This paper explores the heat and mass transfer by hybrid nanofluids flow over a spinning disk in the presence of oxytactic microorganisms. During this study, the Soret and Dufour together with Lorentz force impacts are considered. The worked nano-mixture is assumed to be having time-dependent dynamic viscosity and thermal conductivity and its components are methanol-based hybrid nanofluid comprising $\mathit{CuO}$ and $\mathit{MgO}$ nanoparticles. The disk surface is permeable and various aspects such as thermal radiation, heat generation and Arrhenius activation energy are taken into account. The governing equations are treated numerically and suitable similar transformations are introduced. The obtained results revealed that both of the velocity and temperature gradients are enhanced as the absolute values of unsteadiness parameter and nanoparticles concentrations are rising. However, the flow is slowdown as the temperature-dependent variable viscosity parameter is growing.

An unsteady convection-radiation interaction flow of power-law non-Newtonian nanofluids using the time-fractional derivative is examined. The flow domain is an enclosure that has a free surface located at the top boundaries. Also, the geometry is filled by aluminum foam as a porous medium and the overall thermal conductivity as well as the heat capacity are approximated using a linear combination of the properties of the fluid and porous phases. Additionally, the dynamic viscosity and thermal conductivity of the mixture are expressed as a function of velocity gradients with a fractional power. Marangoni influences are imposed to the top free surface while the bottom boundaries are partially heated. Steps of the solution methodology are consisting of approximation of the time fractional derivatives using the conformable definition, using the finite differences method to discretize the governing system and implementation the resulting algebraic system. The main outcomes reveled that as the fractional order approaches to one, the maximum values of the stream function, the bulk-averaged temperature and cup-mixing temperature are reduces, regardless values of the time.

This study aims to examine the impacts of the variable nanofluid properties on the compressible flow over an inclined irregular surface. The density, dynamic viscosity and thermal conductivity of the nano liquid are assumed to be dependent on the temperature, and the viscous dissipation in this case is introduced. Sinusoidal formulations for the unsmoothed surface together with the governing system in case of ${Gr}_L\to \mathrm{\infty }$ are presented. The temperature on the edge is, also, variable and depending on the discerption function of the surface. The nonlinear radiation is taken into account, and the two-phase model for the nanofluid is applied. A fully implicit finite difference method (FDM) is used to solve the governing system. The major outcomes revealed that the skin friction coefficient and Nusselt number are rising as the compressibility parameter $\delta$ is altered. Also, the maximization of the thermal conductivity-variation ${\beta }_1$ is better for the velocity and temperature behaviors.

This article presents a computational study for the peristaltic pumping within vertical irregular divergence channels filled with magnetic six-constant Jeffrey nanofluids. Various configurations of the outer boundaries are considered, namely, square wave, trapezoidal wave, multisinusoidal wave, and triangular wave. An induced magnetic field together with nanoparticles and mass concentration are considered. Influences of the Dufour and Soret numbers are examined, and the cases of long wavelength and low Reynolds number are applied. All the computations are obtained numerically via MATHEMATICA symbolical software (built-in command ND-Solve), and the obtained results are presented in terms of the axial velocity $u,$ current density $J_z,$ the function of magnetic force $\mathrm{\Phi },$ axially induced magnetic field $h_x,$ nanoparticle fraction profile $\mathrm{\Omega },$ concentration profile $\gamma ,$ temperature profile $\theta ,$ extra stress tensor $S_{xy},$ pressure gradient $\frac{dp}{dx},$ pressure rise ${\mathrm{\Delta }p}_{\mathrm{\lambda }},$ and stream function $\psi .$ The major outcomes revealed that the square wave shape gives higher pressure gradients near the inlet and outlet parts while the multisinusoidal wave gives periodic behaviors of $\frac{dp}{dx}.$ Also, higher axial-induced magnetic fields are given at the higher values of the magnetic Reynolds number.