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, Bangalore M. Shankar, Shaimaa F. Ramadan, Hosahalli E. Mallik and Mohamed S. Mohamed
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Khaled S. Mekheimer: Department of Mathematics, Faculty of Science (Men), Al-Azhar University, Cairo 11884, Egypt
Bangalore M. Shankar: Department of Mathematics, PES University, Bangalore 560085, India
Shaimaa F. Ramadan: Department of Mathematics, Faculty of Science (Girls), Al-Azhar University, Cairo 11884, Egypt
Hosahalli E. Mallik: Department of Mathematics, PES University, Bangalore 560085, India
Mohamed S. Mohamed: Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Mathematics, 2021, vol. 9, issue 11, 1-15

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.

Keywords: linear stability; gold nanoparticles; Jeffreys fluid; radiation; eigenvalue problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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