Magnetic Field Effect on Heat and Momentum of Fractional Maxwell Nanofluid within a Channel by Power Law Kernel Using Finite Difference Method

Abstract

The mathematical model of physical problems interprets physical phenomena closely. This research work is focused on numerical solution of a nonlinear mathematical model of fractional Maxwell nanofluid with the finite difference element method. Addition of nanoparticles in base fluids such as water, sodium alginate, kerosene oil, and engine oil is observed, and velocity profile and heat transfer energy profile of solutions are investigated. The finite difference method involving the discretization of time and distance parameters is applied for numerical results by using the Caputo time fractional operator. These results are plotted against different physical parameters under the effects of magnetic field. These results depicts that a slight decrease occurs for velocity for a high value of Reynolds number, while a small value of $\text{Re}$ provides more dominant effects on velocity and temperature profile. It is observed that fractional parameters $\alpha \text{\hspace{0.17em}and\hspace{0.17em}}\beta$ show inverse behavior against $u\left(y,t\right)$ and $\theta \left(y,t\right).$ An increase in volumetric fraction of nanoparticles in base fluids decreases the temperature profile of fractional Maxwell nanofluids. Using mathematical software of MAPLE, codes are developed and executed to obtain these results.