Analysis of a Two-Phase MHD Free Convection Generalized Water–Ethylene Glycol (50 : 50) Dusty Brinkman-Type Nanofluid Pass through Microchannel

The water–ethylene glycol (50 : 50) nanofluid has applications in the manufacture of polyester as a raw agent, air conditioning systems, antifreeze formulation, dehydrating agents in the gas industry, a precursor in the plastic industry, and convective heat transfer. These developments in nanotechnology and nanoscience have caught the interest of several researchers. Because it keeps machines and engines cool by reducing friction between their different parts, grease is a vital part of many machinery and engines. Also, due to the extensive use of fractional derivatives, this work seeks to evaluate the combined impacts of free convection flow and heat transfer, magnetic field, and Brinkman-type water–ethylene glycol (50 : 50) dusty nanofluid among microchannel. The flow that the buoyant force provides helps to carry heat naturally via convection. While the left plate moves at a consistent velocity and the right plate stays stationary, the fluid is also evenly dispersed with all dust particles that have a spherical form. Partial differential equations (PDE) are used to present the mathematical modeling. The resultant PDEs are generalized by utilizing the Caputo–Fabrizio fractional derivative. The problem’s closed-form solution is produced by combining a Laplace transformation with a finite sine Fourier transformation. It has also been studied that temperature, Brinkman nanofluid, and dust particle velocity relate to a variety of other factors, such as the magnetic parameter, Grashof number, dusty fluid parameter, and volume friction parameter. The graphical outcomes for the dusty fluid, Brinkman nanofluid, and temperature profiles are plotted using Mathcad-15. The Brinkman nanofluid and dusty fluid behave similarly for a variety of embedded factors. It is found that compared to the traditional one, the fractional dusty nanofluid model displays more realistic characteristics. The addition of nanoparticles in water–ethylene glycol (50 : 50) dusty nanofluid enhances the rate of heat transfer up to 41.04478% by increasing their volume fractional.