Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic (MHD), incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted

Estimation of Mass Diffusion Relaxation Time in the Binary Mixture between Two-Phase Bubbly Flow

The mass diffusion relaxation time constant is derived on the basis of relaxed model with unequal phase-mass diffusion for a binary mixture. The mass diffusion and state equations are solved analytically for two finite boundaries. The relaxation time is affected by void fraction and vaporized mass diffusion fraction values. Mass diffusion relaxation time obtained in this work has a larger values than that obtained by Mohammadein [9] and Moby Dick experiment [3]; which satisfied for some values of the physical parameters

The Growth of Vapour Bubble between two-Phase Peristaltic Bubbly Flow inside a Vertical Cylindrical Tube

The behavior of vapour bubble in superheated liquid in a vertical cylindrical tube between two-phase flow densities is discussed under the effect of peristaltic motion of long wavelength and low Reynolds number. The mathematical model is formulated by mass, momentum, and heat equations. The problem solved analytically to estimate the growth of vapour bubbles, temperature and velocity distributions. The growth of vapour bubbles, temperature and velocity distribution proportional with the amplitude ratio, Grashof number, heat source parameter, volume rate, and inversely with density fraction. The present results of bubble growth performed lower values than that obtained by Mohammadein model (2001)

Growth of a Vapour Bubble in a Superheated Liquid of Variable Surface Tension and Viscosity Between Two-phase Flow

The growth of a vapour bubble in a superheated liquid of variable surface tension and viscosity between two finite boundaries is introduced. The problem is solved analytically using the modified method of Plesset and Zwick method. The pressure difference is described in terms of temperature difference and initial pressure difference. The surface tension, viscosity, and initial and final time of bubble growth are derived in terms of some physical parameters. The growth of bubble radius is proportional to the thermal diffusivity, the initial pressure difference and its coefficient. On contrary the growth is inversely proportional to the initial void fraction and the density ratio. Moreover, better agreements with some experimental data are achieved rather than some of previous theoretical efforts

Derivation of Thermal Relaxation Time between Two-Phase Flow under the Effect of Heating Sink

In the present paper, the thermal relaxation time of a mixture surrounding a growing vapour bubbles between two-phase temperatures under the effect of heating sink is investigated. The mathematical model obtained by Mohammadein [6] is extended and solved analytically by using similarity parameters method; which used by Mohammadein [5] between two finite boundaries. Under the initial and final boundaries of growing vapour bubbles, thermal relaxation time is derived in terms of void fraction and affected by initial superheating and thermal diffusivity. Thermal relaxation time under the effect of heating sink performs a lower values than the previous pressure and thermal relaxation times obtained by authors [4,5]. Thermal relaxation time performs a good agreement with Moby Dick experiment [2]

The Analytical and Simplest Resolution of Linear Navier-Stokes Equations

The nonlinear Navier-Stokes equations are converted to the linear diffusion equations by Mohammadein (Appl. Math. & Info. Sci. Lett. (2020). The analytical solutions of linear Navier-Stokes equations only are obtained. In this paper, the pressure gradient is redefined by using Bernoulli concept. The peristaltic incompressible viscous Newtonian fluid flow in a horizontal tube is described by Navier-Stokes equations. The stream function described the flow patterns (laminar, transit and turbulent) for different values of wave lengths. The linear and nonlinear Navier-Stokes equations are satisfied by the obtained analytical solutions based on pressure gradient definition

The Simplest Analytical Solution of Navier-Stokes Equations

The nonlinear convective acceleration term in fluids performs a strong obstacle against the analytical solutions of Navier-Stokes equations up to date. The obtained solutions are valid for long wave lengths only. In this paper, the nonlinear Navier-Stokes equations are converted to the linear diffusion equations based on the concept of linear velocity operator. The simplest analytical solutions of linear Navier-Stokes equations are obtained by using Picard method for a first time for different values of wave lengths and Reynolds number. As an application, the peristaltic incompressible viscous Newtonian fluid flow in a horizontal tube is described by the continuity and linear Navier-Stokes equations. The analytical solutions are obtained in terms of stream function and fluid velocity components. Moreover, the stream function is plotted in a laminar, transit and turbulent flows for different values of parameter δ

Concentration Distribution Around the Gas Bubbles in a Bio Tissue with Acceleration Convection under the Effect of Injection Process

The concentration distribution around growing nitrogen gas bubble in the blood and other bio tissues of divers who ascend to surface too quickly is obtained by Mohammadein and Mohamed model (2010)[3] for variant and constant ambient pressure through the decompression process. In this paper, the growing of gas bubbles and concentration distribution under the effect of injection process with convective acceleration are studied as a modification of Mohammadein and Mohamed model (zero injection)[3]. The growth of gas bubble is affected ascent rate, tissue diffusivity, initial concentration difference, surface tension and void fraction. Mohammadein and Mohamed model (2010) is obtained as a special case from the present model. Results showed that the injection process affects the systemic blood circulation and acceleration the growth of gas bubbles the bio tissues. The study warns the divers to take any kind of injection during the dive process to avoid the incidence of decompression sickness(DCS)

Investigation of the Incompressible Viscous Newtonian Fluids Flow using Three-Dimensions Linear Navier-Stokes Equations

In this paper, the unsteady and nonlinear Navier-Stokes equations in three Cartesian coordinates are converted to the linear diffusion equations based on the concept of linear velocity operator (▁(v ̂ ) . ▁∇). The stream function Ψ(x, y, z, t) represents the analytical solutions of dimensional continuity and linear Navier-Stokes equations. As a physical application, the viscous Newtonian fluid flow in a 3D peristaltic horizontal tube is described by non-dimensional continuity and linear Navier-Stokess equations. The analytical solution in terms of stream function is obtained for different values of time, wavelengths, and Reynolds numbers for a first time. Moreover, the streamlines change from laminar, to transit, and then to turbulent flow with increasing time interval. Authors introduced the 3D analytical solutions of linear and nonlinear Navier-Stokes equations as a millennium problem

Peristaltic Flow for A Mixture of Blood and Gas Bubbles in the Vertical Inferior Mesenteric Vein

In this paper, the viscous blood concentration and gas bubbles flow in the peristaltic vertical inferior mesenteric vein (IMV) are studied. The mass, concentration, and Navier-Stokes equations introduce the mathematical simulation of the current problem in the case of long wavelength and low Reynolds number with an analytical solution. The results introduced that the gradient pressure of a mixture of blood flow with gas bubbles performs larger values than that of blood without gas bubbles. Moreover, the blood concentration, velocity of blood and gas bubbles are very sensitive to the small change in blood density ratio, amplitude ratio, and modified Grashof number