The intention of this study is to carry out a numerical investigation of time-dependent magneto-hydro-dynamics (MHD) Eyring–Powell liquid by taking a moving/static wedge with Darcy-Forchheimer relation. Thermal radiation was taken into account for upcoming solar radiation, and the idea of bioconvection is also considered for regulating the unsystematic exertion of floating nanoparticles. The novel idea of this work was to stabilized nanoparticles through the bioconvection phenomena. Brownian motion and thermophoresis effects are combined in the most current revision of the nanofluid model. Fluid viscosity and thermal conductivity that depend on temperature are predominant. The extremely nonlinear system of equations comprising partial differential equations (PDEs) with the boundary conditions are converted into ordinary differential equations (ODEs) through an appropriate suitable approach. The reformed equations are then operated numerically with the use of the well-known Lobatto IIIa formula. The variations of different variables on velocity, concentration, temperature and motile microorganism graphs are discussed as well as force friction, the Nusselt, Sherwood, and the motile density organism numbers. It is observed that Forchheimer number $Fr$ decline the velocity field in the case of static and moving wedge. Furthermore, the motile density profiles are deprecated by higher values of the bio convective Lewis number and Peclet number. Current results have been related to the literature indicated aforementioned and are found to be great achievement.

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through the Riga plate, which is crucial to the structure of several industrial and entering advancements, including thermal nuclear reactors, flow metres and nuclear reactor design. This article addresses the entropy analysis of Sutterby nanofluid flow over the Riga plate. The Cattaneo–Christov heat and mass flux were used to examine the behaviour of heat and mass relaxation time. The bioconvective motile microorganisms and nanoparticles are taken into consideration. The system of equations for the current flow problems is converted from a highly non-linear partial system to an ordinary system through an appropriate transformation. The effect of the obtained variables on velocity, temperature, concentration and motile microorganism distributions are elaborated through the plots in detail. Further, the velocity distribution is enhanced for a greater Deborah number value and it is reduced for a higher Reynolds number for the two cases of pseudoplastic and dilatant flows. Microorganism distribution decreases with the increased magnitude of Peclet number, Bioconvection Lewis number and microorganism concentration difference number. Two types of graphical outputs are presented for the Sutterby fluid parameter (β = −2.5, β = 2.5). Finally, the validation of the present model is achieved with the previously available literature.

The addition of gyrotactic microbes in the nanoparticles is essential to embellish the thermal efficiency of many systems such as microbial fuel cells, bacteria-powered micro-mixers, micro-volumes like microfluidics devices, enzyme biosensor, and chip-shaped microdevices like bio-microsystems. This analysis investigates the second law analysis in the bioconvection flow of a Carreau nanoliquid through a convectively stretching surface. The heat transports characteristics encountered with Cattaneo–Christove heat flux and thermal radiation. The Buongiorno model is used for nanoliquid, which comprises the Brownian motion and thermophoretic. The appropriate transformation is invoked to change the system of the partial differential equation into ordinary differential equations. Afterward, these equations are classified analytically with the help of the homotopy analysis method. The influence of numerous physical variables is interpreted and elaborated via graphs. The tabular result shows the numerical consequences of different physical flow parameters. It is examined that a more significant Weissenber number We {\rm{We}} results in deprecation in the velocity field. It is appraised that the temperature profile reduces to augment the value of thermal relaxation time. Justification of the current work has existed through previous publishing results. The utilization of Carreau nanoparticles in the shear rate-dependent viscous fluid is of significant importance due to their potential to improve heat and mass transmission.

The current exploration focuses on the impact of homogeneous and heterogeneous chemical reactions on titanium dioxide-ethylene glycol (EG)-based nanoliquid flow over a rotating disk with thermal radiation. In this paper, a horizontal uniform magnetic field is used to regularise the flow field produced by a rotating disk. Further, we conduct a comparative study on fluid flow with and without aggregation. Suitable transformations are used to convert the governing partial differential equations (PDEs) into ordinary differential equations (ODEs). Later, the attained system is solved numerically by means of the shooting method in conjunction with the Runge–Kutta–Fehlberg fourth-fifth-order method (RKF-45). The outcome reveals that the fluid flow without nanoparticle aggregation shows enhanced heat transport than for augmented values of melting parameter. Furthermore, for augmented values of strength of homogeneous and heterogeneous reaction parameters, the mass transfer is greater in fluid flow with aggregation conditions.