In a rectangular region, the multilayered laminar unsteady flow and temperature distribution of the immiscible Maxwell fractional fluids by two parallel moving walls are studied. The flow of the fluid occurs in the presence of Robin’s boundaries and linear fluid-fluid interface conditions due to the motion of the parallel walls on its planes and the time-dependent pressure gradient. The problem is defined as a mathematical model which focuses on the fluid memory, which is represented by a constituent equation with the Caputo time-fractional derivative. The integral transformations approach (the Laplace transform and the finite sine-Fourier transform) is used to determine analytical solutions for velocity, shear stress, and the temperature fields with fluid interface, initial, and boundary conditions. For semianalytical solutions, the algorithms of Talbot are used to calculate the Laplace inverse transformation. We used the Mathcad software for graphical illustration and numerical computation. It has been observed that the memory effect is significant on both fluid motion and temperature flow.

中文翻译：

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具有广义热通量和Robin边界条件的n个不可混分式Maxwell流体的同时流动

在一个矩形区域中，研究了由两个平行移动壁形成的不相容麦克斯韦分馏流体的多层层流非定常流动和温度分布。由于平行壁在其平面上的运动以及随时间变化的压力梯度，流体的流动在存在Robin边界和线性流体-流体界面条件的情况下发生。该问题定义为专注于流体记忆的数学模型，该数学模型由具有Caputo时间分数导数的构成方程表示。积分变换方法（拉普拉斯变换和有限正弦-傅立叶变换）用于确定速度，剪切应力以及具有流体界面，初始条件和边界条件的温度场的解析解。对于半解析解决方案，Talbot算法用于计算拉普拉斯逆变换。我们使用Mathcad软件进行图形化图示和数值计算。已经观察到，记忆效应对于流体运动和温度流动均是显着的。