Homotopy perturbation and numerical solutions for MHD flow of PTT fluid through a channel embedded in a porous medium

An analysis is made of the steady one dimensional flow and heat transfer of an incompressible viscoelastic electrically conducting fluid (PTT model) in a channel embedded in a saturated porous medium. The pressure driven flow is subjected to a transverse magnetic field of constant magnetic induction (field strength). The heat transfer accounts for the viscous dissipation. The governing equation (a non-linear ordinary differential equation) is solved analytically (Homotopy Perturbation Method) and numerically (Runge-Kutta method with shooting technique) providing the consistency of the result. The role of Deborah number substantiates both Newtonian and non-Newtonian aspects of the flow model. The inclusion of two body forces affects rheological property of the flow model considered. Temperature distribution in the boundary layer is shown when the channel surfaces are held at constant temperatures. A novel result of the analysis is that the contribution of viscous dissipation is found to be negligible as the variation of temperature is almost linear across the flow field in the present PTT fluid model indicating preservation of thermal energy loss.

Entropy generation for MHD natural convection in enclosure with a micropolar fluid saturated porous medium with Al2O3Cu water hybrid nanofluid

This contribution gives a numerical investigation of buoyancy-driven flow of natural convection heat transfer and entropy generation of non-Newtonian hybrid nanofluid (Al2O3-Cu) within an enclosure square porous cavity. Hybrid nanofluids represent a novel type of enhanced active fluids. During the current theoretical investigation, an actual available empirical data for both thermal conductivity and dynamic viscosity of hybrid nanofluids are applied directly. Numerical simulation have been implemented for solid nanoparticles, the volumetric concentration of which varies from 0.0% (i.e., pure fluid) to 0.1% of hybrid nanofluids. Heat and sink sources are situated on a part of the left and right sides of the cavity with length B, while the upper and bottom horizontal sides are kept adiabatic. The stated partial differential equations describing the flow are mutated to a dimensionless formulas, then solved numerically via the help of an implicit finite difference approach. The acquired computations are given in terms of streamlines, isotherms, isomicrorotations, isoconcentraions, local Began number, total entropy, local and mean Nusselt numbers. The data illustrates that variations of ratio of the average Nusselt number to the averageNusselt of pure fluid Num+ is a decreasing function of Ha and φ, while e+ is an increasing function of Ha and φ parameters of hybrid nanofluid.

Dual solution for double-diffusive mixed convection opposing flow through a vertical cylinder saturated in a Darcy porous media containing gyrotactic microorganisms

The steady mixed convection flow towards an isothermal permeable vertical cylinder nested in a fluid-saturated porous medium is studied. The Darcy model is applied to observe bioconvection through porous media. The suspension of gyrotactic microorganisms is considered for various applications in bioconvection. Appropriate similarity variables are opted to attain the dimensionless form of governing equations. The resulting momentum, energy, concentration, and motile microorganism density equations are then solved numerically. The resulting dual solutions are graphically visualized and physically analyzed. The results indicate that depending on the systems' parameters, dual solutions exist in opposing flow beyond a critical point where both solutions are connected. Our results were also compared with existing literature.

Effect of Local Thermal Non-Equilibrium On the Stability of the Flow in a Vertical Channel Filled with Nanofluid Saturated Porous Medium

The stability of nanofluid flow in a vertical channel packed with a porous medium is examined for the local thermal non-equilibrium state of the fluid, particle and solid-matrix phases. The effects of Brownian motion along with thermophoresis are incorporated in the nanofluid model. The Darcy-Brinkman model for the flow in a porous medium and three-field model, each representing the fluid, particle and solid-matrix phases separately, for temperature is used. A normal mode analysis is used to obtain the eigenvalue problem for the perturbed state, which is then solved using the Chebyshev spectral collocation technique. The critical Rayleigh number and corresponding wavenumber are presented graphically for the effect of different local thermal non-equilibrium parameters. It is noticed that the influence of LTNE parameters on the convective instability is significant.

Modeling and Parametric Simulation of Microplastic Transport in Groundwater Environments

Efforts to reduce the toxic effects of microplastics (MPs) on the environment have increased globally in recent years. However, the existing models used for the simulation of contaminant transport in groundwater are meant for dissolved substances, which is not suitable for studying MPs. Therefore, in this study, the transport of MPs in a saturated porous medium was modeled by establishing governing equations. Simulations were performed using the finite element method to examine the effects of the parameters of the governing equations on the transport of MPs. The results suggest that it is necessary to reduce the diffusivity of MPs and increase the water flow velocity, porosity, and first-order attachment coefficient to effectively contain this environmental hazard. From the simulation results, it can be derived that a combination of low diffusivity, fast water flow velocity, and high soil porosity may reduce the amount of MPs that are leaked into groundwater environments. The modeling and simulations performed in this study provide a clear understanding of the transport phenomena of MPs with applications in combating water pollution.