Magnetohydrodynamics Flow Past a Moving Vertical Thin Needle in a Nanofluid with Stability Analysis

Abstract

In this study, we intend to present the dynamics of a system based on the model of convective heat and mass transfer in magnetohydrodynamics (MHD) flow past a moving vertical thin needle in nanofluid. The problem is formulated in mathematical form by using Buongiorno’s model with the modified boundary condition. The transformed boundary layer ordinary differential equations are solved numerically using the bvp4c function in MATLAB software. The effects of the involved parameters, including, Brownian motion, thermophoresis, magnetic field, mixed convection, needle size and velocity ratio parameter on the flow, heat and mass transfer coefficients are analyzed. The numerical results obtained for the skin friction coefficients, local Nusselt number and local Sherwood number, as well as the velocity, temperature and concentration profiles are graphically presented and have been discussed in detail. The study reveals that the dual solutions appear when the needle and the buoyancy forces oppose the direction of the fluid motion, and the range of the dual solutions existing depends largely on the needle size and magnetic parameter. The presence of the magnetic field in this model reduces the coefficient of the skin friction and heat transfer, while it increases the coefficient of the mass transfer on the needle surface. A stability analysis has been performed to identify which of the solutions obtained are linearly stable and physically relevant. It is noticed that the upper branch solutions are stable, while the lower branch solutions are not.

Dual Stratified Nanofluid Flow Past a Permeable Shrinking/Stretching Sheet Using a Non-Fourier Energy Model

“…Figure 15 illustrated the smallest eigenvalue σ 1 of both solutions towards ε where σ 1 act as a determinant of the stability solutions. Positive σ 1 implies that the flow is stable whereas negative σ 1 indicates an initial growth of disturbances which resulting that the flow is unstable [55][56][57][58][59][60][61][62][63][64][65]. It is validated from Figure 15 that the first and second solutions have positive and negative σ 1 , respectively which indicates that the first solution is the real solution.…”

“…The execution of the stability analysis is mathematically performed to verify the physical or real solution among all the solutions. There has been much current literature that discussed the importance, formulation and execution of the stability analysis (see Ismail et al [55][56][57], Bakar et al [58,59], Anuar et al [60], Salleh et al [61,62], Najib et al [63], Jamaludin et al [64] and Yahaya et al [65]).…”

Hybrid Nanofluid Flow Past a Permeable Moving Thin Needle

“…Apart from that, the effect of the nanoparticle on the flow over a thin needle was initiated by Grosan and Pop [32] and then extended by Soid et al [33] to a moving needle in a nanofluid. Furthermore, the effect of the magnetic field on the flow past a moving vertical thin needle in a nanofluid was reported by Salleh et al [34].…”

Dual Solutions and Stability Analysis of Micropolar Nanofluid Flow with Slip Effect on Stretching/Shrinking Surfaces

“…It should be noted that Buongiorno's model is considered a two-phase non-homogeneous model in which the slip velocity of the base fluid and nanoparticles are not equal to zero. This model contains seven slip parameters, including diffusiophoresis, inertia, fluid drainage, gravity, Brownian motion, Magnus and thermophoresis [5]. On the other hand, the Tiwari-Das model is one of the single-phase (homogeneous) models in which the thermophysical characteristics of the base fluid are improved with the impact of nanoparticles allied with viscosity and thermal conductivity.…”