Analysis and numerical simulation of fractal-fractional order non-linear couple stress nanofluid with cadmium telluride nanoparticles

Abstract

It is generally considered that fractal-fractional order derivative operators are highly sophisticated mathematical tools that can be applied in a variety of physics and engineering situations to obtain real solutions. By using fractal-fractional derivatives, we can simultaneously investigate fractional order and fractal dimension. Due to extensive applications of fractal-fractional derivatives, in the present article fractal-fractional order model of non-linear Couple stress nanofluid has been analyzed. The homogenous mixture of base fluid and nanoparticles has been formed by the uniform dispersion of cadmium telluride nanoparticles in mineral transformer oil. Primarily, the classical mathematical model has been formulated via relative constitutive equations and then generalized by using fractal-fractional derivative operator. This model has been numerically solved using Crank-Nicolson technique. Using numerical solutions, various graphs are plotted to analyze how physical parameters alter Couple stress nanofluid rheology. As can be seen from the graphical study, couple stress slows down fluid velocity. Adding cadmium telluride nanoparticles to transformer oil increased its efficacy by 15.27%.

Keywords

• Fractal-fractional derivative
• Couple stress fluid
• Cadmium telluride nanoparticles
• Mineral transformer oil
• Crank-Nicolson scheme