On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy

Khaled S Mekheimer,Hosahalli E Mallik,Mohamed S Mohamed,Bangalore M Shankar,Shaimaa F Ramadan

doi:10.3390/math9111302

Khaled S Mekheimer, Hosahalli E Mallik + Show 3 more

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https://doi.org/10.3390/math9111302

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Journal: Mathematics	Publication Date: Jun 6, 2021
Citations: 17	License type: CC BY 4.0

Affiliation: PES University, Taif University, Al Azhar University

Abstract

We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numerous applications in the biomedical industry, such a study is essential. The linear stability is investigated through the normal mode disturbances. The resulting stability problem is an eighth-order ordinary differential complex eigenvalue problem that is solved numerically using the Chebyshev collection method. Its solution provides the neutral stability curves, defining the threshold of linear instability, and the critical parameters at the onset of instability are determined for various values of control parameters. The results for Newtonian fluid and second-grade fluid are delineated as particular cases from the present study. It is shown that the Newtonian fluid has a more stabilizing effect than the second-grade and the Jeffreys fluids in the presence of gold nanoparticles and, Jeffreys fluid is the least stable.

Highlights

Nanofluid is visualized to describe a fluid in which nanometer-sized particles (10–100 nm) are stably suspended in conventional heat transfer basic fluids
We considered the flow of the Jeffreys fluid with gold nanoparticles (GNPS) in a vertical layer and subjecting it to a transverse temperature gradient
We identified that the expansion in the values of NA, and NB amplifies the temperature

Summary

Introduction

Nanofluid is visualized to describe a fluid in which nanometer-sized particles (10–100 nm) are stably suspended in conventional heat transfer basic fluids. The equivalent applies to censure tissues and malignancy present in the human body without settling on the decision of analyzing parts or organs. Infiltration of nano-size gold particles through catheters conveying the necessary medications to the harmed organs has shown surprising outcomes. A modeling study on heated couple-stress fluid peristaltically conveying gold nanoparticles through coaxial tubes was investigated by Hussain et al [1]. The peristaltic blood flow with gold nanoparticles as a third-grade nanofluid in a catheter was studied by Mekheimer et al [2]. Many authors analyzed the mechanism of nanofluids with the application of peristaltic flow [3,4,5,6,7]. For the last few decades, several authors have analyzed the stability of the flow in vertical channels, where their works concern the hydrodynamic stability of pure fluids [8,9,10,11]

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