Abstract In this paper, we have investigated the momentum and heat transfer in an unsteady separated stagnation-point flow of a viscous fluid over a plane surface advancing towards or receding from the normal stagnation flow which impinges on the surface with a variable strain rate s ( t ) , causing the unsteadiness in this flow problem. The flow and heat transfer characteristics are therefore governed by the flow strength (stagnation) parameter a, unsteadiness parameter β, plate velocity (normal) parameter α and Prandtl number P r . The current analysis ensures the existence of the self-similar solutions to this flow problem only when the plate velocity varies directly to the square root of the strain rate s ( t ) . A closed form analytic solution of this flow problem is found for the specific relational values of β = 2 a . The solutions of this flow problem are non unique only under the negative values of β. When the plate surface is advancing towards the normal stagnation flow (i.e., when α > 0), the self-similar boundary layer solution continues for any given values of a and β, whereas for receding of the plate surface from the incoming flow (i.e., for α 0) the boundary layer solution does not exist after a certain value of α depending upon the values of a and β. In the case where receding of the plate surface occurs, the features of the boundary layer flows depend highly on the sum values of the parameters a and β. For ( a + β ) > 0, the boundary layer solution ends with an attached flow solution, while it gets terminated at a reverse flow solution for ( a + β ) 0. And for ( a + β ) = 0, the governing boundary layer equations provide us with the trivial (zero) solutions which are unable to capture the free boundary conditions.

中文翻译：

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在垂直于流动冲击的平面上的不稳定分离的驻点流动和热传递

摘要 在本文中，我们研究了粘性流体在平面上的非定常分离驻点流中的动量和热传递，该平面以可变应变率 s ( t ) ，导致这个流动问题的不稳定。因此，流动和传热特性受流动强度（停滞）参数 a、不稳定参数 β、板速度（法向）参数 α 和普朗特数 P r 控制。当前的分析确保只有当板速度直接变化为应变率 s ( t ) 的平方根时，该流动问题的自相似解才存在。对于 β = 2 a 的特定关系值，找到了此流动问题的封闭形式解析解。这个流动问题的解只有在 β 为负值时才不是唯一的。当板面朝着正常的停滞流前进时（即，当 α > 0 时），对于任何给定的 a 和 β 值，自相似边界层解继续进行，而对于板面从进入流中后退（即, 对于 α 0) 取决于 a 和 β 的值，在特定的 α 值之后，边界层解不存在。在板块表面发生后退的情况下，边界层流动的特征高度依赖于参数 a 和 β 的和值。对于 ( a + β ) > 0，边界层解以附加流解结束，而在 ( a + β ) 0 的逆流解处终止。对于 ( a + β ) = 0，