Abstract
This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.
Highlights
The research on non-Newtonian fluids is very important due to its extensive applications in engineering, industry and biomechanics
It is noteworthy that we introduce the fractional derivative to the energy equation by the viscous dissipation, which indicates that the influence of fractional derivative on the flow is more significant than heat transfer
This paper presents a study on numerical analysis of the incompressible fractional Maxwell fluid due to a power function accelerating plate with the first order slip
Summary
The research on non-Newtonian fluids is very important due to its extensive applications in engineering, industry and biomechanics. Hayat[10,11] presented the radiation effects on MHD flow of Maxwell fluid. Zhao[13] proposed a research on unsteady boundary layer natural convection, heat and mass transfer of Maxwell fluid with fractional derivative. Zhang[14] presented a study on fractional Burgers’ fluid with the effects of the second order slip and viscous dissipation. Yan[15] studied the oscillating flow in rolling motion with the fractional derivative Maxwell model, and Tripathi[16] simulated the peristaltic transport of fractional Maxwell fluids. Shen[26] considered an investigation for radiation heat transfer of MHD viscoelastic fluid with fractional derivative, and Rachid[27] discussed the effects of various parameters on the heat transfer a fractional Maxwell fluid. The studies on fractional viscoelastic fluids are mainly focused on the first boundary conditions of heat transfer. The effects of various physical parameters on the velocity and temperature are discussed through graphical illustrations
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