Analysis of a channel-confined non-Newtonian shear-thinning flow past a pair of mildly heated side-by-side square cylinders

Abstract

The dynamics of a shear-thinning fluid flowing past a pair of mildly heated side-by-side square cylinders, in a confined horizontal flow channel at low Reynolds number (Re), has been investigated. A detailed probe for flow physics in terms of vortex shedding patterns, near-wake streamlines and stretch of isotherms are carried out at Re = 1 and 100 (signifying two-dimensional unseparated steady flow and transient flow). The power-law index (n) is varied from 0.4 to 1 and the side-by-side transverse gap ratio (s/d) ranges from 1 (pressure-driven flow regime) to 5 (momentum-driven flow regime) at a constant value of Prandtl number (Pr) = 50. When the shear-thinning effects in the flow are increased (in the present numerical framework) at Re = 100, the time-averaged streamlines depict an early onset of leading edge flow separations from the pair of side-by-side square cylinders. One can infer from the phase space plots that the flow becomes chaotic with the increase in shear-thinning effect from n = 0.8 to 0.4 and decrease in s/d from 5 to 1. An anti-phase vortex shedding can be characterized by the occurrences of symmetrical structures of negative ζ (where ζ quantifies the accumulation and propagation of the vortices) contours in the downstream and this is realized at Re = 100, n = 0.8 and s/d ≥ 1.7. An in-phase vortex shedding (which occurs at Re = 100, n = 0.4 and all values of s/d) is characterized by asymmetrical occurrences of negative ζ contours which have a tendency of dying down early in the downstream with the increase in the nearness of the side-by-side square cylinders. This is more clearly realized at enhanced shear-thinning effects in the flow. Finally, the variation of time and space-averaged drag flow parameter (C_D) and Nusselt number (Nu) with respect to shear-thinning effects in the flow has been extensively determined.