Impact of fractional magnetohydrodynamic and hall current on ree-eyring fluid flow by using radial basis function method

Abstract

In the present work, an analysis has been arranged to study the Magnetohydrodynamic of Ree-Eyring fluid with the effect of Hall current between two parallel plates. Initially, both plates are at rest then suddenly plates are bought to steady velocities v0 and v1 at y=0 and y=d respectively. The governing problem is converted to the fractional partial differential equation and then numerically solved by using the radial basis functions collocation scheme. The Crank-Nicolson scheme is applied for the discretization of space derivatives. The numerical computation is performed for 0≤α≤1,0≤m≤1,0≤β≤1. The performance of the method is investigated with the help of tabulated results. The obtained results show the efficiency of the method for different parameters. The numerical results are compared for different fractional orders, and it is concluded that decreasing the fractional order increases the velocity which enhances the flow. Results are tabulated for different time levels, and it is concluded that method produces smooth solution for increasing values of T. Time fractional derivatives play a significant role in understanding non-Newtonian fluids and complex flow behaviors. They accurately model resistance forces in fluid flow, particularly in systems with non-standard behavior. This allows for a more detailed analysis of transient phenomena, providing valuable insights into fluid behavior over time. Ultimately, the use of time fractional derivatives enhances our capacity to describe and predict fluid flow in various practical applications such as physiology, biomedicine, and engineering.

Keywords

• Ree-Eyring fluid
• Magnetohydrodynamics
• Hall current
• Radial basis function
• Crank-Nicolson scheme
• Caputo fractional derivative