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.

中文翻译：

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突然膨胀的环形剪切稀化流中的传热增强

摘要 研究了在稳态层流状态下，牛顿流体和剪切稀化的非牛顿流体在突然膨胀的环形管流中的传热增强。质量守恒、动量守恒和能量方程以及幂律本构模型都得到了数值求解。流入惯性、环形直径比、k、幂律指数、n 和 Prandtl 数的影响报告在以下参数范围内：Re = {50, 100, 150}, k = {0, 0.5 , 0.7}; n = {1, 0.8, 0.6}; 和 Pr = {1, 10, 100}。膨胀平面下游的传热增强，即 Nusselt 数大于下游完全发展值，Nu/Nufd > 1，仅在 Pr = 10 和 100 时观察到。 一般来说，较高的 Prandtl 数，幂律指数值，和环形直径比，导致膨胀平面下游更显着的传热增强。对于 Pr = 10 和 100，传热增强随着环形直径比的增加而增加。对于给定的环形直径比和雷诺数，将 Prandtl 数从 Pr = 10 增加到 Pr = 100，对于牛顿流和剪切稀化流，总是会导致更高的峰值 Nu 值 Numax。所有 Numax 值都位于流动重附点的下游，在突然膨胀的圆管流的情况下，即 κ = 0。然而，对于突然膨胀的环形管流，即 κ = 0.5 和 0.7，Numax 值出现在流的上游流动重附点。对于 Pr = 10 和 100，剪切稀化流显示两个局部峰值 Nu/Nufd 值，而牛顿流情况下则显示一个峰值。最高传热增强，Numax/Nufd ≈ 5，