Parametric investigation of the Nernst–Planck model and Maxwell’s equations for a viscous fluid between squeezing plates

Abstract

The Poisson-Boltzmann equation is derived from the assumption of thermodynamic equilibrium where the ionic distribution is not affected by fluid flow. Although this is a reasonable assumption for steady electroosmotic flow through straight micro-channels, there are some important cases where convective transport of ions has nontrivial effects. In these cases, it is necessary to adopt the Nernst-Planck equation instead of the Poisson-Boltzmann equation to model the internal electric field. The modeled system of equations is transformed by similarity transformation to derive the equations of flow field, electric potential, electrokinetic force, entropy generation, and energy equation. The Parametric Continuation Method (PCM) is used to solve the system of ordinary differential equations. It is concluded that decrease in the mass diffusion decreases the anion distribution from lower to upper plate. The Batchelor number decreases the strength of magnetic field. Entropy generation and the Bejan number are maximum near the two plates because of the maximum disorderness due to plate movements and have minimum value in the fluid's center. Also the Eckert number increases viscous heating, which causes the entropy production in the vicinity of the two plates to increase.

Steady Squeezing Flow of Magnetohydrodynamics Hybrid Nanofluid Flow Comprising Carbon Nanotube-Ferrous Oxide/Water with Suction/Injection Effect

“…Table 1 illustrates the thermophysical properties of water and nanomaterial. Table 2 shows the comparison of the proposed model solution with the solution in [35]. A closed agreement has been found in the two results for different values of S and Φ.…”

“…Furthermore, the top plate is moving toward the bottom plate with velocity v = dh dt . Khan et al [35] in their work used both discs are perfectly conducted. In the present problem, electrical forces are ignored as they are much smaller than magnetic forces.…”

“…We have formulated hybrid nanofluid by dissolving the volume fraction of CNT (Φ 2 = 0.5) into the originally formulated ferrofluid (Fe 3 O 4 /H 2 O). The mathematical formulation of the aforementioned hybrid nanofluids by continuity, momentum, magnetic field, and energy conservation equations are as follows [35].…”

Numerical Analysis of Unsteady Hybrid Nanofluid Flow Comprising CNTs-Ferrousoxide/Water with Variable Magnetic Field

“…The purpose of the analysis was to examine the general quality of local thermal non-equilibrium (LTNE) and focus on the impact of nanomaterials (AA7075 and Cu) in the conventional fluids (methanol and NaAlg) using the Tiwari-Das model. They have investigated the heat transfer properties of nanofluids numerically from an engineering point of view at a stretching plate in the porous medium in [21,22]. Song et al [23] analyzed the effect of Marangoni convection, thermal radiation, Soret and Dufour effects, viscous dissipation, nonlinear heat sink/source, and activation energy on MHD nanofluids motion produced by revolving the disk.…”

Numerical Investigation of a Squeezing Flow Between Concentric Cylinders Under the Variable Magnetic Field of Intensity

“…Umavathi et al [25] analyzed the influence of magnetic nanomaterials in incrementing the transport of heat in a tribological system under connective type heating boundary conditions (Robin). Rehan et al [26][27][28] studied the augmented viscosity pattren and heat transfer behaviour of a transient two-dimensional non-compresssible squeezing flow of ion-nano-fluid between two long parallel concentric cylinders. To study heat transfer capacity, three different kinds of nanocomponents like Titanium oxide, Copper and Aluminum of volume fraction from 0.1 to 0.7 nm are suspended into ionic fluid in turns.…”