LAUSR

In this manuscript, to modify the fluid thermophysical properties, the alumina suspended nanoparticles were immersed in two different kinds of base fluids, ethylene glycol with Prandtl number (Pr = 204) and water with (Pr = 6.785). The combination between Powell–Eyring model and micropolar fluid was utilized to describe a 2D steady nanofluid flow along a stretching permeable sheet. An inconvenience through a porous material was illustrated by Darcy–Forchheimer (D–F) expression. As it is known, the nanofluid thermophysical properties are not constants especially in the presence of heat transfer; hence, the viscosity and thermal conductivity were employed as variable functions of the temperature and nanoparticle concentration. As well as in the present work, the microrotation and spin gradient viscosities, which were always constant in all the above studies, have been employed as variable functions of the temperature. The governing mathematical equations have been calculated numerically via the Chebyshev pseudospectral method/Mathematica code. A perfect agreement was obtained between some numerical outcomes and previous published data. Also, the present numerical outcomes for the distributions of temperature, concentration, velocities, skin friction, wall couple stress, Nusselt and Sherwood numbers are represented in tabular form and by drawing against different controlling parameters in the ranges $$ \phi (0 - 20\% ),A(0.01 - 1),\,n(0 - 5),\,\beta_{1} ,\,\beta_{1} ,\,\beta_{3} \,(0 - 0.7),\,$$ $$ {\text{Fr}},\,{\text{Da,}}\,K_{c} ,\,{\text{Sc}}\,(0.1 - 2),\,\Delta \,(0.1 - 10),S\,( - 1\, - \,1)$$ , and $$ M(0 - 20)$$ . In this article, it is confirmed that utilizing the nanofluid viscosity/thermal conductivity as a variable function of both the nanoparticle concentration and the temperature had a great importance and is a vital factor to reinforce the rate of heat transfer. Finally, a new result was gotten in this work; when the variable microrotation viscosity parameter rose, the angular velocity profile raised.