Studying the fractional derivative for natural convection in slanted cavity containing porous media

This paper studies the numerical solution of the unsteady free convention in a slanted cavity under effect of the fractional derivative containing a porous medium. To simplify all the computations, the main equations are mapped from the irregular physical domain into a regular polygon in a shape of a rectangular computational domain utilizing nonlinear axis transformations. Using the finite differences method, the fractional partial differential equations are solved. The primary results are teased in the ordinary case at α = 1 , R a = 1000 and φ = 0.0 and those are found in an excellent agreement with the previous results from the open literatures. The obtained numerical data are represented in terms of the isotherms and streamlines contours as well as the local and average Nusselt numbers at the heated wall. Wide ranges of the key-parameters are considered i.e. orders of the fractional derivatives α and β are varied from 1 to 0.7, the Rayleigh number Ra is varied from 10 2 to 10 4 and the inclination angle takes the values φ = 0 ∘ , 15 ∘ , 30 ∘ and 45 ∘ . The results revealed that the decrease in order of the fractional derivatives enhances the fluid activity while both of the local and average Nusselt numbers are reduced regardless of the Rayleigh number values.