Duality Solutions in Hydromagnetic Flow of SWCNT-MWCNT/Water Hybrid Nanofluid over Vertical Moving Slender Needle

Abstract

Recently, the topic of convection of heat transfer has created an interest among researchers because of its numerous applications in the daily life. The objective of this paper was to study theoretically the problem of mixed convection boundary layer flow and heat transfer of single-wall carbon nanotube (SWCNT) and multi-wall carbon nanotube (MWCNT) in presence of hydromagnetic effects. The problem was initiated by formulating a mathematical model in partial differential equation (PDE) for the hybrid nanofluid flow with appropriate boundary conditions. The similarity equation was used to transform the PDE into an ordinary differential equation (ODE) and solved using bvp4c in MATLAB. The graphical results on variation of skin friction coefficient, Cf, local Nusselt number, Nux, shear stress, f″c and local heat flux, −θ′c with the effects of magnetic, M, size of needle, c, mixed convection parameter, λ and volume fraction of nanoparticles, φ were presented and discussed in detail. The study revealed that duality of solutions appears when the buoyance force is in opposing flow of the fluid motion, λ<0. The presence of M in hybrid nanofluid reduced the skin friction coefficient and heat transfer. On the other hand, the Cf and Nux increased as different concentrations of φ1 and c were added. It gives an insight into the medical field, especially in treating cancer cells. By means, it reveals that CNTs hybrid nanofluid shows high potential in reaching the site of tumors faster compared with nanofluid. A stability analysis has to be carried out. It is noticed that the first solution was stable and physically realizable.

Boundary Layer Stagnation Point Flow and Heat Transfer over a Nonlinear Stretching/Shrinking Sheet in Hybrid Carbon Nanotubes: Numerical Analysis and Response Surface Methodology under the Influence of Magnetohydrodynamics

“…where [43]. The mathematical correlation of the thermal conductivity of hybrid CNTs in this model is also drawn from the most up-to-date research on hybrid CNTs conducted by Aladdin et al [11] and Haider et al [44]. The correlations and specific numeric values for the physical properties can be viewed in Tables 1 and 2.…”

Exploration of Recent Developments of Hybrid Nanofluids

“…Aladdin and Bachok [84] studied the effects of hydromagnetic on mixed convection of hybrid SWCNT-MWCNT/water nanofluid flow past a moving vertical slender needle, while Yasir et al, [85] explored the properties and heat transfer on the stagnation point flow of hybrid SWCNTs-CuO/ethylene glycol oil, over a permeable stretching/shrinking surface with the effects of radiation, heat generation/absorption and aligned magnetic field.…”

Multiple Solutions and Stability Analysis of Magnetic Hybrid Nanofluid Flow Over a Rotating Disk with Heat Generation

“…There are many papers reported the stability analysis of the dual or two solutions (Wahid et al, [39][40][41], Bakar et al, [42][43][44], Aladdin et al, [45][46][47] and Khashi'ie et al, [48]), however, for the multiple solutions (more than two), only few of references are accessible like Waini et al, [49] and Yahaya et al, [50]. Following Merkin [51], Weidman et al, [52] and Harris et al, [53], the suitable transformation for the unsteadiness case:…”