In this thermal investigation, the mixed free convection Casson nanofluid along with heat transfer effects over a vertical plate is addressed. The thermal radiative phenomenon is also considered to improve the heat transfer rate. For base fluid, the engine oil is assumed for which the thermal enhancement is predicted with the suspension of graphene oxide $\left(GO\right)$ and molybdenum disulphide $\left(Mo{S}_2\right)$ nanoparticles. To construct the fractional model, the partial derivative with respect to time is exchanged by the recent definitions of fractional derivatives namely Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) time-fractional derivative and the Laplace scheme is applied to obtain the solution of governing equations. To enhance the innovation of this article different cases of velocity profiles are examined. The effects of different parameters are examined graphically and numerically by varying the values of parameters. The reported results claimed that the simulations performed via AB-time fractional are more stable as compared to the Caputo-Fabrizio time-fractional approach. The velocity profile declines with increasing the fractional parameters while increasing change in velocity has been observed for Grashof number. The nanoparticles temperature shows a lower change due to volume fraction coefficient.

在此热研究中，解决了混合自由对流 Casson 纳米流体以及垂直板上的传热效应。热辐射现象也被认为可以提高传热率。对于基础流体，假设发动机油，通过氧化石墨烯的悬浮液预测其热增强$\left(G哦\right)$ 和二硫化钼 $\left(米○{秒}_2\right)$纳米粒子。为了构建分数模型，通过分数导数的最新定义即 Atangana-Baleanu (AB) 和 Caputo-Fabrizio (CF) 时间分数导数交换关于时间的偏导数，并应用拉普拉斯方案来获得解的控制方程。为了增强本文的创新性，研究了速度剖面的不同情况。通过改变参数值以图形和数字方式检查不同参数的影响。报告的结果声称，与 Caputo-Fabrizio 时间分数方法相比，通过 AB 时间分数执行的模拟更稳定。速度剖面随着分数参数的增加而下降，同时已经观察到 Grashof 数的速度变化增加。