Process intensification deal with the complex fluids in mixing processes of many industries and its performance is based on the flow of fluid, heat and mass transfer. This paper presents the mathematical and Adaptive Neuro-Fuzzy Inference System (ANFIS) models for the unsteady two-dimensional bio-convection flow of Carreau nanofluid incorporating gyrotactic micro-organisms over a slendering stretching sheet with the presence of magnetic field, thermal radiation and multiple slip conditions. Suitable similarity variables are applied to convert the flow equations into higher order ordinary differential equations and solved numerically. The surface-contour plots are utilized to visualize the influence of active parameters on velocity, thermal, nanoparticles concentration and motile microorganisms’ density. The hybrid-learning algorithm comprised of gradient descent and least-squares method is employed for training the ANFIS. The optimal ANFIS models are achieved with root mean squared error (RMSE) and coefficient of determination (R²) values of (0.0338, 0.996487), (0.033607, 0.973544), (0.075168, 0.990476) and (0.051256, 0.996073) for C_f, Nu, Sh and Nn, respectively. The proposed ANFIS models are efficient and predicted the results with higher accuracy.

过程强化处理许多行业混合过程中的复杂流体，其性能基于流体的流动，传热和传质。本文提出了数学和自适应神经模糊推理系统（ANFIS）模型，用于Carreau纳米流体的不稳定二维生物对流，该流体在旋转的细长拉伸片上并入了旋转磁场，并存在磁场，热辐射和多个滑移条件。应用适当的相似性变量将流动方程式转换为高阶常微分方程式，并进行数值求解。表面轮廓图用于可视化有效参数对速度，热，纳米颗粒浓度和运动微生物密度的影响。采用梯度下降法和最小二乘法相结合的混合学习算法训练ANFIS。利用均方根误差（RMSE）和确定系数（R²）的C _f，Nu，Sh和Nn分别为（0.0338，0.996487），（0.033607，0.973544），（0.075168，0.990476）和（0.051256，0.996073）值。所提出的ANFIS模型是有效的，并且可以较高的精度预测结果。