The magnetic dipole effect for thixotropic nanofluid with heat and mass transfer, as well as microorganism concentration past a curved stretching surface, is discussed. The flow is in a porous medium, which describes the Darcy–Forchheimer model. Through similarity transformations, the governing equations of the problem are transformed into non-linear ordinary differential equations, which are then processed using an efficient and powerful method known as the homotopy analysis method. All the embedded parameters are considered when analyzing the problem through solution. The dipole and porosity effects reduce the velocity, while the thixotropic nanofluid parameter increases the velocity. Through the dipole and radiation effects, the temperature is enhanced. The nanoparticles concentration increases as the Biot number and curvature, solutal, chemical reaction parameters increase, while it decreases with increasing Schmidt number. The microorganism motile density decreases as the Peclet and Lewis numbers increase. Streamlines demonstrate that the trapping on the curved stretched surface is uniform.

In this paper, we work on the Cauchy problem of the three-dimensional micropolar fluid equations. For small initial data, in the variable-exponent Fourier–Besov spaces, we achieve the global well-posedness result. The Littlewood–Paley decomposition method and the Fourier-localization technique are main tools to obtain the results. Moreover, the results discussed in our work show the Gevrey class regularity of solution to the Cauchy problem of micropolar fluid equations.

The current communication, manifest mathematical modelling and numerical computations of Sutterby nanofluids with radiant heat assessment subject to heat generation/absorption. The thermophoresis and Brownian motion effects are incorporated via the Buongiorno model in flow governing equations. Moreover, the present analysis reveals the impacts of thermal stratification, velocity slip, and a magnetic field on flow phenomena. The non-Newtonian nature is modelled using Sutterby fluid. The proposed model is formulated mathematically through basic partial differential equations relating mass, momentum, energy, and nanoparticle concentration conservations using boundary layer theory. We adapted the generated governed equations to ordinary differential equations utilizing similarity variables mechanism. Numerical treatment for the reduced system of ordinary differential equations is performed using the built-in MATLAB code bvp4c. The impacts of distinct characterizing parameters on velocity, temperature, and concentration profiles are determined and analyzed via graphs. The existence of velocity slip parameter, fluid flow is significantly dwindle, while the surface friction growth is sophisticated. Brownian and thermophoresis mechanisms degrade the heat transmission rate and escalate the mass flux. The thermal and solutal stratification exhibits opposite conduct for thermal and concentration of the nanoparticles.