Stability Analysis of the Magnetized Casson Nanofluid Propagating through an Exponentially Shrinking/Stretching Plate: Dual Solutions

Abstract

In this research, we intend to develop a dynamical system for the magnetohydrodynamic (MHD) flow of an electrically conducting Casson nanofluid on exponentially shrinking and stretching surfaces, in the presence of a velocity and concertation slip effect, with convective boundary conditions. There are three main objectives of this article, specifically, to discuss the heat characteristics of flow, to find multiple solutions on both surfaces, and to do stability analyses. The main equations of flow are governed by the Brownian motion, the Prandtl number, and the thermophoresis parameters, the Schmid and Biot numbers. The shooting method and three-stage Lobatto IIIa formula have been employed to solve the equations. The ranges of the dual solutions are f w c 1 ≤ f w and λ c ≤ λ , while the no solution ranges are f w c 1 > f w and λ c > λ . The results reveal that the temperature of the fluid increases with the extended values of the thermophoresis parameter, the Brownian motion parameter, and the Hartmann and Biot numbers, for both solutions. The presence of dual solutions depends on the suction parameter. In order to indicate that the first solution is physically relevant and stable, a stability analysis has been performed.

A numerical solution using EFDM for unsteady MHD radiative Casson nanofluid flow over a porous stretching sheet with stability analysis

“…Based on a scale analysis, we put forward a standard boundary layer approximation on the unsteady MHD Casson nanofluid flow with heat and mass transfer and is governed by the following equations with the aforesaid assumptions and relevant boundary conditions 6,[24][25][26][27][28][29][30][31][32][33][34][35] :…”

“…Rafique et al 28 used a nonlinear inclined surface to numerically study the impact of Soret and Dufour effects on the nanofluid flow. Lund et al 29 performed a stability analysis on MHD Casson nanofluid through an exponentially stretching and shrinking sheet. Reza‐E‐Rabbi 30 used a finite difference method to study an unsteady MHD Casson nanofluid, taking into account the effects of Brownian motion and the thermophoresis parameter.…”

Mathematical Analysis of Magnetized Rotating Nanofluid Flow Over nonlinear shrinking surface: Duality and Stability

“…In addition, 𝐹(𝜂, 𝜏), 𝐺(𝜂, 𝜏), 𝐻(𝜂, 𝜏), and 𝐽(𝜂, 𝜏) all their derivatives are assumed small relative to 𝑓 0 (𝜂), 𝑔 0 (𝜂), 𝜃 0 (𝜂), and ∅ 0 (𝜂). Now, substituting the correlation (25) in Equations (20)(21)(22)(23)(24), we get the following resultant Linearized Eigenvalue Problem (LEVP) system as follows:…”

“…The shooting method was then adopted to solve the resultant ODEs and triple solutions were obtained. Some important effects of the MHD on fluid flow can be seen in these articles [22][23][24][25][26][27][28].…”

A Magnetite–Water-Based Nanofluid Three-Dimensional Thin Film Flow on an Inclined Rotating Surface with Non-Linear Thermal Radiations and Couple Stress Effects

“…The flow over a stretching sheet has attracted significant attention in the last few years due to its unique nature and industrial applications. Different studies on stretching sheets can be found in detail in the papers [44][45][46][47][48][49]. Gosh et al [50] used the Tiwari and Das model to investigate the couple stress magnetite-water-based nanofluid motion near a bi-directional stretchable surface incorporating the effects due to non-linear thermal radiations.…”