Purpose

This study aims to explore the idea of solving the problem of squeezing nanofluid flow between two parallel plates using a novel mathematical method.

Design/methodology/approach

The unsteady squeezing flow is a coupled fourth-order boundary value problem with flow velocity and temperature as the desired unknowns. In the first step, the conditions that guarantee the existence of a unique solution are obtained. Then following Green’s function-based approach, an iterative method for solving the problem is developed.

Findings

The accuracy of the method is examined by comparing the obtained results with existing numerical data, indicating excellent agreement between the two. In addition, the effects of nanoparticle shape and volume fraction on the flow and heat transfer characteristics are addressed. The results reveal that although the nanoparticle shape strongly affects the temperature distribution in the squeezing flow, it only has a slight impact on the velocity field. Furthermore, the highest and lowest Nusselt numbers belong to the platelets and spherical nanoparticles, respectively.

Originality/value

A semi-analytical method with computational support is developed for solving the unsteady squeezing flow problem. Moreover, the existence and uniqueness of the solution are discussed for the first time.

中文翻译：

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关于挤压纳米流体流动问题解的存在唯一性和Green-Picard迭代

目的

本研究旨在探索使用新的数学方法解决两个平行板之间挤压纳米流体流动问题的想法。

设计/方法/方法

非定常挤压流是一个耦合的四阶边值问题，流速和温度作为所需的未知数。第一步，获得保证唯一解存在的条件。然后按照格林的基于函数的方法，开发了解决问题的迭代方法。

发现

通过将获得的结果与现有数值数据进行比较来检查该方法的准确性，表明两者之间具有极好的一致性。此外，还讨论了纳米颗粒形状和体积分数对流动和传热特性的影响。结果表明，虽然纳米颗粒形状对挤压流中的温度分布有很大影响，但对速度场的影响很小。此外，最高和最低的努塞尔数分别属于血小板和球形纳米粒子。

原创性/价值

开发了一种具有计算支持的半解析方法来解决非定常挤压流动问题。此外，首次讨论了解的存在唯一性。