The unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible, and electrically conducting fluid passing through a vertical plate embedded in a porous medium in the presence of chemical reactions and thermal radiation is investigated. The effects of the Hall current, rotation and Soret are studied. Using the perturbation approach, one can obtain an accurate analytical solution to the governing equations for the fluid velocity, fluid temperature, and species concentration, provided that the initial and boundary conditions are acceptable. It is possible to obtain expressions for the shear stress, rate of heat transfer, and rate of mass transfer for both plates with the ramping temperature and isothermal conditions. On the one hand, the numerical values of the primary and secondary fluid velocities, fluid temperature, and species concentration are presented graphically. On the other hand, the numerical values of the shear stress and rate of mass transfer for the plate are presented in tabular form for various values of the relevant flow parameters. These values are given for a range of pertinent flow parameters. It was determined that an increase in the Hall and Soret parameters over the whole fluid area leads to a corresponding increase in the resulting velocity. The resultant velocity continually climbs to a high level due to the contributions of the thermal and solute buoyancy forces. Lowering the heat source parameter reduces the temperature distribution, resulting in a lower overall temperature. When there is a rise in the chemical reaction parameter over the whole fluid area, there is a corresponding decrease in the concentration. The concentration buoyancy force, Hall current, and Prandtl number reduce the skin friction. On the other hand, the permeability of the porous medium, rotation, chemical reaction, the Soret number, thermal buoyancy force, and mass diffusion all have the opposite effects on the skin friction.

Curved veins and arteries make up the human cardiovascular system, and the peristalsis process underlies the blood flowing in these ducts. The blood flow in the presence of hybrid nanoparticles through a tapered complex wavy curved channel is numerically investigated. The behavior of the blood is characterized by the Casson fluid model while the physical properties of iron (Fe₃O₄) and copper (Cu) are used in the analysis. The fundamental laws of mass, momentum and energy give rise the system of nonlinear coupled partial differential equations which are normalized using the variables, and the resulting set of governing relations are simplified in view of a smaller Reynolds model approach. The numerical simulations are performed using the computational software Mathematica’s built-in ND scheme. It is noted that the velocity of the blood is abated by the nanoparticles’ concentration and assisted in the non-uniform channel core. Furthermore, the nanoparticles’ volume fraction and the dimensionless curvature of the channel reduce the temperature profile.

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.

Background: The improvement of the thermal conductivity of nanofluids is practical for different processes such as drug delivery, manufacturing of crystals, polymer processing, food and drink, cancer treatment, oil and gas, paper making and for many more. The bioconvection phenomenon has engrossed the attention of numerous researchers for its many applications in biotechnology, mechanical and electrical engineering. Bioconvection nanofluids are more prominent in the fields of biomedicine, pharmacy, nanodrug delivery, biomedical, automotive cooling and the military. Purpose: The major purpose of the current work was to determine the numerical and statistical analysis of a novel thermal radiation and exponential space-based heat source on the bioconvective flow of a pseudoplastic 3D nanofluid past a bidirectional stretched Riga surface. The behavior of the Arrhenius activation energy (AAE) and thermal radiation are also disclosed. Methodology: Suitable similarity transformations were used to transmute the partial differential equations of the flow-modeled phenomena into the structure of ordinary differential ones. The numerical solutions for the renewed set of ODEs were tackled by the bvp4c shooting algorithm built-in MATLAB software. Furthermore, the statistical analysis was computed by applying response surface methodology (RSM). Research implications: The numerical analysis is valid for the incompressible three-dimensional, magnetized flow of a pseudoplastic bioconvection nanofluid through a bidirectional surface with Riga plate aspects in the occurrence of activation energy. Social implications: The flow across three dimensions has quite important implementations in various fields, for example, polymer production, material production technology, the manufacturing of nano-biopolymer computer graphics, industry, powered engineering, aeroplane configurations, etc. The current analysis is more applicable in nanotechnology. Results: The consequences of flow control parameters over flow profiles were studied and explained under the graphic structures. Numerical outcomes were computed and discussed in detail. From the results, it was noted that the velocity field was increased via a larger mixed convection parameter. The temperature distribution was boosted via the thermal Biot number. The concentration of nanoparticles declined via the greater Lewis number. Furthermore, the motile microorganisms field was reduced via the Peclet number. Originality: Until now, no investigation has been recognized to examine the consequences of the bioconvection flow of three-dimensional pseudoplastic nanofluids past a Riga plate containing motile microorganisms utilizing the shooting method called bvp4c. Conclusions: From the results, it was concluded that nanofluids are more helpful for heat transfer increments. Furthermore, from the experimental design observed, the response declined via the thermophoresis parameter, which was significant from the ANOVA observed model.

This article describes the incompressible two-dimensional heat and mass transfer of an electrically conducting second-grade fluid flow in a porous medium with Hall and ion slip effects, diffusion thermal effects, and radiation absorption effects. It is assumed that the fluid is a gray, absorbing–emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. It is assumed that the liquid is opaque and absorbs and emits radiation in a manner that does not result in scattering. It is considered an unsteady laminar MHD convective rotating flow of heat-producing or absorbing second-grade fluid across a semi-infinite vertical moving permeable surface. The profiles of velocity components, temperature distribution, and concentration are studied to apply the regular perturbation technique. These profiles are shown as graphs for various fluid and geometric parameters such as Hall and ion slip parameters, radiation absorption, diffusion thermo, Prandtl number, Schmidt number, and chemical reaction rate. On the other hand, the skin friction coefficient and the Nusselt number are determined by numerical evaluation and provided in tables. These tables are then analysed and debated for various values of the flow parameters that regulate it. It may be deduced that an increase in the parameters of radiation absorption, Hall, and ion slip over the fluid region increases the velocity produced. The resulting momentum continually grows to a very high level, with contributions from the thermal and solutal buoyancy forces. The temperature distribution may be more concentrated by raising both the heat source parameter and the quantity of radiation. When one of the parameters for the chemical reaction is increased, the whole fluid area will experience a fall in concentration. Skin friction may be decreased by manipulating the rotation parameter, but the Hall effect and ion slip effect can worsen it. When the parameter for the chemical reaction increases, there is a concomitant rise in the mass transfer rate.