In this study, we have addressed the flow of hybrid nanofluid ($Cu-A{l}_2{O}_3$-Sodium Alginate), nanofluid ($Cu$-Sodium Alginate), and nanofluid ($A{l}_2{O}_3$-Sodium Alginate). Flow is because of the heated boundary of the channel and its different movements. The flow is modelled using Casson fluid's momentum equation, and the heat equation is generalized using the generalized Fourier’s law based on Caputo-time fractional derivatives. The non-dimensional fractional partial differential equations are solved using the Laplace and Fourier transforms. The velocity and temperature show variations for different values of the fractional parameter; also, the plots are drawn for the classical model. The temperature distribution increases for the volume fractions of the nanoparticles and has maximum vales for hybrid nanoparticles with the highest chosen volume fractions values. Furthermore, intensification in heat transfer rate is increased due to hybrid nanoparticles.

在这项研究中，我们已经解决了混合纳米流体的流动（$C你-\mathrm{一种}{升}_2{哦}_3$-海藻酸钠），纳米流体（$C你$-海藻酸钠）和纳米流体（$\mathrm{一种}{升}_2{哦}_3$-海藻酸钠）。流动是由于通道的加热边界及其不同的运动。流动使用卡松流体的动量方程建模，热方程使用基于卡普托时间分数阶导数的广义傅立叶定律进行概括。无量纲分数式偏微分方程使用拉普拉斯和傅立叶变换求解。速度和温度显示了分数参数的不同值的变化；此外，绘图是为经典模型绘制的。温度分布随纳米颗粒的体积分数而增加，并且对于具有最高选择的体积分数值的混合纳米颗粒具有最大值。此外，由于混合纳米粒子，传热速率的增强增加。