Abstract This article presents a two-dimensional theoretical study of hemodynamics through a diseased permeable artery with a mild stenosis and an aneurysm present. The effect of metallic nanoparticles on the blood flow is considered, motivated by drug delivery (pharmacology) applications. Two different models are adopted to mimic non-Newtonian characteristics of the blood flow; the Casson (viscoplastic) fluid model is deployed in the core region and the Sisko (viscoelastic) fluid model employed in the peripheral (porous) region. The revised Buongiorno two-component nanofluid model is utilized for nanoscale effects. The blood is considered to contain a homogenous suspension of nanoparticles. The governing equations are derived by extending the Navier-Stokes equations with linear Boussinesq approximation (which simulates both heat and mass transfer). Natural (free) double-diffusive convection is considered to simulate the dual influence of thermal and solutal buoyancy forces. The conservation equations are normalised by employing appropriate non-dimensional variables. The transformed equations are solved numerically using the finite element method with the variational formulation scheme available in the FreeFEM++ code. A comprehensive mesh-independence study is included. The effect of selected parameters (thermophoresis, Brownian motion, Grashof number, thermo-solutal buoyancy ratio, Sisko parameter ratio, and permeability parameter) on velocity, temperature, nanoparticle concentration, and hemodynamic pressure have been calculated for two clinically important cases of arteries with stenosis and an aneurysm. Skin-friction coefficient, Nusselt number, volumetric flow rate, and resistance impedance of blood flow are also computed. Colour contours and graphs are employed to visualize the simulated blood flow characteristics. It is observed that by increasing the thermal buoyancy parameter, i.e. Grashof number (Gr), the nanoparticle concentration and temperature decrease, whereas velocity increases with an increment in the Brownian motion parameter (Nb). Furthermore, velocity decreases in the peripheral porous region with elevation in the Sisko material ratio (m) and permeability parameter (k’). The simulations are relevant to transport phenomena in pharmacology and nano-drug targeted delivery in haematology.

中文翻译：

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通过具有狭窄和动脉瘤的患病动脉的双流体非牛顿纳米血流动力学的计算流体动力学模拟

摘要 本文通过具有轻度狭窄和动脉瘤的患病可渗透动脉，对血流动力学进行了二维理论研究。考虑到金属纳米粒子对血流的影响，其动机是药物递送（药理学）应用。采用两种不同的模型来模拟血流的非牛顿特性；Casson（粘塑性）流体模型部署在核心区域，Sisko（粘弹性）流体模型部署在外围（多孔）区域。修正的 Buongiorno 双组分纳米流体模型用于纳米级效应。血液被认为含有均匀的纳米颗粒悬浮液。控制方程是通过使用线性 Boussinesq 近似（模拟传热和传质）扩展 Navier-Stokes 方程推导出来的。自然（自由）双扩散对流被认为是模拟热和溶质浮力的双重影响。通过使用适当的无量纲变量对守恒方程进行归一化。使用 FreeFEM++ 代码中可用的变分公式方案，使用有限元方法对转换后的方程进行数值求解。包括全面的网格独立性研究。选定参数（热泳、布朗运动、格拉肖夫数、热溶浮力比、Sisko 参数比和渗透率参数）对速度、温度、纳米颗粒浓度的影响，已经计算了两个具有临床意义的动脉狭窄和动脉瘤病例的血流动力学压力和血流动力学压力。还计算皮肤摩擦系数、努塞尔数、体积流量和血流的阻力阻抗。采用彩色轮廓和图形来可视化模拟的血流特性。据观察，通过增加热浮力参数，即格拉肖夫数 (Gr)，纳米粒子浓度和温度降低，而速度随着布朗运动参数 (Nb) 的增加而增加。此外，随着 Sisko 材料比率 (m) 和渗透率参数 (k') 的升高，外围多孔区域的速度降低。这些模拟与药理学中的运输现象和血液学中的纳米药物靶向递送有关。