Study of Jeffrey Fluid Motion Through Irregular Porous Circular Microchannel Under the Implications of Electromagnetohydrodynamic and Surface Charge-Dependent Slip

Source abstract

This work analyzes the non-Newtonian electromagnetohydrodynamic (EMHD) flow in an irregular circular porous microchannel while incorporating the consequences of surface charge-dependent slip boundary conditions. The Jeffrey fluid is employed to examine the non-Newtonian behavior, such as elasticity. The boundary walls of the channel are considered in the form of periodic sinusoidal wave function. The mathematical formulation is developed using the momentum equation, modified Darcy’s law, the continuity equation, and Ohm’s law. The perturbation method is used to derive the solutions up to second-order approximation. The analytical expression for the velocity field and volumetric flow rate are explicitly presented. At the zeroth-order, a nonhomogeneous partial differential equation is solved, and the solutions are presented in terms of Bessel functions. The first-order problem defined by a homogeneous partial differential equation is solved using the method of separation of variables. At the second-order, a homogeneous partial differential equation is obtained, and the solution form is prescribed by the boundary conditions, consisting of a radially varying mean component and a second-harmonic angular contribution. Two- and three-dimensional plots are used to analyze and discuss the impacts of key parameters, namely the Reynolds, Darcy, and Hartmann numbers, channel corrugation amplitude and wave number, surface charge density, and the relaxation and retardation times on the velocity field and flow rate. It is found that elastic memory causes a proportional growth between the flow rate and the relaxation time, emphasizing the consequences of surface charge application in conjunction with corrugations. Conversely, maintaining a short retardation time mitigates changes in wave amplitude and surface charge. While prolonging it lessens the flow rate and diminishes corrugations and surface charge effects. The Darcy number dampens the velocity and the flow rate, while its enhancement reduces the impact of surface charge density and corrugations amplitude. For high Reynolds number, a ring phenomenon emerges which is attenuated by increased Darcy number, preventing the formation of trapped boluses close to the border. Ignoring surface charge amplifies the flow rate while its consideration diminishes the latter with reinforced impacts of surface charge and wall corrugations at higher Reynolds number.