Heat transfer enhancement in suddenly expanding annular shear-thinning flows

Abstract

Heat transfer enhancement in suddenly expanding annular pipe flows of Newtonian and shear-thinning non-Newtonian fluids is studied within the steady laminar flow regime. Conservation of mass, momentum, and energy equations, along with the power-law constitutive model are numerically solved. The impact of inflow inertia, annular-diameter-ratio, k, power-law index, n, and Prandtl numbers, is reported over the following range of parameters: Re = {50, 100, 150}, k = {0, 0.5, 0.7}; n = {1, 0.8, 0.6}; and Pr = {1, 10, 100}. Heat transfer enhancement downstream of the expansion plane, i.e., Nusselt numbers greater than the downstream fully developed value, Nu/Nufd > 1, is only observed for Pr = 10 and 100. In general, higher Prandtl numbers, power-law index values, and annular-diameter-ratios, result in more significant heat transfer enhancement downstream of the expansion plane. Heat transfer augmentation, for Pr = 10 and 100, increases with the annular-diameter-ratio. For a given annular-diameter-ratio and Reynolds numbers, increasing the Prandtl number from Pr = 10 to Pr = 100, always results in higher peak Nu values, Numax, for both Newtonian and shear-thinning flows. All Numax values are located downstream of the flow reattachment point, in the case of suddenly expanding round pipe flows, i.e., κ = 0. However, for suddenly expanding annular pipe flows, i.e., κ = 0.5 and 0.7, Numax values appear upstream the flow reattachment point. For Pr = 10 and 100, shear-thinning flows display two local peak Nu/Nufd values, in comparison with one peak value in the case of Newtonian flows. The highest heat transfer enhancement, Numax/Nufd ≈ 5, is observed at κ = 0.7, n = 0.6, and Pr = 100.