Abstract—

In this work, we have effectively used the numerical inversion of the Laplace transform to study the time-dependent thin heated film flow of a viscoelastic fluid flowing on an infinitely long flat substrate. Exact and analytical solutions are obtained in some limiting cases. The model describing this problem is a system of equations, coupling the linearized Navier–Stokes equation of the viscoelastic fluid with regard for gravity as an external force and the temperature relation for the energy profile. By assuming that the fluids are incompressible, we first derive a new system of equations, by taking into account additional terms, due to the insoluble surfactants and the viscoelastic properties. The velocity and temperature profiles are shown and the influence of coupling constant, viscoelastic parameters and the interfacial surfactants on the liquid film are discussed in detail. The validity of our solutions is verified by the numerical results to show the effects of different parameters involved and to show how the fluid flow evolves with time.

中文翻译：

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非牛顿液体加热振荡层的动力学建模

摘要-

在这项工作中，我们有效地使用了拉普拉斯变换的数值反演来研究在无限长的平坦基底上流动的粘弹性流体随时间变化的薄膜加热流。在某些限制情况下，可以获得精确的和解析的解决方案。描述该问题的模型是一个方程组，将粘弹性流体的线性化Navier-Stokes方程与重力作为外力，将温度关系与能量分布耦合起来。通过假定流体是不可压缩的，由于不溶性表面活性剂和粘弹性，我们首先通过考虑其他项来推导新的方程组。显示了速度和温度曲线，以及耦合常数的影响，详细讨论了液膜上的粘弹性参数和界面活性剂。数值结果验证了我们解决方案的有效性，以显示所涉及的不同参数的影响并显示流体随时间如何演变。