Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition

Abstract

The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative).

Dual Solutions and Stability Analysis of a Hybrid Nanofluid over a Stretching/Shrinking Sheet Executing MHD Flow

“…The problem of the unsteady MHD flow of the Cu − Al 2 O 3 / water hybrid nanofluid in the presence of the thermal radiation effect over the stretching/shrinking sheet is examined. Two methods are adopted to carry out the numerical computations of the current problem, a shooting method is used to get the dual solutions of ODEs (6)(7)(8) in MAPLE software 2018, and the computation of the stability analysis is carried out by employing a 3-stage Labatto IIIa formula in a BVP4C solver in MATLAB 2017b. The impacts of φ Cu unsteadiness parameter S and suction parameter S on the f (0), −θ (0), f (η), and θ(η) were exhibited graphically and examined.…”

“…This model has been constructed by considering a solid volume fraction of nanoparticles in the base fluid, and, later, the governing equations have been solved numerically by employing the finite volume method. As a result, this model has been widely considered by many scientists, engineers, and mathematicians, such as Benzema et al [3], Dero et al [4], Lund et al [5,6], Dogonchi, et al [7,8], Amini, et al [9], Zaib et al [10], Raza et al [11], Rasool et al [12,13], Dinarvand et al [14], and Roşca, et al [15] to investigate different types of flow. Furthermore, to keep the demand of the high heat transfer rate from industries and other sectors, researchers have introduced a new kind of the nanofluid by considering the two different types of the solid particles in the single convectional base fluid.…”

Dual Solutions and Stability Analysis of Magnetized Hybrid Nanofluid with Joule Heating and Multiple Slip Conditions

“…Nanofluid can be defined as a mixture of nano-sized particles of solid in a base fluid. Later, many researchers worked on nanofluids experimentally and theoretically [2][3][4][5][6][7][8]. Consequently, these investigations lead to greater efforts to enhance the heat transfer rate, yet nobody can conclude and claim that a mixture of a particular type of base fluid with a particular kind of nanoparticle can produce the highest rate of heat transfer [9][10][11][12][13][14].…”

Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface

“…The shooting technique along with the Runge Kutta method of the fourth order is employed in order to obtain the numerical solutions of Equations (11)-(13) subject to the boundary conditions. Shooting method helps to reduce the third order ODEs (11)- (13) into the first-order ODEs, such that…”

“…Shah et al, [11] examined micropolar nanofluid with the effect of the Casson parameter in the channel and stated that the thermal boundary layer becomes thicker for the higher values of the Brownian motion parameter. Some papers have recently shown some development on the micropolar fluid [12][13][14][15][16].…”