Porous Regime Research Articles

Mathematical modeling of cross diffusion effect on bioconvective Casson nanofluid over multi slips porous stretching surface

Purpose and significance Cross diffusion is a phenomenon that arises when various species are diffusing at the same time in a mixture. These are crucial in many industrial, environmental, and material processes for analyzing and forecasting temperature distribution, concentration profiles, and overall system behavior. Thus, cross-diffusion effects on Casson nanofluid across nonlinear stretching sheet are considered. In addition, the influence of magnetohydrodynamics (MHD) with multi slip boundary conditions implanted in porous regime is examined. The novelty of this study is the complex interactions and phenomenon of non-Newtonian Casson nanofluid with bioconvective multi slips conditions, which has an essential contribution in interdisciplinary nature. Methodology By employing similarity transformation, governing equations undergo a transformation into ordinary differential equations (ODEs), and solved using 5th-order Runge–Kutta–Fehlberg method via shooting technique. Graphical representations are utilized to depict effects of various parameters, accompanied by detailed explanations. Outcome The results obtained affirm that nonlinear stretching parameter leads to a deceleration of velocity profile, while temperature profile is observed to enhance with Eckert and Dufour numbers. Additionally, enhancement in the concentration profile occurred due to the Soret number. The comparison of current findings with prior research revealed great accuracy. Meanwhile, a graphical representation of skin friction, Nusselt number, and Sherwood number are presented. This investigation demonstrates that skin friction decreases by 10% with an improvement of M from 0.4 to 1.6. Furthermore, it is identified that there is a 31% rise in Sherwood number when Lewis number is accelerated from 1.0 to 1.5.

Magnetohydrodynamic bioconvective flow past an elongated surface with convective heat transport, and velocity slip in a non‐Darcian porous regime

AbstractIn recent times, bioconvection has numerous uses, like, biological and biotechnological problems. The present study describes the magnetic bioconvective Buongiorno's flow model with microorganisms in a stretchable area with convective heat transfer and second‐order velocity slip in a non‐Darcian porous regime. Here, the influence of variable viscosity, viscous dissipation, Joule heating, and heat source/sink are considered in the occurrence of higher‐order chemical reactions. Employing proper similarity transformations leading equations are transformed to dimension‐free form. The transformed equations are solved via MATLAB bvp4c problem solver. This study's main objective is to graphically analyze the effects of different pertinent factors on the density of motile microorganisms, velocity, concentration, temperature, number of motile microorganisms' density, skin friction, mass transport rate, and heat transport rate. The main findings drawn from this study are viscosity and magnetic parameter lowers the fluid velocity. Biot number increases fluid temperature, but reduces heat transport rates and skin friction. Schmidt and Eckert numbers reduce the fluid concentration. A rise of 0.3 in bioconvective Rayleigh number and 0.2 in buoyancy ratio number causes a percentage drop in velocities of 8.79% and 3.91% (approximately), respectively, in the neighborhood of the sheet. Furthermore, the increase in Peclet number by 0.2 lowers the density number of microorganisms by 28%. Additionally, the profile of motile microorganisms is improved by thermophoresis impact, while it is diminished by chemical reaction.

Effect of magnetic field on viscous flow through porous wavy channel using boundary element method

AbstractThe study aims to investigate the effect of uniform inclined magnetic field on two‐dimensional flow of a steady, viscous incompressible fluid at low Reynolds number through a porous wavy channel. We consider a channel having sinusoidal walls filled with a fully saturated porous medium. The porous regime is assumed to be homogenous and isotropic. The viscous flow through a porous regime is governed by Brinkman equation, where the viscous forces are dominant. This allows us to assume the no‐slip boundary conditions at the walls of the wavy channel. Boundary element method (BEM) based on non‐primitive variables namely, stream function‐vorticity variables is used to solve the Brinkman equation. Further, we consider a very small magnetic Reynolds number to eliminate the magnetic‐induced equation. We analyzed that an increase in Hartman number, porosity, and reduction in inclination angle of magnetic field, wave amplitude, and Darcy number led to a reduction in horizontal velocity, whereas an increase in Hartman number, porosity, wave amplitude, and decrease in Darcy number and angle of inclination of magnetic field led to an increase in vertical velocity. Moreover, the flow reversal phenomena occur in the vicinity of the crest regime of the porous wavy channel for high wave amplitude and low Hartman number. The proposed investigation has widespread applications, such as drug delivery systems to target the drug precisely, magneto‐hydrodynamic pumps to regulate the blood flow in artificial hearts to reduce the risk of blood clotting, and so forth.

Entropy analysis on thermophoretic magnetohydrodynamic Couette flow over a deformable porous channel with temperature‐dependent viscosity and thermal conductivity

AbstractIn this study, we have investigated magnetohydrodynamic Couette flow across a deformable porous regime with entropy generation having equal suction and injection velocities. The aim of this work is to analyze the novel impact of thermophoresis deposition, activation energy, and magnetic effect by considering viscosity and thermal conductivity as dependent on temperature in a deformable porous regime. The dimensional equations are turned into nonlinear ordinary differential equations (ODEs) through proper similarity variables. To solve these ODEs, we utilized the MATLAB bvp4c approach. Graphs are used to study the behavior of many physical parameters such as skin friction, Bejan number, velocity, displacement, entropy generation, concentration, and temperature. It is found that the viscosity parameter reduces the solid displacement, whereas it enhances the fluid concentration. Due to the impact of suction/injection and drag parameters, fluid velocity becomes reduced. The thermal conductivity parameter raises entropy generation and temperature, but it decays the Bejan number. The volume fraction parameter plays an interesting behavior in skin friction. Moreover, the current work is compared with prior research work while neglecting the newly introduced effects, and the results remain consistent.

DARCY FORCHHEIMER FLOW OF WILLIAMSON FLUID PAST A STRETCHING SHEET WITH VARIABLE THERMAL CONDUCTIVITY

The primary objective of this experiment is to examine the motion of molecules of Williamson micropolar fluid moving along a stretchable sheet set in a porous regime with microrotation in presence of magnetic field. The coupled partial differential equations are converted into a system of ODEs using appropriate similarity transformations. To solve the system of ODEs, BVP4C solver has been employed with relative tolerance of . To make sure the present study is stable and convergent, all the outcomes are compared to the earlier findings. The impression of various parameters on velocity, temperature and microrotation profile are illustrated with the help of graph. The graph of entropy generation and skin friction and Nusselt number is also plotted against various governing parameters. Through this investigation it is found that Nusselt number can be increases by regulating the porous parameter and the viscosity of the Williamson fluid. The drag at the surface can be minimized by increasing the strength of magnetic field and Williamson fluid parameter. The implication of this study can be found in industrial field where entropy of the system plays an important role for better performance and stability.

Magnetohydrodynamic Couette flow of alumina–water nanofluid over a deformable porous channel under uniform transverse magnetic field with entropy optimisation

The present study is concerned about magnetohydrodynamic Couette flow of nanofluid with entropy analysis in the presence of injection and suction over a deformable permeable channel containing nanoparticles of alumina (Al2O3). The influences of non-linear thermal radiation and activation energy are considered. The leading partial differential equations are simplified to non-linear ordinary differential equations by applying appropriate similarity transformation. The simplified governing equations are solved by utilising MATLAB bvp4c finite difference technique. Here, we observed the behaviour of various physical parameters on solid displacement, temperature, velocity, concentration, entropy generation, Bejan number and skin friction. Observation reflects that drag parameter enhances solid displacement, while reduces fluid velocity, and a significant behaviour is seen in skin friction. Radiation parameter and chemical reaction parameter diminish the fluid temperature and concentration, respectively. Moreover, volume fraction parameter reflects some significant behaviour for entropy generation number and Bejan number. Rate of heat transfer enhances due to the raising of radiation parameter. Fluid flow through a deformable porous regime established by biological applications such as study on articular cartilage, artery walls, skin, soft tissue and so on.

Yield Stress Impact on Magnetohydrodynamic Jeffery Hybrid Nanofluid Flow Over a Moving Porous Surface: Buongiorno’s Model

The main goal of the present study is to explore the flow of Jeffrey hybrid nanofluid crossing through a moving porous surface with the existance of magnetic field, heat sink/source, yield stress and chemical reaction impact. Nusselt number is characterized by the process of thermal radiation. The partial equations are governed during the moved coordinate’s porous regime that is depicting the flow for Buongiorno’s model. Employing similarity transformations, the obtained equations were turned into non-linear ordinary differential equations. The controlled equations were solved by RKF45 via shooting technique. The focus is in examining physical characteristics such as heat flux at the wall, temperature distribution, velocity of flow, and surface friction for a variety of related parameters. The analysis explained that higher permeability and parameters of yield stress, generation of heat and magnetic field enhance distribution of temperature and slow down the heat transfer. The mass transport is upsurged with increasing chemical reaction and heat source. The model is prepared as an application in processes of thermal engineering.

Micropolar Hydromagnetic Fluid Over a Vertical Surface in Darcian Regime: An Analytical Approach

In the present paper, the researcher investigates the mutual impact of radiative heat and mass exchange on hydromagnetic micropolar fluid moving along an infinite vertical surface in a porous regime. The goal of the research is to investigate the impact of convective temperature and mass flow on hydromagnetic motion of micropolar fluid across a vertical plate ingrained in a porous regime. The conservation equations with appropriate boundary conditions are resolved analytically by assuming a convergent series solution and thus obtained the analytical solutions for velocity, angular velocity (microrotation), temperature and molar-concentration. The novelty of the current work is that it takes heat transfer into account while considering for the impacts of chemical reaction in a micropolar fluid flow of reactive diffusing species. The influence of different physical variables on temperature, molar-concentration, velocity and angular velocity of the fluid molecules have been presented graphically for dual solutions. It is seen that the micropolar parameter and porosity of the medium play a significant behaviour over the momentum and thermal boundary layers. This investigation may involve with various disciplines of chemical engineering, bio-mechanics and medical sciences. The outcomes of the present study have significant applications in MHD generators and geothermal resource extraction.

THE CONVECTIVE FLOW OF MAXWELL FLUID DRIVEN BY TWO ROTATING AND SPINNING DISKS

The present work addresses the axisymmetric flow of Maxwell fluid between two stretchable and rotating disks with porous regime. The influence of velocity slip and convective heat transfer are considered to govern the flow. The energy equation is modeled using Cattaneo-Christov heat flux model. The resulting mass, momentum and energy PDE’s are converted to ODE’s by using the Von Karman similarity transformations. Successive linearization method is implemented for numerical solution. The tangential velocity of the fluid increases with the rotating speed of the disks. The enhancement in the convective heat transfer of lower disc results in the rise of temperature profiles whereas temperature falls with the rise in Biot number of the upper disk.

Gyrotactic microbes’ movement in a magneto-nano-polymer induced by a stretchable cylindrical surface set in a DF porous medium subject to non-linear radiation and Arrhenius kinetics

ABSTRACT Because of its numerous uses in biotechnology, bioengineering, biosensors, and bioinformatics, bioconvection involving microbes and nanoparticles has attracted interest in academic circles. In this study, thermal bio-convection involving swimming microbes over a stretching cylindrical surface with wall slip embedded in a porous regime will be numerically simulated and mathematically represented by the cumulative consequences of an inclination magnetic field, non-linear heat radiation, Brownian motion, thermophoresis, Arrhenius kinetics, and stratification. The study employs the Sutterby fluid model to characterize the rheological behaviour of nano-polymeric suspension and uses the Darcy–Forchheimer (DF) model to account for porous media impedance in the transport equations. The study also employs similarity transformations to convert the set of non-linear PDFs into a collection of paired ODEs. These converted ODEs are subsequently solved by employing the numerical integration approach Runge–Kutta–Fehlberg (RKF-45) and a shooting algorithm. The effects of key physical elements on transport profiles are demonstrated using tables and figures. The simulated findings showed that nanoparticle concentration dramatically improved with growing the chemical reaction and activation energy parameters. However, it can be acknowledged that increasing the Darcy number reduces the velocity components while increasing the Forchheimer number has the opposite impact.

Regression analysis and features of negative activation energy for MHD nanofluid flow model: A comparative study

This article elucidates the impact of activation energy on magnetohydrodynamic (MHD) stagnation point nanofluid flow over a slippery surface in a porous regime with thermophoretic and Brownian diffusions. Negative activation energy is scarce in practice, but the impact of negative activation energy could not be neglected as it is noticed in chemical processes. The rate of some Arrhenius-compliant reactions is retarded by increasing the temperature and is therefore associated with negative activation energies, such as exothermic binding of urea or water. In some processes, the temperature dependence of the pressure-induced unfolding and the urea-induced unfolding of proteins at ambient pressure give negative activation energies. The present mathematical model is solved with successive linearization method (a spectral technique). A comparison of results is made for negative and positive values of activation energy. Apart from it, the quadratic multiple regression model is discussed briefly and explained with bar diagrams. It is observed that with rise in unsteadiness parameter from 0 to 1 (taking positive activation energy), skin friction and Sherwood number are increased by 9.36% and 19% respectively, and Nusselt number is decreased by 26%. However, for negative activation energy, 9.36% and 112% enhancement is observed in skin friction and Sherwood number, respectively.

Free convective oscillatory flow due to inclined perpendicular shield subject to the thermos-diffusion and suction effects

An unsteady free convective flow of an electrically conducting viscous fluid due to accelerated inestimable inclined perpendicular shield has been presented in presence of heat and mass transfer phenomenon. The applications of thermos-diffusion and heat source are also incorporated. The chemical reaction consequences are considered in the concentration equation. The compelling meadow is considered to be homogeneous and practical perpendicular to the flow direction. Further, the oscillatory suction effects are also taken into observations for porous regime. The closed form expressions are resulted with implementation of perturbation approach. The non-dimensional expression for the proposed governing system is yield out with entertaining appropriate variables. The graphically influence of parameters is studied. Following to obtained observations, it is claimed that declining deviation in velocity is predicted with chemical reactive factor. Further, less thermal transport between container to fluid is noticed for radiative absorption parameter.

Magnetohydrodynamic flow around an elongated cylinder in non-Darcian porous regime with higher order chemical reaction and Soret/Dufour effects

Here, we consider magnetohydrodynamic flow of an incompressible, time independent fluid past an elongated cylinder surrounded in a non-Darcian porous regime with magnetic flux supplied at an acute angle. The Soret/Dufour effects and the higher order chemical reactions are also included in the present study. The subsequent governing equations are resolved using the MATLAB-bvp4c method. The flow velocity appears to decrease with the growth of the Reynolds number, inertia parameter, magnetic field and angle of inclination of the magnetic flux, but improves with the Darcy number. The inertia parameter enhances the fluid temperature and skin friction. Further order of chemical reaction, Soret/ Dufour number plays a significant role in the system.

Scrutiny of convective MHD second‐grade fluid flow within two alternatively conducting vertical surfaces with Hall current and induced magnetic field

AbstractThe focus of this paper is to examine the heat and mass transport behavior of transient magnetohydrodynamics second‐grade fluid (elastico‐viscous fluid) flow within a vertical channel bounding the porous regime with the Hall phenomenon and induced magnetic field (IMF). The flow system consists of a strong transverse magnetic field that gives rise to the Hall phenomenon and IMF. The right vertical surface of the channel is conducting and oscillations in its plane in the vertical direction while the left vertical surface of the channel is nonconducting and stationary. The suitable dimensionless setup transforms the flow model into a simplified comparable model which is solved analytically with the assistance of the method of separation of variables. Numerical computation is performed with the aid of MATHEMATICA software to explore the results from the analytical solutions. The results of the investigation are helpful in analyzing the nature of the elastic‐viscous fluids. A noteworthy result noted from the investigation is that there appears a reverse flow in the direction of normal flow when the magnetic interaction parameter is large. For the small magnetic interaction parameter, such a flow is not seen. Hall current reduces the strength of the principal IMF and induces the strength of the secondary generated magnetic field. Furthermore, it is explored that the elastico‐viscous nature of the second‐grade fluid has a tendency of enhancing the principal flow and principal‐produced magnetic field.

Cattaneo–Christov model for triple diffusive natural convection flows over horizontal plate with entropy analysis embedded in porous regime

This research interprets the features of triple diffusion in naturally convected viscous material flow through a horizontal plate embedded in a porous regime. The heat and mass transmission process is evaluated by the implication of Cattaneo and Christov (CC) models of energy and mass diffusions. Entropy analysis is executed with the help of the second law of thermodynamics. The homogeneous and local thermal equilibrium is assumed for porous medium. The physically modeled expressions are reframed into an ordinary differential system. This re-structured system of expressions is computed numerically by the implication of the Runge–Kutta Fehlberg method. The computed solutions are visualized graphically and in numeric forms. The validation of present solutions is reported by the comparative benchmark with already available results in a limiting sense. It is evident that the opposing and assisting flows show higher entropy generation at the convective wall. An increment in surface entropy generation rate is achieved for higher thermal and solutal relaxation times.

Effects of yield stress and chemical reaction on magnetic two-phase nanofluid flow in a porous regime with thermal ray

This study investigates consequences of the steady flow of nanofluid via contracting cylinder utilizing the mathematical Buongiorno's model of nanofluid. Herein, the influence of magnetic field and porous materials are discussed in this paper. The parameters of heat sink/source and radiation are taken into respect. Furthermore, the react of chemical and the yield stress within the nanoingredients too, take up a new niche in this research. The transformations of similarity facilitate the paradigm of partial differential equations into ordinary differential equations. To hit the solutions of the nonlinear equations, the spectral local linearization method has been utilized. Consequences are discussed with diagrams and discussions. The physical consignments as a local Sherwood number, local Nusselt number and drag force are displayed. Excellent advancement in transmit of mass and heat is spotted, which can be conceived through graphs. Results elucidate that the transport of heat increased by increasing the porous medium permeability, thermal radiation, chemical reaction and magnetic field, but raising the heat sink/source and yield stress reduce the heat transfer, whereas the adverse behavior is noticed with the transmit of mass for these parameters.

Dynamical behaviour of magneto-copper-titania/water-ethylene glycol stream inside a gyrating channel

Inspired by the latest deeds of nanomaterials and their novel features in science and engineering sectors, a detailed mathematical model is presented to investigate an unsteady magneto-buoyancy-driven flow of a non-Newtonian (Casson model) chemically bonded hybrid nano liquid (copper-titania/water-ethylene glycol mixture) streaming through a gyrating channel with fluctuating wall temperature and concentration confined by the porous regime. Hybridized nanoparticles (copper-titania) are dispersed into the water-ethylene glycol mixture (vol.60–40%) hybrid base Casson liquid. Hall currents, porous resistance, thermal radiation, and Dufour impacts are hypothesized in the flow system. This model’s governing partial differential equations are derived from the generic laws of conservation of momentum, energy, and mass. These derived equations are rendered dimensionless by incorporating the normalization variables and parameters. The solutions of the dimensionless transport equations are realized in the closed-form followed by an analytical approach. The stipulated graphs and tables are designed to scrutinize the physical and theoretical upshots of a variety of essential system parameters on the critical dynamical functions or variables. Our simulation results based on set parameters disclose that Hall currents have a propensity to accelerate the fluid flow in the vertical direction and lessen the magnitude of the fluid velocity along the cross-flow direction. Amplifying frequency parameter recommends a diminution in the temperature and concentration profiles. The pattern of streamlines, heatlines, and masslines is drawn to envisage the flow and transport features in the gyrating channel. The novelty of this thermal model is that significance of rotating hybrid suspension and dominating magnetic field along with Hall currents is identified. Due to the rotation of the system, the flow is noticeably amended by the centrifugal and Coriolis forces. The present model is, of course, of great practical and technological importance, for example, chemical engineering, material science, mineral and cleaning oils manufacturing, and plastic and polymer industries.

Outlining the Impact of Melting on Mhd Casson Fluid Flow Past a Stretching Sheet in a Porous Medium with Radiation

This article focused on framing the characteristics of melting heat transfer in a porous medium induced by thermal radiation on (MHD) Casson fluid flow. The current model is used to predict the porous regime's viscoelastic action of water. First, the governing PDE is converted to ODE through an effective similarity transformation, and then the formed nonlinear equations are solved using the Runge-Kutta Fehlberg-45 order method. It illustrates and examines a detailed analysis of certain parameters on the velocity, temperature, coefficient of skin friction, and reduced number of Nusselt. The results indicate that velocity profile decreases in M and around but an opposite temperature pattern. In addition, an improvement in R and Me results in the amount of Nusselt number. The present analysis results are compared with the available works in particular situations, and more agreement has been observed.

MHD stagnation point flow of Fe3O4/Cu/Ag-CH3OH nanofluid along a convectively heated stretching sheet with partial slip and activation energy: Numerical and statistical approach

In this study, we have explored the influences of nonlinear thermal radiation and heat generation on MHD stagnation point flow of methanol (CH3OH)-based nanofluid along a permeable stretching sheet embedded in a porous regime. The impacts of viscous dissipation, velocity slip, convective boundary condition, thermophoresis, activation energy, concentration slip and binary chemical reaction are also taken into account. The nanoparticles considered in the present study are Fe3O4, Cu and Ag. The governing partial differential equations are then transformed into a system of coupled ordinary differential equations by the application of appropriate similarity variables. A shooting technique based on the Runge-Kutta-Fehlberg method is implemented to tackle the dimensionless set of equations. The impacts of various characterizing parameters on nanofluid velocity, temperature and concentration profiles are determined and analyzed via graphs. Moreover, the computed values of the quantities of engineering interest (local skin friction, Nusselt and Sherwood numbers) are presented in tabular form and discussed. The quadratic regression analysis estimation for local surface drag coefficient, local heat and mass transfer rates are also presented through tables. This work may find its significant applications in high temperature and cooling processes, space technology, paints, medicines, conductive coatings, cosmetics, bio-sensors, and to name a few.

Thermal transport analysis in stagnation-point flow of Casson nanofluid over a shrinking surface with viscous dissipation

In arteries blood flow is the usual example for a Casson fluid flow among the other vital utilizations of this fluid model. Thus, it would be helpful to study the Brownian motion diffusion and thermophoresis diffusion in Casson fluid for biomedical applications. In this analysis, the electrically conducting Casson nanofluid, with suction and convective boundary condition, has been addressed in a shrinking surface. The mechanism of convective heat transfer has been elaborated with Ohmic heating and viscous dissipation effects. The numerical solutions to the governing equations have been obtained by applying the similarity transformation to the nonlinear partial differential equations. The present model is employed to examine the viscoplastic characteristics in the porous regime. This dimensionless ruling problem, along with physical boundary conditions, is handled numerically by using a Runge–Kutta Fehlberg scheme. The outcomes of the present study show that the rate of heat and mass transfer at the surface of the shrinking sheet enhances with the growth in Casson fluid parameter and magnetic parameter. Furthermore, it is observed that the shear stress at the wall rises with the increment in magnetic parameter. Moreover, unsteadiness parameter is the decreasing function of heat and mass transfer rates.