dual solutions

MHD Reiner–Philippoff Fluid over a Shrinking Surface with the Impact of Aluminium Alloy Nanoparticles

The study of fluid flow and heat transfer over shrinking surfaces is crucial for applications in materials processing, thermal management, and nanotechnology.  When combined with hybrid nanofluids, these systems offer enhanced heat transfer and boundary layer control, making them valuable for advanced energy systems and microfluidic technologies.  This manuscript primarily investigates the behavior of MHD Reiner--Philippoff (RP) fluid, particularly emphasizing the role of AA7075–AA7072/methanol hybrid nanofluid on a permeable shrinking surface.  The original model, expr

Boundary layer flow and heat transfer towards a stretching or shrinking cylinder within carbon nanotubes with hydromagnetic effects

The numerical investigation of stagnation point flow past a stretching or shrinking cylinder in carbon nanotubes with the presence of hydromagnetic effects is examined.  This study has been solved by ordinary differential equations obtained using the similarity transformation that transformed from the governing equations along with the boundary conditions, then implemented the bvp4c solver in MATLAB software platform, ensuring accurate results.  Considering two types of base fluids, namely water and kerosene.  Also, single-wall and multi-wall types of carbon nanotubes a

Three-dimensional rotating viscous flow past a permeable stretching/shrinking sheet with convective boundary condition

The study of three-dimensional rotating boundary layer flow approaching a stretching or shrinking surface under convective boundary conditions is presented in this paper.  This study expands the scope of previous researchers' work to encompass broader scenarios, including situations involving mass transfer (suction) on the wall, the Biot number and cases featuring a shrinking surface.  It is found that the increase of suction and rotating parameters leads to a noticeable rise in both the local skin friction coefficients and the local Nusselt number, and the solutions to the governing ordina

Double solutions and stability analysis of slip flow past a stretching/shrinking sheet in a carbon nanotube

A stagnation point flow past a stretching/shrinking surface in carbon nanotubes (CNTs) with slip effects is investigated in this paper.  Applying transformations of similarity, the governing partial differential equations are modified to the nonlinear ordinary differential equations.  Afterward, they are numerically solved in Matlab by the bvp4c solver.  The single-wall CNTs and multi-wall CNTs are used, including water as a base fluid.  The effects of the flow parameters are investigated, shown in the form of graphs, and physically evaluated for the dimensionless velocity, temperature, ski