Jafeer M Burhan, Mustafa M
School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan.
Sci Rep. 2021 Feb 25;11(1):4514. doi: 10.1038/s41598-021-83864-z.
Von Kármán problem of infinite disk is re-examined when fluid under consideration is elastico-viscous, satisfying the constitutive relations of Walters-B model. Main target here is to demonstrate how the presence of elasticity alters heat transfer phenomenon for the said problem especially when heat dissipation term is included in the analysis. We assume a self-similarity solution that results in a system of coupled non-linear equations. An easy to use package BVPh 2.0 based on the homotopy analysis method is used to present series solutions for values of elastico-viscous fluid parameter ([Formula: see text]) in the range [Formula: see text]. Residuals are evaluated numerically at various order of approximations which depict that obtained solutions converge to the exact solutions. Boundary layer is substantially suppressed due to the consideration of elastico-viscous fluid assumption. Furthermore, velocity of the entrained fluid is inversely proportional to the parameter [Formula: see text]. The results predict a substantial drop in heat transfer rate whenever elasticity effects are present. A considerable role of heat dissipation towards thickening of thermal boundary layer is apparent from the findings.
当所考虑的流体为弹粘性流体，满足沃尔特斯 - B模型的本构关系时，对无限圆盘的冯·卡门问题进行了重新研究。这里的主要目标是证明弹性的存在如何改变上述问题的传热现象，特别是在分析中包含热耗散项时。我们假设一个自相似解，这会导致一个耦合非线性方程组。使用基于同伦分析方法的易于使用的软件包BVPh 2.0来给出弹粘性流体参数（[公式：见原文]）在[公式：见原文]范围内的级数解。在不同近似阶数下对残差进行数值评估，结果表明所得到的解收敛于精确解。由于考虑了弹粘性流体假设，边界层得到了显著抑制。此外，夹带流体的速度与参数[公式：见原文]成反比。结果预测，只要存在弹性效应，传热速率就会大幅下降。研究结果表明，热耗散对热边界层增厚起着相当大的作用。
