Exploring the movement of blood in a blood vessel has been fascinated by clinicians and biomedical researchers because it is predominant in cell tissue engineering, drug targeting and various treatments like hypothermia, hyperthermia, and cancer. It is noticed that numerous non-Newtonian rheological fluids like Carreau fluid, tangent hyperbolic fluid, Eyring–Powell fluid and viscoelastic fluid manifest the characteristics of blood flow. Further, the investigation of entropy generation can be used to raise the performance of medical equipments. Consequently, the present mathematical model scrutinizes the transport characteristics and entropy generation of the peristaltic Eyring–Powell nanofluid in a permeable vertical divergent channel in the presence of dissipation and linear radiation. The non-similar variables are employed to convert the dimensional partial differential equations into dimensionless form which are tackled by the Homotopy perturbation method. The impacts of emerging parameters like Eyring–Powell parameters, left and right wall amplitudes, thermophoresis, mean flow rate, radiation, permeability parameter, Brownian motion, Eckert number, Hartman number on Eyring–Powell nanofluid axial velocity, temperature, and concentration are manifested. Present results disclose that the thermal Grashof number highly inflates the pressure rise. Eyring–Powell nanofluid temperature reduces for uplifting the linear radiation parameter. Growing values of the non-uniform parameter lead to move the trapping bolus towards the left and right wall. The total entropy generation diminishes for magnifying the temperature difference parameter.

临床医生和生物医学研究人员着迷于探索血管中的血液运动，因为它在细胞组织工程，靶向药物和低温，高温和癌症等各种治疗中占主导地位。注意到许多非牛顿流变流体，如Carreau流体，正切双曲线流体，Eyring-Powell流体和粘弹性流体，都表现出了血流的特征。此外，熵产生的研究可用于提高医疗设备的性能。因此，本数学模型详细研究了在存在耗散和线性辐射的情况下，可渗透的垂直发散通道中蠕动的Eyring-Powell纳米流体的传输特性和熵的产生。使用非相似变量将维偏微分方程转换为无量纲形式，并通过同伦摄动法加以解决。出现了诸如Eyring–Powell参数，左右壁振幅，热泳，平均流速，辐射，渗透率参数，布朗运动，Eckert数，Hartman数等新兴参数对Eyring–Powell纳米流体轴向速度，温度和浓度的影响。 。目前的结果表明，热格拉斯霍夫数极大地加剧了压力上升。Eyring–Powell纳米流体的温度降低，从而提高了线性辐射参数。非均匀参数的值不断增加，导致诱集弹药向左右壁移动。