Hybrid Carbon Nanotube Flow near the Stagnation Region over a Permeable Vertical Plate with Heat Generation/Absorption

Nur Syazana Anuar,Ioan Pop,Norfifah Bachok

doi:10.3390/math9222925

Nur Syazana Anuar, Ioan Pop + Show 1 more

Open Access

https://doi.org/10.3390/math9222925

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Abstract

This research explored the mixed convection flow past a vertical plate immersed in a hybrid carbon nanotube near the stagnation point. The hybrid carbon nanotube was synthesized by the mixture of two nanoparticles, namely multi-wall (MWCNT) and single-wall (SWCNT) carbon nanotubes immersed in water (base fluid). In addition, attractive aspects of suction/injection and heat generation/absorption effects were incorporated. Similarity variables were used to convert the partial differential equations describing the fluid into ordinary (similarity) differential equations before being solved numerically using Matlab software. The simultaneous impact of several parameters on velocity and temperature profiles, skin friction coefficient, and local Nusselt number were represented with graphs. Dual solutions were observed for some pertinent parameters, which led to stability analysis. This analysis interpreted that merely the first numerical solution is stable. In addition, hybrid nanoparticle, injection effect, and heat-generation parameters led to a decreased range of solutions, whilst the suction effect and heat-absorption parameters acted in the opposite manner. Besides, it is noted that the rate of heat transfer for hybrid carbon nanotube was higher when compared with carbon nanotube and ordinary fluid. Additionally, the heat absorption and buoyancy-assisting flow parameters magnified the heat transfer rate.

Highlights

Many researchers are fascinated by nanofluid due to its rapid advancement in nanotechnology and modern sciences
The present research contributes to the analysis of SWCNT–multi-wall carbon nanotube (MWCNT)/water hybrid
) . selected values flow when the plate is vertical with suction/injection and heat generation/absorption eftion ( φ1 and φ2 ) when s = 0.2 (Figures 4 and 6) and s = −0.2 (Figures 5 and 7)

Summary

Introduction

Many researchers are fascinated by nanofluid (i.e., mixing nanoparticles in the base fluid) due to its rapid advancement in nanotechnology and modern sciences. The idea of using hybrid nanofluid flourished, attracting several researchers to study the thermal behavior of some nanoparticles such as metallic [7,8], ferrite [9,10], and carbon nanotube [11,12] in fluid flow through various surfaces and effects. [35,36,37,38]) have mathematically performed of the stability analysis of solutions in their recent work This theoretical study would benefit engineers who are conducting experiments on hybrid carbon nanotubes, and the findings areof expected the cost of future experiments. The inviscidIn flow present research, a hybrid carbon nanotube (SWCNT–MWCNT/water) was formed by velocity is U e ( x ) = a x , where a ( > 0 ) is the stagnation point’s velocity, while the sheet’s dispersing 1% of multi-wall carbon nanotube (MWCNT) nanoparticles into the base fluid.

Stability Analysis

Analysis of Results

Concluding Remarks

Findings

Methods