New fractional approach for CMC and water based hybrid nanofluid with slip boundary layer: Applications of fractal fractional derivative

Abstract

The physical significance of the Fractal fractional derivative, one of the most fascinating and modern analytical techniques, to the thermal flow is described in this paper. Free convection, which is the flow of an erratic, incompressible viscous fluid on a vertically inclined plate, has been considered in this work. Two types of base fluids, namely water and carboxymethyl cellulose, are used in the presence of graphene oxide (GO) and molybdenum disulfide (MoS2) nanoparticles. The flow is subject to slip possessions due to the inclined surface. The non-dimensional leading equations for thermal and momentum, under Boussinseq's approximation, can be solved by employing a Laplace transformation scheme, the fractal fractional derivative, and a more recent and improved definition of a fractional mathematical term. The thermal expressions are modeled using the Laplace transformation. The effect and comparison of various parameters are then visually and quantitatively analyzed after this activity. We, therefore, proposed that a water-based nanofluid's thermal profile and velocity are marginally higher than those of a hybrid nanofluid based on carboxymethyl cellulose. The momentum profile additionally illustrates the dual behavior of the flowing hybrid nanofluid as the fluid parameter of the Brinkman type increases.

Keywords

• Brinkman type fluid
• Sinusoidal conditions
• Laplace transformation
• Slip effects
• Fractal fractional derivatives