Numerical investigation of laminar compressible natural convection flow in asymmetrically and isothermally heated open-ended inclined channel

This study presents a numerical investigation of laminar compressible natural convection flow induced under high-temperature difference in an open-ended inclined parallel-walled channel heated isothermally and asymmetrically at the top wall (hot plate facing downwards) while the lower plate is considered adiabatic. The investigation is carried out with air (Pr=0.72) as the working fluid for a temperature difference of 110 °C from the ambient, over of range of modified Rayleigh number 6.2×10¹ to 1.6×10⁴ and inclination of channel varying between 10 and 90° with respect to horizontal position. For the simulation, compressible governing equations without Boussinesq approximation is solved by employing new modified all-speed Roe scheme with matching preconditioning method, dual time-stepping technique and utilizing the modified Local One-dimensional Inviscid (LODI) relations suitable for compressible natural convection flow as non-reflecting boundary conditions at the inlet and outlet of the channel. Average Nusselt number based on inter-plate spacing increases with the increase of modified Rayleigh number and also with the increase of inclination from the horizontal position. This increase in average Nusselt number can be described by the variation of the level of thermal saturation inside the channel. Significant reduction in average Nusselt number is observed in the combined zone of lower angle of inclination and lower modified Rayleigh number. Visualization of fluid flow (temperature contour and velocity magnitude contour) indicates the existence of both fully developed flow and developing flow regime within the span of investigated modified Rayleigh number. Based on the investigation, a composite correlation between average Nusselt number and product of modified Rayleigh number and the sine of the angle of inclination considering as a single parameter is presented which can be conveniently used for designing of engineering application dealing with natural convection heat transfer under high-temperature difference.