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The effects of a chemical reaction and radiative heat flux in a nonlinear mixed thermo-solutal convection flow of a viscoelastic nanoliquid from a stretchable surface are investigated theoretically. Newtonian heating is also considered. The upper-convected Maxwell (UCM) model is deployed to represent the non-Newtonian characteristics. The model also includes the influence of thermal radiation that is simulated via an algebraic flux model. Buongiorno’s two-component nanofluid model is implemented for thermophoretic and Brownian motion effects. Convective thermal and solutal boundary conditions are utilized to provide a more comprehensive evaluation of temperature and concentration distributions. Dimensionless equations are used to create the flow model by utilizing the appropriate parameters. The computed models are presented through a convergent homotopic analysis method (HAM) approach with the help of Mathematica-12 symbolic software. Authentication of HAM solutions with special cases from the literature is presented. The impact of various thermophysical, nanoscale and rheological parameters on transport characteristics is visualized graphically and interpreted in detail. Temperatures are strongly enhanced with Brownian motion and thermophoresis parameters. Velocity is boosted with the increment in the Deborah viscoelastic number and mixed convection parameter, and the hydrodynamic boundary layer thickness is reduced. A stronger generative chemical reaction enhances concentration magnitudes, whereas an increment in the destructive chemical reaction reduces them and also depletes the concentration boundary layer thickness. Temperature and concentration are also strongly modified by the conjugate thermal and solutal parameters. Greater radiative flux also enhances the thermal boundary layer thickness. Increasing the Schmidt number and the Brownian motion parameter diminish the concentration values, whereas they elevate the Sherwood number magnitudes, i.e. enhance the nanoparticle mass transfer rate to the wall.

A mathematical model is developed to study laminar, nonlinear, non-isothermal, steady-state free convection boundary layer flow and heat transfer of a micropolar viscoelastic fluid from a vertical isothermal cone. The Eringen model and Jeffery’s viscoelastic model are combined to simulate the non-Newtonian characteristics of polymers, which constitutes a novelty of the present work. The transformed conservation equations for linear momentum, angular momentum and energy are solved numerically under physically viable boundary conditions using a finite difference scheme (Keller Box method). The effects of Deborah number (De), Eringen vortex viscosity parameter (R), ratio of relaxation to retardation times (λ), micro-inertia density parameter (B), Prandtl number (Pr) and dimensionless stream wise coordinate (ξ) on velocity, surface temperature and angular velocity in the boundary layer regime are evaluated. The computations show that with greater ratio of retardation to relaxation times, the linear and angular velocity are enhanced whereas temperature (and also thermal boundary layer thickness) is reduced. Greater values of the Eringen parameter decelerate both the linear velocity and micro-rotation values and enhance temperatures. Increasing Deborah number decelerates the linear flow and Nusselt number whereas it increases temperatures and boosts micro-rotation magnitudes. The study is relevant to non-Newtonian polymeric thermal coating processes.

The large time behavior of passive contaminant in non-Newtonian peristaltic blood flow in a two-dimensional (2D) channel (capillary) has been examined in this paper. The power-law model is employed in order to highlight the non-Newtonian blood characteristic. The study was conducted using the Reynolds decomposition technique, which converts a 2D transport problem into a 1D transport model in which species concentration can be decomposed into sectional average concentration and variation from its mean value. For flow velocity, the same decomposition method is used. This allows the derivation of the dispersion coefficient and convection coefficient. Using Fick's law, the advection–diffusion equation is modified by replacing these coefficients by their corresponding average values and analytical solutions for the mean concentration are derived. In the absence of peristalsis effects (γ = 0), i.e., for the straight rigid channel, the dispersion coefficient is invariant along the channel length. With increasing modulation (peristaltic wave) parameter, γ , there is a strong elevation in advection coefficient in the initial half of the channel with a subsequent suppression in the second half of the channel, indicating that the location in the channel strongly influences advection characteristics. Advection coefficient is significantly elevated with increment in power-law rheological index (for shear-thinning fluids, n < 1) across the channel length and exhibits an oscillatory nature due to the peristaltic waves. In the shear-thickening range (n > 1), with progressive increase in n, an increment in peristaltic modulation parameter, γ , induces a marked reduction in the axially average relative advection coefficient. Dispersion coefficient is initially boosted along the early section of the channel with increment in modulation parameter whereas further long the channel this trend is reversed. Increasing aspect ratio and Péclet number consistently boost dispersion coefficient along the entire channel length. The study provides a solid benchmark for further generalized simulations with computational fluid dynamics. [ABSTRACT FROM AUTHOR]