The prime focus of this work is to investigate the thermal behavior of ethylene glycol and water based $\gamma {\mathrm{Al}}_2{\mathrm{O}}_3$ nanofluids for free convective flow through a stationary channel. The imposition of uniform magnetic effects is assumed in the normal direction of the vertical channel, which is nested in a porous material. The Fourier law for estimation of the thermal flux is generalized by dint of the Prabhakar fractional derivative. The viscosity and thermal conductivity of considered nanofluids are measured by employing experimentally evaluated relations of these quantities. Some dimension-free quantities are introduced and the resulting generalized unit-less fractional governing equations are solved analytically with the assistance of the Laplace transformation. Several tables and graphical illustrations are provided to anticipate the influence of various factors on flow distribution and temperature profile. A comprehensive study comprised of multiple parts such as anticipation of the thermal performance, variation in skin friction coefficient, and parametric impacts on thermal and velocity profiles is conducted to deeply analyze and compare the behavior of $\gamma {\mathrm{Al}}_2{\mathrm{O}}_3-{\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{O}}_2$ and $\gamma {\mathrm{Al}}_2{\mathrm{O}}_3-{\mathrm{H}}_2\mathrm{O}$ nanofluids. The outcomes suggest that there is a noteworthy enhancement in heat transfer rate due to an increase in fractional parameters. The enhancement in volume proportion of nanoparticles reduces the velocity of nanofluid. Moreover, the improvement in heat transfer rate of ethylene glycol and water due to the dispersion of $\gamma {\mathrm{Al}}_2{\mathrm{O}}_3$ nanoparticles is 7.98% and 10.68% respectively.

这项工作的主要重点是研究乙二醇和水基的热行为$\gamma {\mathrm{铝}}_2{\mathrm{○}}_3$用于通过固定通道的自由对流流动的纳米流体。假设在垂直通道的法线方向施加均匀磁效应，该通道嵌套在多孔材料中。用于估计热通量的傅里叶定律通过 Prabhakar 分数导数进行推广。所考虑的纳米流体的粘度和热导率是通过采用这些量的实验评估关系来测量的。引入了一些无量纲量，并借助拉普拉斯变换对得到的广义无单位分数控制方程进行解析求解。提供了几个表格和图形说明来预测各种因素对流量分布和温度分布的影响。$\gamma {\mathrm{铝}}_2{\mathrm{○}}_3-{\mathrm{C}}_2{\mathrm{H}}_6{\mathrm{○}}_2$和$\gamma {\mathrm{铝}}_2{\mathrm{○}}_3-{\mathrm{H}}_2\mathrm{○}$纳米流体。结果表明，由于分数参数的增加，传热率显着提高。纳米颗粒体积比例的增加降低了纳米流体的速度。此外，由于乙二醇的分散，乙二醇和水的传热率提高$\gamma {\mathrm{铝}}_2{\mathrm{○}}_3$纳米粒子分别为 7.98% 和 10.68%。