Narrow Results

This study investigates the interaction between fluid dynamics and electromagnetic fields, a complex problem that has not been extensively studied. The Lorentz force, which arises due to the interaction between magnetic fields and currents in a fluid is considered in this study. This research investigates the effects of a magnetic field, couple stress, and slip velocity on the behavior of a squeeze film (SF) formed between a porous flat and spherical plate. The Stokes equation for couple stress fluids is used to produce a generalized version of the Reynolds equation, which is then used to determine the film pressure. Also, this study considers the impact of a constant magnetic field orthogonal to the plate. The fluid in the porous region is governed by modified Darcy law. The effect of a uniform magnetic field perpendicular to the plate is considered. The bearing characteristics pressure, squeeze film time, and load-carrying capacity are graphically presented. The results revealed that the load-carrying capacity, pressure, and squeeze film time are reduced with a rise in slip and porousness parameters. The slip parameter decreases the values of film pressure, squeeze time, and load-carrying capacity as related to the no-slip case.

In this paper, we are interested in studying the initial value problem for parabolic problem associated with the Caputo–Fabrizio derivative. We deal the problem in two cases: linear inhomogeneous case and nonlinearity source term. For the linear case, we derive the convergence result of the mild solution when the fractional order $\alpha \to 1^{-}$ under some various assumptions on the initial datum. For the nonlinear problem, we show the existence and uniqueness of the mild solution using Banach fixed point theory. We also prove the convergence result of the mild solution when the fractional order $\alpha \to 1^{-}$.