A Stability Analysis of Solutions in Boundary Layer Flow and Heat Transfer of Carbon Nanotubes over a Moving Plate with Slip Effect

Abstract

The flow and heat transfer characteristics of both single-wall and multi-wall carbon nanotubes (CNTs) with water and kerosene as base fluid on a moving plate with slip effect are studied numerically. By employing similarity transformation, governing equations are transformed into a set of nonlinear ordinary equations. These equations are solved numerically using the bvp4c solver in Matlab which is a very efficient finite difference method. The influence of numerous parameters such as nanoparticle volume fraction, velocity ratio parameter and first order slip parameter on velocity, temperature, skin friction and heat transfer rate are further explored and discussed in the form of graphical and tabular forms. The results reveal that dual solutions exist when the plate and free stream move in the opposite direction and slip parameter was found to widen the range of the possible solutions. However, skin friction coefficients decrease, whereas the heat transfer increases in the presence of slip parameter. Single-wall carbon nanotubes (SWCNTs) give higher skin friction and heat transfer compared to multi-wall carbon nanotubes (MWCNTs) due to the fact that they have higher density and thermal conductivity. A stability analysis is carried out to determine the stability of the solutions obtained.

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]).…”

Stagnation Point Flow and Heat Transfer over an Exponentially Stretching/Shrinking Sheet in CNT with Homogeneous–Heterogeneous Reaction: Stability Analysis

“…Furthermore, the stability of the steady flow solution f (η) = f o (η), θ(η) = θ o (η), and g(η) = g o (η) comply with the boundary value problem (30), (31), and (35), and the following terms are introduced: (37) where F(η, τ), H(η, τ), and G(η, τ) are relatively small compared to f o (η), θ o (η), and g o (η), and γ is an unknown eigenvalue. Substitute Equation (37) into Equations (30), (31), and (35), and the following linearized problem is obtained:…”

“…The stability of steady flow f o (η), θ o (η), and g o (η) are investigated by setting τ = 0, and hence F(η) = F o (η), H(η) = H o (η), and G(η) = G o (η) in Equations (38)-(40) describe the initial growth or decay of the solution (37). Therefore, the final equations are in the following form:…”

“…Inspired by Merkin [28], the problem of stability analysis was studied by Weidman et al [29], Merrill et al [30], and Harris et al [31]. Following these, numerous researchers, such as Ishak [32], Nazar et al [33], Awaludin et al [34], Najib et al [35,36], and Anuar et al [37], implemented the stability analysis for dual solutions in their works.…”