increased from 0.1 to 0.5. Average Nusselt number enhancements were observed with higher corrugation numbers and wave amplitudes, while the number and size of eddies were sensitive to Rayleigh numbers. Enclosure inclination significantly affected the formation of vortices, particularly at angles of 60° and 75°.