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The significance of studying biological interactions of micro swimmers in a complex wavy canal with MHD effects lies in its potential to provide insight into the behavior and dynamics of microorganisms in natural environments that contain complex fluid flow and magnetic fields. Current investigation explores the biological interactions between micro swimmers and Cross fluid with inclined MHD effects in a complex wavy canal. There are several factors of medium for micro swimmers like nature, magnetic field, liquid rheology and position. These interactions are hereby witnessed by utilizing the Cross fluid along with Taylor swimming sheet model under the influence of porous and inclined magnetic effect. Furthermore, two-dimensional complex wavy cervical canal is being utilized at inclined angle. By help of lubrication assumption, reduction of momentum equation is made and hence fourth-order differential equation associated with boundary conditions is obtained. Bvp4c command in Matlab is utilized for this boundary value problem. Obtained bvp4c solution is verified with finite difference method and found smooth agreement. Magnetic force enhances the swimming speed and reduction is seen for the power dissipation and effective role is seen for swimming motion with cross fluid rheology. The channel walls (peristaltic nature) and porous medium can be utilized as alternative factors to control the speed of the propeller. [ABSTRACT FROM AUTHOR]

Heat transference in fluid mechanism has a deep influence in real‐life applications like hot‐mix paving, recovery of energy, concrete heating, heat spacing, refineries, distillation, autoclaves, reactors, air conditioning, and so forth. In this attempt, findings related to energy exchange with features of infinite shear rate viscosity model of Carreau nanofluid by placing inclined magnetic dipole over the wedge are made. The main role in the transportation of heat is exercised by incorporating facts of radiation, nonuniform heat sink source, Brownian motion, thermophoresis, and chemical reaction. The mathematical system of the infinite shear rate viscosity model of Carreau nanofluid gives a system of partial differential equations and furthermore, these are moved into ordinary differential equations. A numerical procedure is applied via shooting/bvp4c to obtain numerical results. Inclined magnetic dipole gives a lower velocity of Carreau nanofluid. Due to the relaxation time factor velocity of Carreau fluid gets down. A* causes to generate the heat internally, so due to this, temperature increases rapidly. The increasing rate of temperature is found very high for the growing Hartmann number. The rate of mass transport becomes low for gradual increment in the parameter of thermophoresis, wedge angle, and Prandtl. Inclined magnetic dipole gives a lower velocity of Carreau nanofluid. Due to the relaxation time factor, the velocity of the Carreau fluid goes down. The absence and presence of magnetic numbers have no influence on velocity, temperature, and concentration files for Le, Rd, θf, γ, We, β, Pr, Nb, Nt, A. [ABSTRACT FROM AUTHOR]

Significance: Heat transport in the blood within a wedge-shaped artery is significant in biomedical engineering field like develop therapeutic strategies, drug delivery to specific regions of the artery, vicinity of narrowed or blocked arteries and catheter-based treatments such as angioplasty or thermal ablation.Motive: This study investigates the heat transport analysis of trihybrid nanofluid (blood) over wedge-shaped artery with mathematical model of Cross fluid. This study incorporates three nanoparticles, graphene oxide (GO), titanium dioxide (TiO2), and aluminum oxide (Al2O3) in base fluid blood. The wedge-shaped artery is chosen due to its relevance to biomedical applications and it reflects the nature of blood flow in real vascular structures. Heat transport is scrutinized through thermal radiations and flow rate is inspected through inclined magnetic field.Methodology: The bvp4c and Levenberg–Marquardt Neural Network (LM-NN) supervised neural scheme is used to predict the numerical outcome of this study.Findings: Incorporation of nanoparticles made rapid heat transport of blood in wedge-shaped artery. Velocity of blood is decreased with high Weissenberg number and magnetic force. The temperature of a blood in a wedge-shaped artery increases with positive non-uniform heat source/sink parameters and decreases with negative non-uniform heat source/sink parameters. [ABSTRACT FROM AUTHOR]

Highlights: What are the main findings? The problem of 2-D Prandtl nanofluid past a moving wedge is investigated in detail; Tri-hybrid nanoparticles are considered here; Heat and mass transmission evaluations are conducted in the presence of endothermic/exothermic chemical reactions; The moving wedge is considered; What is the implication of the main finding? LobattoIIIA scheme is implemented for the numerical solution of modeled PDEs. Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick's second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter α brings about a decrement in fluid velocity and augmentation in thermal conductivity ϵ , thermal radiation R d , thermophoresis parameter N t and endothermic/exothermic reaction Ω , and fitted rate constant n accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature. [ABSTRACT FROM AUTHOR]

Cross fluid is one of the important kinds of non-Newtonian fluid, which is most beneficial for the transport of heat and mass. The current model is to investigate the deformation in nanofluid at very high/low shear rate and has the capacity to characterize the properties of nanofluid in shear thinning/thickening region. The impacts of homogeneous-heterogeneous chemical process (HHCP) and Lorentz forces (LFs) on 3-D radiative magnetized Cross nanofluid using two stretching rotatory disks are also presented. HHCP is launched to depict the viscous dissipation, mass transport, joule heating, thermal radiation and heat transport. The nanofluid velocity is investigated in the inclined magnetic field based on the LFs. For the heat's transportation of time and space based on the non-uniform heat sink/source with convective boundary conditions is also indicated. The governed partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) and numerically treated with the reputed bvp4c and Keller–Box schemes. Moreover, it is also observed that the increment in the rotation rate of disk, the enhancement in velocities of Cross nanofluid, the greater magnetic parameter drops sharply and escalation in temperature for strong LFs. [ABSTRACT FROM AUTHOR]

The present study is related to the effects of activation energy and thermophoretic diffusion on steady micropolar fluid along with Brownian motion. The activation energy and thermal conductivity of steady micropolar fluid are also discussed. The equation of motion, angular momentum, temperature, concentration, and their boundary conditions are presented for the micropolar fluid. The detail of geometry reveals the effects of several parameters on the parts of the system. The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. The comparison of the obtained results by the shooting technique and the numerical bvp4c technique is presented. The behavior of local skin friction numbers and couple stress number is tabulated for different parameters, and some figures are plotted to present the different parameters. For uplifting the values of AE for parameter λ A , the concentration profile is increased because of the Arrhenius function, and AE increases with the reduction of this function. The increasing values of the parameter of rotation G show the decrement in velocity because of the rotation of the particle of the fluid, so the linear motion decreases. Thermophoresis is responsible for shifting the molecules within the fluid, and due to this, an increment in boundary layer thickness is found, so by a greater value of N t , the concentration profile decreases and temperature profile goes down. [ABSTRACT FROM AUTHOR]