The present study investigates the combined effects of non-Newtonian rheology and unsteady nature of the fluid on dispersion of a soluble substance between two coaxial cylinders having wall permeability at the outer wall with the flowing fluid is modelled as Casson fluid. Generalized dispersion method in combination with a finite difference scheme is used to study the dispersion phenomenon. Using the generalized dispersion model, the entire process of dispersion is expressed in terms of three transport coefficients viz., absorption, convection, and dispersion (effective diffusion) coefficients. These transport coefficients are evaluated numerically using Crank-Nicolson finite difference method. The mean concentration is expressed in terms of these transport coefficients. Effects of annular gap, yield stress, Womersley frequency parameter, amplitude of the pressure pulsation, and the absorption parameter on the transport coefficients and mean concentration are studied. Flow unsteadiness is observed influencing the dispersion coefficient both quantitatively and qualitatively. It is observed that, as Womersley number increases the fluctuation of the dispersion coefficient increases and the magnitude of dispersion coefficient decreases for small values of time (< 0.5) and increases for later values of time.

中文翻译：

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具有壁吸收的非定常非牛顿流体环流中的对流扩散

本研究研究了非牛顿流变学和流体的不稳定特性对可溶物质在两个同轴圆柱体之间流动的综合影响，该圆柱体在外壁具有壁渗透性，流动流体被建模为卡森流体。采用广义色散法结合有限差分法研究色散现象。使用广义色散模型，整个色散过程用三个传输系数来表示，即吸收系数，对流系数和色散（有效扩散）系数。这些传输系数使用Crank-Nicolson有限差分法进行数值评估。平均浓度用这些传输系数表示。环形间隙，屈服应力，Womersley频率参数的影响，研究了压力脉动的振幅，吸收系数对输运系数和平均浓度的影响。观察到流动不稳定，从数量和质量上都影响分散系数。可以观察到，随着Womersley数的增加，色散系数的波动增大，色散系数的幅度在较小的时间值（<0.5）下减小，而在较晚的时间值上增大。