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.

Bioconvection phenomena for MHD Williamson nanofluid flow over an extending sheet of irregular thickness are investigated theoretically, and non-uniform viscosity and thermal conductivity depending on temperature are taken into account. The magnetic field of uniform strength creates a magnetohydrodynamics effect. The basic formulation of the model developed in partial differential equations which are later transmuted into ordinary differential equations by employing similarity variables. To elucidate the influences of controlling parameters on dependent quantities of physical significance, a computational procedure based on the Runge–Kutta method along shooting technique is coded in MATLAB platform. This is a widely used procedure for the solution of such problems because it is efficient with fifth-order accuracy and cost-effectiveness. The enumeration of the results reveals that Williamson fluid parameter $\lambda$, variable viscosity parameter ${\Lambda }_{\mu }$ and wall thickness parameter $\varsigma$ impart reciprocally decreasing effect on fluid velocity whereas these parameters directly enhance the fluid temperature. The fluid temperature is also improved with Brownian motion parameter $Nb$ and thermophoresis parameter $Nt$. The boosted value of Brownian motion $Nb$ and Lewis number $Le$ reduce the concentration of nanoparticles. The higher inputs of Peclet number $Pe$ and bioconvection Lewis number $Lb$ decline the bioconvection distribution. The velocity of non-Newtonian (Williamson nanofluid) is less than the viscous nanofluid but temperature behaves oppositely.

The rheology of different materials at the micro and macro levels is an area of great interest to many researchers, due to its important physical significance. Past experimental studies have proved the efficiency of the utilization of nanoparticles in different mechanisms for the purpose of boosting the heat transportation rate. The purpose of this study is to investigate heat and mass transport in a pseudo-plastic model past over a stretched porous surface in the presence of the Soret and Dufour effects. The involvement of tri-hybrid nanoparticles was incorporated into the pseudo-plastic model to enhance the heat transfer rate, and the transport problem of thermal energy and solute mechanisms was modelled considering the heat generation/absorption and the chemical reaction. Furthermore, traditional Fourier and Fick’s laws were engaged in the thermal and solute transportation. The physical model was developed upon Cartesian coordinates, and boundary layer theory was utilized in the simplification of the modelled problem, which appears in the form of coupled partial differential equations systems (PDEs). The modelled PDEs were transformed into corresponding ordinary differential equations systems (ODEs) by engaging the appropriate similarity transformation, and the converted ODEs were solved numerically via a Finite Element Procedure (FEP). The obtained solution was plotted against numerous emerging parameters. In addition, a grid independent survey is presented. We recorded that the temperature of the tri-hybrid nanoparticles was significantly higher than the fluid temperature. Augmenting the values of the Dufour number had a similar comportment on the fluid temperature and concentration. The fluid temperature increased against a higher estimation of the heat generation parameter and the Eckert numbers. The impacts of the buoyancy force parameter and the porosity parameter were quite opposite on the fluid velocity.

The purpose of this research is to investigate the consequence of thermophoretic particle deposition (TPD) on the movement of a TiO₂/water-based micropolar nanoliquid surface in the existence of a porous medium, a heat source/sink, and bioconvection. Movement, temperature, and mass transfer measurements are also performed in the attendance and nonappearance of nanoparticle aggregation. The nonlinear partial differential equations are transformed into a system of ordinary differential equations using appropriate similarity factors, and numerical research is carried out using the Runge-Kutta-Felhberg 4th/5th order and shooting technique. The obtained results show that improved values of the porous constraint will decline the velocity profile. Improvement in heat source/sink parameter directly affects the temperature profile. Thermophoretic parameter, bioconvection Peclet number, and Lewis number decrease the concentration and bioconvection profiles. Increases in the heat source/sink constraint and solid volume fraction will advance the rate of thermal dispersion. Nanoparticle with aggregation exhibits less impact in case of velocity profile, but shows a greater impact on temperature, concentration, and bioconvection profiles.

The current investigations are related to presenting the characteristics of flow at very high and low shear rates along with the melting process over the geometry of Riga plate. Carreau nanofluid is most appropriate mathematical viscosity model that can deal with low and high shear rates. Transportation of energy is discussed through melting conditions, thermal radiation and viscous dissipation. In this study, electromagnetic hydrodynamic aspect of nanofluid is discussed by using electromagnetic surface (Riga plate) and this system generates Lorentz force parallel to wall that keeps its effect on velocity of nanofluid. Partial differential equations (PDEs) are moved in ordinary differential equations and numerical approach named Keller Box and Shooting scheme are exercised to fetch the numerical solution of the system. An augmentation in Q leads to an enrichment in an external magnetic field. The velocity as well as momentum boundary layer booms by the virtue of an improvement in an external magnetic field. The viscosity of the nanofluid increases by the virtue of a magnification in β. Nanofluid becomes more radiated and absorbs more heat as a result of magnification in Nr, which escalates the heat transfer rate.