The effects of elasticity on flow structures and forced convection heat transfer of a viscoelastic fluid around a cylinder were studied numerically using a finite volume method for the first time. In addition, the effects of viscous dissipation on flow and heat transfer parameters were studied over a wide range of Brinkman number (Br). The accurate non-linear Phan-Thien–Tanner model was used to describe the viscoelastic behavior of a polymer solution with a high retardation ratio (β = 0.6) over a wide range of Weissenberg (Wi) and Reynolds numbers (Re). The fluid properties were considered to be temperature-dependent. The results showed that the role of elastic effects in vortex shedding is a depreciator for Wi 0.5. The Nusselt number was monotonically increased up to 52.2% with increasing Wi, β, Prandtl number (Pr), and Br over a wide range. The elastic forces affected the physical parameters by contrasting with the viscous forces so that the effects of elastic forces were weaker for high Reynolds numbers. Both hydrodynamic and thermal boundary layers were thinner in a viscoelastic fluid, compared to a Newtonian fluid. In addition, a correlation for variations of the drag coefficient with Wi and two correlations for variations of drag coefficient and Strouhal number with Re for Newtonian and viscoelastic fluid were proposed. Finally, the effects of Wi, Pr, Br, and model parameters on the Nu, St, drag, and lift coefficient and the distribution of stress components, velocity, and temperature were examined.

中文翻译：

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存在粘性耗散时弹性对圆柱周围粘弹性流体非定常强制对流传热的影响

首次使用有限体积法数值研究了弹性对圆柱体周围粘弹性流体的流动结构和强制对流传热的影响。此外，在广泛的 Brinkman 数 (Br) 范围内研究了粘性耗散对流动和传热参数的影响。精确的非线性 Phan-Thien-Tanner 模型用于描述具有高延迟比 (β = 0.6) 的聚合物溶液在广泛的魏森伯格 (Wi) 和雷诺数 (Re) 范围内的粘弹性行为。流体特性被认为与温度有关。结果表明，弹性效应在涡旋脱落中的作用是 Wi 0.5 的贬值因子。随着 Wi、β、普朗特数 (Pr) 和 Br 在很宽的范围内增加，努塞尔数单调增加至 52.2%。弹性力通过与粘性力形成对比来影响物理参数，因此对于高雷诺数，弹性力的影响较弱。与牛顿流体相比，粘弹性流体中的流体动力边界层和热边界层都更薄。此外，对于牛顿流体和粘弹性流体，提出了阻力系数变化与 Wi 的相关性以及阻力系数和 Strouhal 数变化与 Re 的两个相关性。最后，检查了 Wi、Pr、Br 和模型参数对 Nu、St、阻力和升力系数以及应力分量、速度和温度分布的影响。与牛顿流体相比，粘弹性流体中的流体动力边界层和热边界层都更薄。此外，对于牛顿流体和粘弹性流体，提出了阻力系数变化与 Wi 的相关性以及阻力系数和 Strouhal 数变化与 Re 的两个相关性。最后，检查了 Wi、Pr、Br 和模型参数对 Nu、St、阻力和升力系数以及应力分量、速度和温度分布的影响。与牛顿流体相比，粘弹性流体中的流体动力边界层和热边界层都更薄。此外，对于牛顿流体和粘弹性流体，提出了阻力系数变化与 Wi 的相关性以及阻力系数和 Strouhal 数变化与 Re 的两个相关性。最后，检查了 Wi、Pr、Br 和模型参数对 Nu、St、阻力和升力系数以及应力分量、速度和温度分布的影响。