Optimization of response function on hydromagnetic buoyancy-driven rotating flow considering particle diameter and interfacial layer effects: Homotopy and sensitivity analysis

Alumina is one of the modern era and most utilized ceramic materials. One example of an electrical insulating substance is alumina. It has an enhanced temperature, chemical stability and higher thermal conductivity. It is mostly used in medical, industry, household items, military purposes, production of batteries and electrical parts. Therefore, the authors have formulated a mathematical model of the three-dimensional magnetohydrodynamic mixed convective flow of a nanofluid containing Alumina nanoparticles past a stretching surface. Preliminary assumptions bound the nanofluid flow to be rotational, electrically conducting, dissipative, buoyancy driven, thermally heated and convective. An important investigation based on the effects of nanoparticle diameter and nanolayer of the nanofluid makes the novelty of this investigation. The modeled problem is solved with a homotopic approach, which is suitable for the solution of the highly nonlinear differential equations and has quick convergence. The outcomes of the present analysis are shown with the help of Tables and Figures. The outcomes showed that the higher resistive force at the sheet surface caused by the higher solid volume fraction (varies from 1% to 4%), diminishes the primary velocity, while escalates the secondary velocity. Additionally, the greater solid volume fraction (which ranges from 1% to 4%) raises the thermal conductivity of the nanofluid flow, resulting in an increasing conduct in the thermal function. The enhancing nanolayer to base fluid conductivity ratio (which ranges from 1.1 to 65.25), results in an increase in both velocities and thermal functions, gives the nanofluid flow a higher thermal conductivity. Additionally, the local Nusselt number and skin friction increase as a result of the higher thermal conductivity. The primary velocity and temperature are reduced due to the decrease in thermal and momentum boundary layer thicknesses brought on by the rising nanoparticle diameter (which ranges from 1 nm to 50 nm). The rate of heat transfer is significantly achieved at the higher levels of the volume fraction and radiation factor while heat source is at lower level. The friction rate at the surface is dominant at higher level values of magnetic and volume fraction factor and medium level of rotation factor. The transport of heat has highest sentivity at the middle level of thermla radaition and volume fraction of the nanoparticle and low level of heat source, while the highest sensitivity of friction factor is observed at the middle level of thermal rotation and high level nanoparticle volume fraction and magnetic factor.