Three-dimensional flow of a nanofluid over a permeable stretching/shrinking surface with velocity slip: A revised model

Abstract

A reformulation of the three-dimensional flow of a nanofluid by employing Buongiorno’s model is presented. A new boundary condition is implemented in this study with the assumption of nanoparticle mass flux at the surface is zero. This condition is practically more realistic since the nanoparticle fraction at the boundary is latently controlled. This study is devoted to investigate the impact of the velocity slip and suction to the flow and heat transfer characteristics of nanofluid. The governing partial differential equations corresponding to the momentum, energy, and concentration are reduced to the ordinary differential equations by utilizing the appropriate transformation. Numerical solutions of the ordinary differential equations are obtained by using the built-in bvp4c function in Matlab. Graphical illustrations displaying the physical influence of the several nanofluid parameters on the flow velocity, temperature, and nanoparticle volume fraction profiles, as well as the skin friction coefficient and the local Nusselt number are provided. The present study discovers the existence of dual solutions at a certain range of parameters. Surprisingly, both of the solutions merge at the stretching sheet indicating that the presence of the velocity slip affects the skin friction coefficients. Stability analysis is carried out to determine the stability and reliability of the solutions. It is found that the first solution is stable while the second solution is not stable.

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

“…Table 3. Numerical values of −θ (0) and −φ (0) for the case of dual stratified nanofluid over shrinking sheet (ε = −1) and stretching sheet (ε = 1) when The existence of dual solutions for S > 2 in the present study is in accordance to the result by Miklavčič and Wang [2], Fang et al [4], Jusoh et al [5] and Soomro et al [6]. It is apparent from these previous studies that the flow will produce two solutions by employing S > 2 for a suitable combination of the control parameters.…”

“…The nanofluid velocity profile, as depicted in Figure 5, elevates while the temperature and concentration (see Figures 6 and 7) deteriorate with an upsurge of the suction parameter. This is due to the suction which can diminish the momentum boundary layer thickness and therefore enhance the flow near to the sheet [5]. Besides, suction also allows the heated fluid movement towards the wall surface and develops both thermal and concentration boundary layer thickenesses.…”

“…Fang et al [4] analytically investigated viscous flow over shrinking rate with a slip condition and also concluded that the imposition of wall mass suction would induce two solutions. Jusoh et al [5] also concluded that the application of suction at certain values of the involving parameters contributed to the appearance of the second solution. Very recently, Soomro et al [6] obtained dual solutions for mixed convective flow of a viscous fluid with copper nanoparticles over a permeable shrinking cylinder.…”

Stability Analysis of Darcy-Forchheimer Flow of Casson Type Nanofluid Over an Exponential Sheet: Investigation of Critical Points

“…Since flow is probably not going to occur on a shrinking surface, they added sufficient suction at a boundary to create vorticity in the boundary layer. Many researchers have considered a shrinking surface, including Naveed et al [30], Jusoh et al [31], Othman et al [32], Khan and Hafeez [33], Naganthran et al [34], and Qing et al [35]. Rahman et al [36,37] investigated Buongiorno's model on exponentially shrinking surfaces and found dual solutions.…”

A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow with Zero Nanoparticles Flux Condition and Anisotropic Slip

“…Muhammad et al [19] also imposed coupled effects of convective heat and zero nanoparticles flux on conditions for Darcy-Forchheimer flow of Maxwell nanofluid. In addition, research works on the zero nanoparticles flux condition were also considered by Rehman et al [20], Rahman et al [21], Uddin et al [22], ur Rahman et al [23] and Jusoh et al [24]. Furthermore, studies on the boundary layer problem utilizing Buongiorno's model of nanofluid were also conducted by these researchers [25][26][27][28][29][30][31].…”