Study of mixed convection flow of power‐law fluids in a skewed lid‐driven cavity

Abstract

This study conducts a numerical simulation of mixed (combined) convective non‐Newtonian fluid flow inside a two‐dimensional cavity (skewed) having a moving lid. The upper and bottom extremities of the cavity with different temperatures and two insulated side walls cause natural convection. Moreover, the forced convection is maintained by the motion of the lid with constant velocity. The governing equations are nondimensionalized with appropriate transformations and then transformed into curvilinear coordinates. A finite volume numerical procedure with a collocated grid arrangement is used to solve these equations. Comparisons with previously reported results are carried out, which shows an excellent agreement. Non‐Newtonian behaviors such as pseudo‐plastic (shear‐thinning) and dilatant (shear‐thickening) are considered using the power‐law model, and thus the power‐law index is chosen accordingly. A wide range of the governing dimensionless parameters which affect the mixed convection flow inside the skewed cavity, including Grashof number ( 1 0 2 ≤ G r ≤ 5 × 1 0 4 ), Richardson number ( 0.000625 ≤ R i ≤ 5 ), Reynolds number ( R e = 100 and 400), and power‐law index ( 0.7 ≤ n ≤ 1.3 ). The Prandtl number ( P r = 10) is fixed and the skew angles ( φ = 4 5 ∘ , 9 0 ∘ , and 13 5 ∘ ) are considered for acute, right‐angle, and obtuse angles. The obtained numerical outcomes of the study are shown graphically and also in tabular form for vertical and horizontal velocities, streamlines, isotherms, temperature distributions, and the rate of heat transfer and insight physics of the flow features, are discussed thereafter. It can be concluded that the rate of heat transfer in the present case is sensitive to the skew‐angle as well as power‐law index, and the maximum heat transfer occurs in the case of dilatant (shear‐thickening) fluid.