Dual nature solutions of unsteady MHD hybrid Carbon nanotubes across expanding/contracting cylinder

Abstract

Carbon nanotubes (CNTs) have proven their value in diverse multidisciplinary applications. For this purpose, the current study sheds light on time-reliant properties of electrically conducting flow of hybrid carbon nanotubes, scenario involving joule dissipation at a permeable cylinder that can expand and shrink. To get a precise insight into numerical outcome, the unsteady governing momentum and energy equations in cylindrical coordinates rendered into pertinent ODEs via incorporating the rescaling technique, Thereafter, the rendered equations cracked numerically via a built-in function in MATLAB (BVP4C) package. Notably, the sundry parameters yield two distinct solutions in both assisting and opposing zones, so the flow separation is identified. The governing physical factors are well explored through various graphical forms with physical explanations. Graphical observations declare, that heightening the value of curvature and volume fraction parameters contributes to speed up the onset of turbulence flow, augmentation in skin friction rate is noted through unsteadiness, magnetic field, and curvature parameters. Additionally, the stability assessment clearly specifies the mathematical robustness of the first branch as time passes. This study stands out for it is an inimitable configuration that holds significant addition in optimization of modern heat transfer applications.

Keywords

• MHD
• Unsteady flow
• Hybrid carbon nanotubes
• Stretching/ Shrinking cylinder
• Duality solution