We have explored multiple solutions for non-Newtonian Casson nanofluid flow past a moving extending sheet under the influence of variable thermal conductivity and nonlinear radiation through a permeable medium with convective boundary conditions. The governing equations are transformed to ODEs by similarity transformations and then solved numerically by the Chebyshev pseudospectral (CPS) method. Dual solutions are obtained for velocity, temperature and nanoparticle concentration distributions with different values of physical parameters. In the present analysis, it was found that, the nonlinearity formula for thermal radiation gives a realistic description of nanofluid mathematical model depending on the existence of nanoscale particles. Furthermore, the concentration of nanoparticles is highly influenced by nonlinear thermal radiation due to the sizes of nanofluid, where linear radiation has a weak effect on the concentration distributions of nanoparticles. These results are very important in medicine, and more specifically for reinforcing the delivery of drugs through the skin, as the nanoparticle entrapment of drugs enhances delivery to, or absorption by, target cells. The transdermal drug delivery system offers huge clinical advantages over other dosage forms. As transdermal drug delivery offers controlled as well as predetermined rate of release of the drug into the patient, it can keep up steady-state nanofluid concentration.

中文翻译：

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非线性热辐射拉伸片上非牛顿纳米流体流动的多种解决方案：在透皮给药中的应用

我们已经探索了非牛顿卡森纳米流体在可变热导率和非线性辐射的影响下通过具有对流边界条件的可渗透介质流过移动延伸片的多种解决方案。通过相似变换将控制方程转换为 ODE，然后通过切比雪夫伪谱 (CPS) 方法进行数值求解。对于具有不同物理参数值的速度、温度和纳米颗粒浓度分布，获得双解。在目前的分析中，发现热辐射的非线性公式根据纳米级粒子的存在给出了纳米流体数学模型的真实描述。此外，由于纳米流体的大小，纳米粒子的浓度受非线性热辐射的影响很大，其中线性辐射对纳米粒子的浓度分布影响很小。这些结果在医学中非常重要，更具体地说，对于加强药物通过皮肤的递送，因为药物的纳米颗粒包裹增强了靶细胞的递送或吸收。与其他剂型相比，透皮给药系统具有巨大的临床优势。由于透皮给药提供受控以及预定的药物释放到患者体内的速率，因此它可以保持稳态纳米流体浓度。更具体地说，用于加强药物通过皮肤的输送，因为药物的纳米颗粒包裹增强了靶细胞的输送或吸收。与其他剂型相比，透皮给药系统具有巨大的临床优势。由于透皮给药提供受控以及预定的药物释放到患者体内的速率，因此它可以保持稳态纳米流体浓度。更具体地说，用于加强药物通过皮肤的输送，因为药物的纳米颗粒包裹增强了靶细胞的输送或吸收。与其他剂型相比，透皮给药系统具有巨大的临床优势。由于透皮给药提供受控以及预定的药物释放到患者体内的速率，因此它可以保持稳态纳米流体浓度。