Free convection in an inclined cavity filled with a nanofluid and with sinusoidal temperature on the walls: Buongiorno's mathematical model

Purpose This paper aims to develop a numerical study of the steady natural convection in an inclined square porous cavity filled by a nanofluid with sinusoidal temperature distribution on the side walls and adiabatic conditions on the upper and lower walls. Design/methodology/approach Governing equations transformed in terms of the dimensionless variables using the Darcy-Boussinesq approximation have been solved numerically using a central finite-difference scheme. The Gaus-Siedel iteration technique was used for the system of discretized equations. The two-phase nanofluid model including the Brownian diffusion and thermophoresis effects has been considered for simulation of nanofluid transport inside the cavity. Findings The numerical results of streamlines, isotherms and isoconcentrations are investigated and the effect of different important parameters, such as inclination angle of the cavity, amplitude ratio of the sinusoidal temperature or phase deviation, is discussed. The results obtained for no inclination of the cavity are compared and successfully validated with previous reported results of the literature. The important findings of the study are focused on the changes made by the inclination angle and the periodic thermal boundary conditions, on the heat and fluid flow. Originality/value The originality of the present study is given by the mathematical model presented for an inclined cavity, the numerical solution with new results for inclined cavity and the applications for design of solar energy devices such as solar collectors in which the boundary conditions vary with time because of changes in weather conditions.