Study of aspect ratio effect in combined shear-driven and pressure-difference driven flow characterization of a third grade fluid in a rectangular channel

Combined shear-driven and pressure-difference driven flow of a third grade fluid through a rectangular channel is studied as it has wide applications in extrusion, glass-fibre drawing, blood flow in arteries etc.. Pressure-difference driven flow case can be retrieved by setting the upper walls velocity to be zero. First, governing equation is formulated from the constitutive equation of third grade fluid considering hydro-dynamically fully developed flow, where the axial velocity is independent of the axial coordinate. The dimensionless governing equation is solved using the least square method using Symbolic Computation in MATLAB. As no experimental result or other numerical or analytical results are reported in the literature, the equation is again solved by least square homotopy perturbation method and standard numerical technique. Results from both these methods are compared for validation. In addition, velocity distribution in the limit of vanishing aspect ratio is compared with that of the previously reported results of third grade fluid flow between parallel plates. In both the cases, results are in close match which validate the results of the present study. Influence of aspect ratio, third grade fluid parameter on velocity distribution are analyzed. In case of combined shear- driven and pressure-difference driven flow, the effect of favourable and adverse pressure gradient is discussed. It is noted that increase in aspect ratio, arrests the flow separation and back flow in the channel. Increase in third-grade fluid parameter also increases the flow resistance with consequent prevention of flow separation and back flow.