Flow and Heat Transfer of a Dusty Williamson MHD Nanofluid Flow over a Permeable Cylinder in a Porous Medium

This study investigates the flow and heat transfer of dusty Williamson (MHD) Nanofluid flow over a stretching permeable cylinder in a porous medium. Dusty Williamson Nanofluid was considered due to its thermal properties and potential benefits of increasing the heat transfer rate. Firstly, partial differential equations are transformed into coupled non-linear ordinary differential equations through a similarity variables transformation. The resulting set of dimensionless equations is solved analytically by using the Homogony Perturbation Method (HPM). The effects of the emerging parameters on the velocity and temperature profiles as well as skin-friction coefficient and Nusselt number are publicized through tables and graphs with appropriate discussions. The present result has been compared with published papers and found to be in agreement. To the best of author’s knowledge, there has been sparse research work in the literature that considers the effect of dust with Williamson Nanofluid and also solving the problem analytically. Therefore to the best of author’s knowledge, this is the first time analytical solution has been established for the problem. The results revealed that the fluid velocity of both the fluid and dust phases decreases as the Williamson parameter increases. Motivated by the above limitations and the gaps in past works, therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science, industry and engineering.

Flow and heat transfer of a nanofluid through a porous medium due to stretching/shrinking sheet with suction,magnetic field and thermal radiation

This study investigates the suction and magnetic field effects on the two-dimensional nanofluid flow through a stretching/shrinking sheet at the stagnation point in the porous medium with thermal radiation.The governing partial differential equations(PDEs)are converted into ordinary differential equations(ODEs)using the similarity transformation.The resulting ODEs are then solved numerically by using the bvp4c solver in MATLAB software.It was found that dual solutions exist for the shrinking parameter values up to a certain range.The numerical results obtained are compared,and the comparison showed a good agreement with the existing results in the literature.The governing parameters’effect on the velocity,temperature and nanoparticle fraction fields as well as the skin friction coefficient,the local Nusselt number and the Sherwood number are represented graphically and analyzed.The variation of the velocity,temperature and concentration increase with the increase in the suction and magnetic field parameters.It seems that the thermal radiation effect has increased the local Sherwood number while the local Nusselt number is reduced with it.

Analysis of a Stagnation Point Flow with Hybrid Nanoparticles over a Porous Medium

The unsteady stagnation-point flow of a hybrid nanofluid over a stretching/shrinking sheet embedded in a porous medium with mass transpiration and chemical reactions is considered.The momentum and mass transfer problems are combined to form a system of partial differential equations,which is converted into a set of ordinary differential equations via similarity transformation.These ordinary differential equations are solved analytically to obtain the solution for velocity and concentration profiles in exponential and hypergeometric forms,respectively.The concentration profile is obtained for four different cases namely constant wall concentration,uniform mass flux,general power law wall con-centration and general power law mass flux.The effect of different physical parameters such as Darcy number Da^(1-1),mass transpiration parameter V_(C),stretching/shrinking parameter (d),chemical reaction parameter(β)and Schmidt number (Sc)on velocity and concentration profile is examined.Results show that,the axial velocity will decreases as the shrinking sheet parameter increases,regardless of whether the suction or injection case is examined.The concentration decreases with an increase in the shrinking sheet parameter and the chemical reaction rate parameter.

Slip Condition Effects on Unsteady MHD Fluid Flow with Radiative Heatflux over a Porous Medium

The objective of this paper is to study unsteady magneto hydrodynamic (MHD) free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium. The temperature is assumed to be oscillating with time. The solution obtained shows different profiles of effects of slip conditions on primary and secondary velocity. Also, the effects of various parameters on temperature, concentration, primary and secondary velocity profiles were presented graphically. The result indicated the secondary velocity is enhanced with increase in slip parameter. Primary velocity demonstrated opposite trend.

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

Formation Characteristics of CO_(2) Hydrates in the Presence of Porous Media and NaCl

Hydrate-based CO_(2) sequestration is an effective method for reducing the greenhouse effect,and the presence of porous media and NaCl can impact the formation characteristics of hydrates.This study uses the constant volume temperature search method to investigate the effects of quartz sand particle size(0.006‒0.03 mm),water saturation(30%–90%),and NaCl concentration(1%‒9%)on the phase equilibrium and kinetics of CO_(2) hydrates within a temperature range of 273‒285 K and pressure range of 1.0‒3.5 MPa.The results indicate that a decrease in quartz sand particle size or an increase in NaCl concentration shifts the hydrate phase equilibrium curve towards lower temperatures and higher pressures,making hydrate generation conditions more demanding.In different particle size systems,there are no significant changes in the rate of CO_(2) hydrate formation or conversion rate.The highest hydrate conversion rate of 71.1%is observed in a 0.015 mm particle size system.With increasing water saturation,both the generation rate and conversion rate of CO_(2) hydrates show a trend of first increasing and then decreasing.Meanwhile,low concentrations of NaCl(1%–3%)are found to enhance the formation and conversion rates of CO_(2) hydrates.However,as NaCl concentration increases,the rate of CO_(2) hydrate formation and conversion rate decrease.

Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology,acoustics,geophysics and earthquake engineering.Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials.The system is composed of ideal fluid,porous medium,and underlying elastic solid.By numerical examples,the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed.The results show that the existence of the porous medium,especially in the partially saturated case,may significantly affect the dynamic pressures of the overlying fluid.

Slip flow of Maxwell viscoelasticity-based micropolar nanoparticles with porous medium: a numerical study

This article presents the mass and heat transport aspects in viscoelastic nanofluid flows under the presence of velocity slip conditions. To explore the nonNewtonian behavior, a Maxwell viscoelasticity-based micropolar is considered. Moreover, a porous medium saturates the stretching sheet. A set of similarity variables is introduced to derive the dimensionless ordinary differential equations of velocity, concentration, and temperature profiles. The numerical solution is computed by using the MATLAB bvp4c package. The salient flow features of velocity, concentration, and temperature profiles are described and discussed through various graphs. It is observed that with an increase in the slip parameter, the micro-rotation velocity also increases. The temperature of nanoparticles gets maximum values by varying the viscoelastic parameter and the porosity parameter while an opposite trend is noted for the micro-rotation parameter. The local Nusselt number and the local Sherwood number increase by increasing the viscoelastic parameter, the porosity parameter, and the slip velocity parameter. The graphical computation is performed for a specified range of parameters, such as 0 ≤ M ≤ 2.5, 0 ≤σm ≤ 2.5, 0 ≤ K1 ≤ 1.5, 0.5 ≤ Pr ≤ 3.0, 0 ≤σ≤ 1.5, 0.5 ≤ Sc ≤ 2.0, 0.2 ≤ Nb ≤ 0.8, and 0.2 ≤ Nt ≤ 0.8.

ON THE INTERACTION OF WATER WAVES AND SEABED BY THE POROUS MEDIUM MODEL

The interaction of water waves and seabed is studied by using Yamamoto's model, which takes into account the deformation of soil skeletal frame, compressibility of pore fluid flow as well as the Coulumb friction. When analyzing the propagation of three kinds of stress waves in seabed, a simplified dispersion relation and a specific damping formula are derived. The problem of seabed stability is further treated analytically based on the Mohr-Coulomb theory. The theory is finally applied to the coastal problems in the Lian-Yun Harbour and compared with observations and measurements in soil-wave tank with satisfactory results.

Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.

Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction

This paper presents the study of convective heat and mass transfer characteristics of an incompressible MHD visco-elastic fluid flow immersed in a porous medium over a stretching sheet with chemical reaction and thermal stratification effects. The resultant governing boundary layer equations are highly non-linear and coupled form of partial differential equations, and they have been solved by using fourth order Runge-Kutta integration scheme with Newton Raphson shooting method. Numerical computations are carried out for the non-dimensional physical parameters. Here a numerical has been carried out to study the effect of different physical parameters such as visco-elasticity, permeability of the porous medium, magnetic field, Grashof number, Schmidt number, heat source parameter and chemical reaction parameter on the flow, heat and mass transfer characteristics.

COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION

In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ=0 and 0〈μ〈 2N/n（m-1）＋2 or γ 〉 0 and 1/p-1 〈 μ 〈 2N/N（m-1）＋2 then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S（RN）, there exists an initial-value u0 ∈ C（RN） with limx→∞ uo（x）= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u（tβ, t）, Where β = 2-μ（m-1）/4.

MHD flow of nanofluids over an exponentially stretching sheet in a porous medium with convective boundary conditions

This article concentrates on the steady magnetohydrodynamic （MHD） flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper （Cu）, Silver （Ag）, Alumina （A1203） and Titanium Oxide （TiO2）. Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.

HOMOGENIZATION OF A STATIONARY NAVIER-STOKES FLOW IN POROUS MEDIUM WITH THIN FILM

The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition.At the end of the article,＂Darcy＇s law＂is rigorously derived from this model as the parameter ε tends to zero,which is independent of the coordinates towards the thickness.

Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation(absorption)

The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.

Revisiting the methods for gas permeability measurement in tight porous medium

Permeability is a key parameter to describe fluid transport properties of porous medium; however, the permeability measurement is extremely difficult for tight porous medium, e.g. fine-grained rock or dense soil. In this paper, three methods for gas permeability measurement, i.e. steady state method, pulse decay method(PDM) and pressure oscillation method(POM), are first reviewed and then their advantages and drawbacks are discussed. Both analytical and numerical solutions of gas permeability are presented for the tight porous medium. The results show that the analytical method is relatively simple but only valid under certain conditions, whilst the numerical method is more robust and generic, which can take into account several factors such as porosity, saturation, gas leakage, and unconventional boundary conditions. The influence of the effective porosity on the permeability determination is further analyzed using the proposed numerical method. In this study, new pressure data interpretation procedures for PDM and POM are proposed, and the obtained results can serve as a guidance to define a proper method for permeability measurement of the tight porous medium.

Linear stability of triple-diffusive convection in micropolar ferromagnetic fluid saturating porous medium

The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fluid layer contained between two free boundaries. A linear stability analysis and a normal mode analysis method are carried out to study the onset convection. For stationary convection, various parameters such as the medium permeability, the solute gradients, the non-buoyancy magnetization, and the micropolar parameters （i.e., the coupling parameter, the spin diffusion parameter, and the micropolar heat conduction parameter） are analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for a sufficiently large value of the buoyancy magnetization parameter M1. The principle of exchange of stabilities is found to be true for the micropolar fluid heated from below in the absence of the micropolar viscous effect, the microinertia, and the solute gradients. The micropolar viscous effect, the microinertia, and the solute gradient introduce oscillatory modes, which are non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained.

Large-eddy simulation of fluid mixing in tee with sintered porous medium

Mixing processes of hot and cold fluids in a tee with and without sin- tered copper spheres are simulated by FLUENT using the large-eddy simulation （LES） turbulent flow model and the sub-grid scale （SGS） Smagorinsky-Lilly （SL） model with buoyancy. Comparisons of numerical results of the two cases with and without sintered copper spheres show that the porous medium significantly reduces velocity and temper- ature fluctuations because the porous medium can effectively restrict the fluid flow and enhance heat transfer. The porous medium obviously increases the pressure drop in the main duct. The porous medium reduces the power spectrum density （PSD） of tempera- ture fluctuations in the frequency range from 1 Hz to 10 Hz.

Natural convection of nanofluid over vertical plate embedded in porous medium: prescribed surface heat flux

The aim of the present paper is to analyze the natural convection heat and mass transfer of nanofluids over a vertical plate embedded in a saturated Darcy porous medium subjected to surface heat and nanoparticle fluxes. To carry out the numerical solution, two steps are performed. The governing partial differential equations are firstly simplified into a set of highly coupled nonlinear ordinary differential equations by appropriate similarity variables, and then numerically solved by the finite difference method. The obtained similarity solution depends on four non-dimensional parameters, i.e., the Brownian motion parameter （Nb）, the buoyancy ratio （Nr）, the thermophoresis parameter （Nt）, and the Lewis number （Le）. The variations of the reduced Nusselt number and the reduced Sherwood number with Nb and Nt for various values of Le and Nr are discussed in detail. Simulation results depict that the increase in Nb, Nt, or Nr decreases the reduced Nusselt number. An increase in the Lewis number increases both of the reduced Nusselt number and the Sherwood number. The results also reveal that the nanoparticle concentration boundary layer thickness is much thinner than those of the thermal and hydrodynamic boundary layers.

Peristaltic flow of couple stress fluid through uniform porous medium

Investigation concerning peristaltic motion of couple stress fluid is made. An incompressible couple stress fluid occupies the porous medium. Mathematical anal- ysis is presented through large wavelength and low Reynolds number. Exact analytical expressions of axial velocity, volume flow rate, pressure gradient, and stream function are calculated as a function of couple stress parameter. The essential feature of the analysis is a full description of influence of couple stress parameter and permeability parameter on the pressure, frictional force, mechanical efficiency, and trapping.