Abstract
Titanium alloy nanoparticle has a variety of applications in the manufacturing of soap and plastic, microsensors, aerospace design material, nano-wires, optical filters, implantation of surgical, and many biological treatments. Therefore, this research article discussed the influence of nonlinear radiation on magneto Williamson fluid involving titanium alloy particles through a thin needle. The arising system of partial differential equations is exercised by the similarity transformations to get the dimensional form of ordinary differential equations. The dual nature of solutions is obtained by implementing bvp4c. The study of stability has been carried out to check which of the results are physically applicable and stable. Influences of pertinent constraints on the flow field are discussed with the help of graphical representations and the method validation is shown in Table 1. The results imply that more than one result is established when the moving needle and the free-stream travel in the reverse directions. Moreover, the magnetic parameter accelerates the severance of boundary-layer flow, while the separation delays in the absence of the nanoparticle. The velocity gradient of nanofluid decays owing to the Williamson parameter in both branches of the outcome, while the temperature shrinks in the first or upper branch solution (stable one) and uplifts in the second or lower branch solution (unstable one). The size of the needle decreases the velocity in the upper solution and accelerates in the lower solution. The patterns of streamlines are more complicated due to the reverse direction of the free stream and thin needle.
Highlights
Titanium alloy nanoparticle has a variety of applications in the manufacturing of soap and plastic, microsensors, aerospace design material, nano-wires, optical filters, implantation of surgical, and many biological treatments
Multiple solutions of axisymmetric flow passing from a slim needle moving in the opposite or the same path to the free stream were obtained by the researcher Ishak et al
Entropy analysis of flow passing from a thin needle in a parallel stream with radiation influence was investigated by Afridi et al
Summary
(Ti6Al4V) suspended in Williamson fluid through a thin moving needle with nonlinear thermal radiation: stability scrutinization. Qw Heat-flux (Wm−2) F Similarity fuction for velocity Rex , Rer Local Reynolds number Rd Radiation parameter S1 Extra stress-tensor T1 Temperature (K) Tw Temperature of the wall (K) T∞ Ambient temperature (K) uw Velocity (m/s) u∞ Free-stream velocity (m/s) (u1, v1) Velocity components (m/s) We Weissenberg number (r1, x1) Radial and axial directions (m). Greek symbols Velocity ratio parameter νf Kinematic viscosity of the base fluid (m2/s) αf Thermal diffusivity (m2/s) μ0, μ∞ Limiting viscosities at zero and infinite shear stresses ( Nsm−2) γ1 Shear stress θ Dimensionless temperature θr Temperature ratio parameter φ Volume fraction of nanoliquid σ Electric conductivity of nanofluids ( Sm−1) σ ∗ Stefan Boltzmann constant ( Wm−2 K−4) ρ Nanofluid density (kg m−3) μ Viscosity of nanoliquid (Kg m −1 s−1) ρcp Heat capacity of nanoliquid (J/K) Ŵ1 Time relaxation (s) ψ1 Stream function η Similarity variable τw Wall shear stress
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