In this paper, we explored the impact of thermally radiative MHD flow of Williamson nanofluid over a stretchy plate. The flow in a stretchy plate is saturated via Darcy–Forchheimer relation. Cattaneo–Christov heat-mass flux theory is adopted to frame the energy and nanoparticle concentration equations. Additionally, the mass transfer analysis is made by activation energy and binary chemical reaction. Activation energy is invoked through the modified Arrhenius function. The intention of the current investigation is to enhance the heat transfer rate in industrial processes. The non-Newtonian nanofluids have more prominent thermal characteristics compared to ordinary working fluids. The governing models are altered into ODE models, and these models are numerically solved by applying the MATLAB bvp4c algorithm. The graphical and tabular interpretations have scrutinized the impact of sundry distinct parameters. The fluid speed escalates for enhancing the Richardson number, and it falls off for higher values of the Weissenberg number. It is noticed that the fluid temperature declines for higher values of the Brownian motion parameter and it grows for larger values of the thermophoresis parameter. The activation energy enriches the heat transfer gradient and suppresses the local Sherwood number. Additionally, the more significant heat transfer gradient occurs in heat-absorbing nonradiative viscous nanofluid and a smaller heat transfer gradient occurs in heat-generating radiative Williamson nanofluid. Also, we noticed that a higher heat transfer gradient appears in the Fourier model than in the Catteneo–Christov model. In addition, the comparative results are confirmed and reached an outstanding accord.

The consequence of periodic body acceleration and thermal radiation in the pulsating flow of MHD Casson nanofluid through a porous channel is addressed. A flow of the nanofluid injected through the lower plate is considered while sucked out through the upper plate with a similar velocity. The thermal radiation term is incorporated in the heat transfer equation. The governing equations corresponding to velocity and temperature are converted from partial differential equations to a system of ordinary differential equations by employing similarity variables. The perturbation technique is applied to solve the governing flow equations. The impact of diverse parameters on flow features is graphically analyzed. The result reveals that adding the nanoparticle has enhanced the velocity profile of the base fluid. Moreover, an increase in the periodic body acceleration results in enlarging velocity and temperature.

This work addresses 3D bioconvective viscoelastic nanofluid flow across a heated Riga surface with nonlinear radiation, swimming microorganisms, and nanoparticles. The nanoparticles are tested with zero (passive) and nonzero (active) mass flux states along with the effect of thermophoresis and Brownian motion. The physical system is visualized via high linearity PDE systems and nondimensionalized to high linearity ordinary differential systems. The converted ordinary differential systems are solved with the aid of the homotopy analytic method (HAM). Several valuable and appropriate characteristics of related profiles are presented graphically and discussed in detail. Results of interest such as the modified Hartmann number, mixed convection parameter, bioconvection Rayleigh number, and Brownian motion parameter are discussed in terms of various profiles. The numerical coding is validated with earlier reports, and excellent agreement is observed. The microorganisms are utilized to improve the thermal conductivity of nanofluid, and this mechanism has more utilization in the oil refinery process.