Boundary layer flow and heat transfer of Cu-Al2O3/water over a moving horizontal slender needle in presence of hydromagnetic and slip effects

Research on boundary layer flow and heat transfer has been growing since their importance in industrial and technological processes has been recognized. The boundary layer flow over a horizontally and vertically slender (thin) needle with irregular size has created interest among researchers due to its infinite use in biomimetics field, biomedical, aerodynamics, and engineering purposes. The intention here is to study the two-dimensional steady hybrid nanofluid over a slender horizontal needle with water as its base, copper (cu), and alumina oxide (Al2O3) as the combination of nanoparticles in the presence of hydromagnetic and slip effect in the flow. A partial differential equation (PDEs) was set to govern the fluid flow model. Through similarity requirement, the PDE is transformed into ordinary differential equations (ODEs) and analysed using bvp4c in MATLAB 2019a. The influence of hydromagnetic (MHD), M, slip effect, sigma, needle thickness, c, and nanoparticle volume fraction, phi on velocity, f' (eta), temperature, theta(eta), skin friction coefficient, C-f and local Nusselt number, Nu(x) are clearly presented. Throughout the study, it shows that duality of solutions presents in a certain range when epsilon(c) < epsilon <= = 1 and unique solution at epsilon > -1. The range on the dual solutions broadens as sigma increased, which contradicts with M, sigma and c that decreases as both of these values increased. Hence, a stability analysis is imposed. The reduction on skin friction between the needle and fluid can been seen when values of M, sigma and c increased. Meanwhile, it also noted that the heat transfer rate on the needle surface increased drastically when sigma is increased while opposite trait is found for M and c. hybrid nanofluid possesses better results in increasing the C-f and heat transfer rate compared to nanofluid.

Automated summary

The study shows the existence of dual solutions within a specific range, with a unique solution in another range. The range of dual solutions decreases as hydromagnetic, slip effect, and needle size increase. Reduction in skin friction between the needle and fluid is observed when hydromagnetic, slip effect, and needle size increase.