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Effect of aspect ratio on natural convection in power-law liquids from a heated horizontal elliptic cylinder

机译:纵横比对加热的水平椭圆圆柱体幂律液体中自然对流的影响

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摘要

The influence of aspect ratio and shear-dependent viscosity on free convection heat transfer from a horizontal heated elliptic cylinder in power-law fluids has been investigated. In particular, the coupled momentum and energy equations have been solved numerically over the following ranges of conditions: Grashof number, 10 ≤Cr≤10~5; Prandtl number, 0.72 ≤Pr≤100; power-law index, 0.3 ≤n ≤1.5 and aspect ratio, 0.2 ≤E≤ 5. The new extensive results demonstrate the influence of the Grashof number (Gr), Prandtl number (Pr), power-law index (n) and aspect ratio (E) on the macroscopic heat and momentum transfer characteristics like local and average values of Nusselt number (Mi) and drag coefficients (C_D). Further insights are developed by examining the structure of the flow and temperature fields adjacent to the cylinder. Broadly speaking, all else being equal, shear- thinning fluid behaviour promotes heat transfer whereas shear-thickening viscosity has a deleterious effect on it with reference to that in Newtonian fluids. Also, the rate of heat transfer gradually increases as the cylinder shape passes from blunt to slender with respect to the direction of gravity. Finally, the present numerical values of the Nusselt number are correlated using a simple analytical form which facilitates interpolation of the present results for the intermediate values of the governing parameters. The paper is concluded by presenting detailed comparisons with the previous numerical and experimental results available in the literature, especially in Newtonian fluids.
机译:研究了纵横比和剪切粘度对幂律流体中水平加热椭圆圆柱自由对流传热的影响。特别地,在以下条件范围内已经数值地求解了耦合动量和能量方程:Grashof数,10≤Cr≤10〜5;普朗特数,0.72≤Pr≤100;幂律指数0.3≤n≤1.5和纵横比0.2≤E≤5。新的广泛结果证明了格拉斯霍夫数(Gr),普朗特数(Pr),幂律指数(n)和纵横比的影响宏观热和动量传递特性上的比率(E),例如努塞尔数(Mi)的局部和平均值以及阻力系数(C_D)。通过检查圆柱体附近的流场和温度场的结构,可以得到更多的见解。广义上讲,在所有其他条件相同的情况下,剪切稀化流体的行为会促进传热,而剪切增稠性的粘度对牛顿流体的影响则是有害的。而且,随着圆柱形状相对于重力方向从钝形变为细长形,传热速率逐渐增加。最后,使用简单的分析形式将努塞尔数的当前数值关联起来,这有助于对控制参数的中间值的当前结果进行插值。通过与文献中现有的数值和实验结果进行详细比较,得出本文的结论,特别是在牛顿流体中。

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