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 motive of the current analysis is to examine the role of gyro-tactic microorganisms to reveal their behaviour in heat and mass transfer in time-dependent MHD flow of Cross fluid accounted through nanoparticles. Non-linear thermal radiative, viscous dissipation, Soret and Dufour effect are also scrutinized with constraining conditions. By applying the suitable alteration the system of PDE’s is transmuted into ODE’s. The transmuted ODE’s are utilized through RK-4 along with shooting technique. Moreover, the impact of various emerging variables on the velocity, temperature, concentration and density of motile microorganisms are deliberated numerical and graphical. The outcomes are presented through plots. The outcomes illustrated those enhancements in the value of Weissenberg number We result in a reduction in motile density microorganism while the opposite effect is examined in the velocity slip effect. In addition, an intensifying microorganism profile is observed with velocity slip effect, Peclet number. Comparisons have been prepared with previously published literature and found an outstanding agreement.

The current approach considered the unsteady 2D laminar second law analysis on Williamson hybrid nanoliquid in a porous medium under the effect of the thermal radiative flow towards a convectively heated stretching sheet. Propylene glycol P G ( C 3 H 8 O 2 ) is employed as the base liquid in this study, and the nanoparticles are Molybdenum disulfide M O S 2 and Zinc Oxide Z n O . The purpose of the current study is to maximize the energy and mass transfer rate for industrial and engineering applications. The primary contribution of this study is to discuss heat transmission via thermal radiation, suction, and the porous parameter on the flow of a William hybrid nanoliquid. The constitutive Maxwell flow model, heat transport, and entropy generation can be reduced to ordinary differential equations by similarity transformations. The Bvp4c technique is used on these generating ODEs for the numerical technique in the methodology section. Fluid friction, heat transmission, and Joule heating are used to calculate the entropy generation number. Graphs and tables are used to investigate the effects of dimensionless parameters on flow variables and entropy generation. The primary results suggest that hybrid Maxwell nanofluid is a more efficient heat conductor than regular nanofluid. A significant drop in the velocity field is supported by the Williamson W e , Unsteady β , and porosity γ factors γ . The temperature profile is significantly raised by the Biot number B i , thermal radiation R d , and suction factor S . Moreover, it has been found that entropy increases with radiation R d but reduces in Brinkman number B r against the Bejan number profile. Our results for a few specific situations were compared with previously published data to establish the validity of the current study, and it was discovered that they were in strong agreement.

The physiological systems and biological applications that have arisen during the past 15 years depend heavily on the microscale and nanoscale fluxes. Microchannels have been utilized to develop new diagnostic assays, examine cell adhesion and molecular transport, and replicate the fluid flow microenvironment of the circulatory system. The various uses of MHD boundary flow in engineering and technology are extensive, ranging from MHD power generators and the polymer industry to MHD flow meters and pumps and the spinning of filaments. In this investigation, the (Magnetohydrodynamic) MHD flow of Prandtl nanofluid is investigated along with mixed convection, energy activation, microorganism, and chemical reaction. The flow model is considered through partial differential equations in dimensionless form which is then integrated numerically via considering the Bvp4c technique. The outcome is numerous emerging physical parameters over velocity profile, temperature, mass concentration, and microorganism with the separate pertinent quantities such as the Prandtl fluid parameter, elastic fluid parameter, magnetic field, mixed convection parameter, activation energy, chemical reaction, Brownian motion, thermophoretic force, Prandtl number, and Schmidt number. The friction factor, rate of heat transfer and Sherwood number, and density of microbes are revealed numerically and graphically. The outcomes indicate that the Prandtl fluid parameter and elastic fluid parameter tend to enhance the velocity profile. It is also noted that the Prandtl fluid parameter depreciates the thermal rate with the addition of the concentration profile while the opposite trend is recorded for activation energy. Obtained numerical outcomes are correspondingly compared with the current statistics in limiting cases and a close match is obtained.