Porous effects on the fractional modeling of magnetohydrodynamic pulsatile flow: an analytic study via strong kernels

An accurate measurement of pulsatile flow is frequently encountered in exhaust and intake manifolds of internal combustion and Stirling engines. Keeping this view, a mathematical modeling of magnetohydrodynamic pulsatile flow is proposed on the basis of modern fractional differentiations (Atangana-Baleanu and Caputo-Fabrizio fractional operators) in the presence of porosity. The modeling of magnetohydrodynamic pulsatile flow is based on non-integer-order partial differential equation of velocity field. The solvability of fractional differential equation of velocity field is tackled via Hankel and Laplace transform techniques. The proposed fractional modeling is verified from general fractional solutions of velocity field of pulsatile flow on the imposed initial and boundary conditions for sinusoidal oscillation. The general fractional solutions of velocity field of pulsatile flow have been retrieved for porous and non-porous velocity field and magnetized and non- magnetized velocity field as well. Finally, our results suggest that time-dependent pulsatile flow of velocity field needs accurate and reproducible generation of pulsatile flow as a function of time.