Purpose

The purpose of this study is to investigate the two-dimensional unsteady inclined stagnation point flow and thermal transmission of Maxwell fluid on oscillating stretched/contracted plates. First, based on the momentum equation at infinity, pressure field is modified by solving first-order differential equation. Meanwhile, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

Design/methodology/approach

Highly coupled model equations are transformed into simpler partial differential equations (PDE) via appropriate dimensionless variables. The approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are acquired by homotopy analysis method for the first time, to the best of the authors’ knowledge.

Findings

Results indicate that because of tensile state of plate, streamline near stagnation point disperses to both sides with stagnation point as center, while in the case of shrinking plate, streamline near stagnation point is concentrated near stagnation point. The enhancement of velocity ratio parameter leads to increasing of pressure variation rate, which promotes flow of fluid. In tensile state, surface friction coefficient on both sides of stagnation point has opposite symbols; when the plate is in shrinkage state, there is reflux near the right side of the stagnation point. In addition, although the addition of unsteady parameters and thermal relaxation parameters reduce heat transfer efficiency of fluid, heat transfer of fluid near the plate can also be enhanced by considering thermal relaxation effect when plate shrinks.

Originality/value

First, approximate analytical solutions of unsteady inclined stagnation point flow on oscillating stretched and contracted plates are researched, respectively. Second, pressure field is further modified. Finally, based on this, thermal relaxation characteristic of fluid is described by Cattaneo–Christov thermal diffusion model.

中文翻译：

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变压场拉伸/收缩板上麦克斯韦流体的非定常倾斜驻点流动和热传递

目的

本研究的目的是研究麦克斯韦流体在振荡拉伸/收缩板上的二维非定常倾斜驻点流动和热传递。首先，基于无穷远处的动量方程，通过求解一阶微分方程修正压力场。同时，利用Cattaneo-Christov热扩散模型描述了流体的热弛豫特性。

设计/方法/途径

高度耦合的模型方程通过适当的无量纲变量转换为更简单的偏微分方程 (PDE)。据作者所知，首次通过同伦分析方法获得了振动拉伸和收缩板上非定常倾斜驻点流的近似解析解。

发现

结果表明，由于板处于拉伸状态，驻点附近的流线以驻点为中心向两侧分散，而在收缩板的情况下，驻点附近的流线集中在驻点附近。流速比参数的增大导致压力变化率增大，从而促进流体的流动。在拉伸状态下，驻点两侧的表面摩擦系数符号相反；当板处于收缩状态时，驻点右侧附近有回流。此外，虽然非定常参数和热松弛参数的加入降低了流体的传热效率，但考虑板收缩时的热松弛效应也可以增强板附近流体的传热。

原创性/价值

首先，分别研究了振动伸缩板上非定常倾斜驻点流的近似解析解。二是压力场进一步改造。最后，在此基础上，利用Cattaneo-Christov热扩散模型描述了流体的热弛豫特性。