Heat and Mass Transfer in MHD Micropolar Flow Over a Vertical Moving Porous Plate in a Porous Medium

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of a transverse magnetic field. The plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Also, the results of the skin-friction coefficient, the couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of fluid properties and flow conditions.     

The Effect of Double Dispersion on Natural Convection Heat and Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

The effect of power law index parameter of the non-Newtonian fluid on free convection heat and mass transfer from a vertical wall is analyzed by considering double dispersion in a non-Darcy porous medium with constant wall temperature and concentration conditions. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. In this case a similarity solution is possible. The variation of heat and mass transfer coefficients with the governing parameters such as power law index, thermal and solutal dispersion parameters, inertia parameter, buoyancy ratio, and the Lewis number is discussed for a wide range of values of these parameters.     

Peristaltic Flow of a Maxwell Model Through Porous Boundaries in a Porous Medium

In the present investigation we have presented the peristaltic flow of a linear Maxwell model through porous boundaries in a porous medium. The governing non-dimensional partial differential are solved in wave frame by using regular perturbation method and assumed form of solution. We have discussed the problem only for free pumping case. The effects of various physical parameters involved in the problem have been investigated and shown graphically.     

Flow and Heat Transfer Through a Polygonal Duct filled with a Porous Medium

The fully developed flow and H1 heat transfer in a polygonal duct filled with a Darcy–Brinkman medium is studied. The efficient method of boundary collocation is used. The problem is governed by the duct shape and a non-dimensional parameter s which characterizes the inverse square root of permeability. Asymptotic formulas for small and large s are derived.     

膨胀性非牛顿流体多孔介质流动的模拟分析

在表征体元尺度采用格子Boltzmann方法分析膨胀性非牛顿流体在多孔介质中的流动,基于二阶矩模型在演化方程中引入表征介质阻力的作用力项,求解描述渗流模型的广义Navier-Stokes方程．采用局部法计算形变速率张量,通过循环迭代得到非牛顿粘度和松弛时间．对多孔介质的Poiseuille流动进行分析,通过比较发现结果与孔隙尺度的解析解十分吻合,并且收敛较快,表明方法合理有效．分析了渗透率和幂律指数对速度和压力降的影响,研究结果表明,膨胀性流体的多孔介质流动不符合达西规律,压力降的增加幅度小于渗透率的减小幅度．当无量纲渗透率Da小于10-5时,流道中的速度呈现均匀分布,并且速度分布随着幂律指数的减小趋于平滑．压力降随着幂律指数的增加而增加,Da越大幂律指数对压力降的影响越明显．     

Hall and Porous Boundaries Effects on Peristaltic Transport Through Porous Medium of a Maxwell Model

Peristaltic motion induced by sinusoidal traveling wave of incompressible, electrically conducting Maxwell fluid in the porous walls of a two-dimensional channel through a porous medium has been investigated in the presence of a constant magnetic field. The Hall effect has been taken into account. Modified Darcy??s law has been used in the flow modeling. The fluid entering the flow region through one plate is considered at the same rate as it is leaving through the other plate. The problem is formulated using a perturbation expansion in terms of small amplitude ratio. We have discussed the problem only for free pumping case. This work can be considered as mathematical modeling to the case of gall bladder with stones. Finally, the effects of various parameters of interest are discussed and shown graphically.     

Influence of Heat and Mass Transfer on Newtonian Biomagnetic Fluid of Blood Flow Through a Tapered Porous Arteries with a Stenosis

Heat and mass transfer effects on Newtonian biomagnetic fluid of blood flow through a tapered porous artery with a stenosis is investigated. Governing equations have been modeled by treating blood as Newtonian biomagnetic fluid. The governing equations are simplified under the assumption of mild stenosis. Exact solutions have been evaluated for velocity, temperature, and concentration profiles. The effects of Newtonian nature of blood on velocity, temperature, concentration profile, wall shear stress, shearing stress at the stenosis throat and impedance of the artery are discussed graphically. Stream lines have been presented in last section of the article.     

Jump Condition for Diffusive and Convective Mass Transfer Between a Porous Medium and a Fluid Involving Adsorption and Chemical Reaction

In this paper, mass transfer at the fluid–porous medium boundaries is studied. The problem considers both diffusive and convective transport, along with adsorption and reaction effects in the porous medium. The result is a mass flux jump condition that is expressed in terms of effective transport coefficients. Such coefficients (a total dispersion tensor and effective reaction and adsorption coefficients) may be computed from the solution of the corresponding closure problem here stated and solved as a function of the Péclet number (Pe), the porosity and a local Thiele modulus. For the case of negligible convective transport (i.e., ), the closure problem reduces to the one recently solved by the authors for diffusion and reaction between a fluid and a microporous medium.     

Peristaltic Hemodynamic Flow of Couple-Stress Fluids Through a Porous Medium with Slip Effect

The present investigation deals with a theoretical study of the peristaltic hemodynamic flow of couple-stress fluids through a porous medium under the influence of wall slip condition. This study is motivated towards the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. Reynolds number is small enough and the wavelength to diameter ratio is large enough to negate inertial effects. Analytical solutions for axial velocity, pressure gradient, frictional force, stream function and mechanical efficiency are obtained. Effects of different physical parameters reflecting couple-stress parameter, permeability parameter, slip parameter, as well as amplitude ratio on pumping characteristics and frictional force, streamlines pattern and trapping of peristaltic flow pattern are studied with particular emphasis. The computational results are presented in graphical form. This study puts forward an important observation that pressure reduces by increasing the magnitude of couple-stress parameter, permeability parameter, slip parameter, whereas it enhances by increasing the amplitude ratio.     

Brinkman Flow of a Viscous Fluid Through a Spherical Porous Medium Embedded in Another Porous Medium

An analytical investigation for a two-dimensional steady, viscous, and incompressible flow past a permeable sphere embedded in another porous medium is presented using the Brinkman model, assuming a uniform shear flow far away from the sphere. Semi-analytical solutions of the problem are derived and relevant quantities such as velocities and shearing stresses on the surface of the sphere are obtained. The streamlines inside and outside the sphere and the radial velocity are shown in several graphs for different values of the porous parameters \({\sigma _1 =(\mu /\tilde {\mu }) (a/\sqrt{K_1 })}\) and \({\sigma _2 =(\mu /\tilde {\mu }) (a/\sqrt{K_2 })}\) , where a is the radius of the sphere, μ is the dynamic viscosity of the fluid, \({\tilde {\mu }}\) is an effective or Brinkman viscosity, while K ₁ and K ₂ are the permeabilities of the two porous media. It is shown that the dimensionless shearing stress on the sphere is periodic in nature and its absolute value increases with an increase of both porous parameters σ ₁ and σ ₂.     

Modeling of Heat and Mass Transfer in a Fractured Porous Medium

While fractured formations are possibly the most important contributors to the production of oil worldwide, modeling fractured formations with rigorous treatments has eluded reservoir engineers in the past. To date, one of the most commonly used fractured reservoir models remains the one that was suggested by Warren and Root nearly four decades ago. In this paper, a new model for fractures embedded in a porous medium is proposed. The model considers the Navier-Stokes equation in the fracture (channel flow) while using the Brinkman equation for the porous medium. Unlike the previous approach, the proposed model does not require the assumption of orthogonality of the fractures (sugar cube assumption) nor does it impose incorrect boundary conditions for the interface between the fracture and the porous medium. Also, the transfer coefficient between the fracture and matrix interface does not need to be specified, unlike the cases for which Darcy's law is used. In order to demonstrate the usefulness of the approach, a two-dimensional model of a fractured formation is developed and numerical simulation runs conducted.

The proposed model is derived through a series of finite element modeling runs for various cases using the Navier-Stokes equation in the channel while maintaining the Brinkman equation in the porous medium. Various cases studied include different fracture orientations, fracture frequencies, and thermal and solutal constraints. The usefulness of the proposed model in modeling complex formations is discussed. Finally, a series of numerical runs also provided validity of the proposed model for the cases in which thermal and solutal effects are important. Such a study of double diffusive phenomena, coupled with forced convection, in the context of fractured formations has not been reported before.     

Radiative and Thermal Dispersion Effects on Non-Darcy Natural Convection with Lateral Mass Flux for Non-Newtonian Fluid from a Vertical Flat Plate in a Saturated Porous Medium

The problem of natural convective heat transfer for a non-Newtonian fluid from an impermeable vertical plate embedded in a fluid-saturated porous medium has been analyzed. Non-Darcian, radiative and thermal dispersion effects have been considered in the present analysis. The governing boundary layer equations and boundary conditions are cast into a dimensionless form and simplified by using a similarity transformation. The resulting system of equations is solved by using a double shooting Runge–Kutta method. The effect of viscosity index n, the conduction–radiation parameter R, the non-Darcy parameter Gr*, the thermal dispersion parameter Ds and the suction/injection parameter f_w on the fluid velocities, temperatures and the local Nusselt number are discussed.     

Free Fluid Flow Through a Visco-Deformable Porous Medium with a Moving Boundary

One-dimensional Darcy-law flow through a porous matrix representing a high-viscosity liquid is investigated. The flow develops in a region which depends on time due to sedimentation. The problem considered simulates the geological process of sedimentation in a basin. In accordance with geological data, the permeability and viscosity coefficients of the matrix are assumed to depend nonlinearly on the porosity. The asymptotic properties of the flow are described for large times. The agreement between the results of asymptotic and numerical solutions is satisfactory at intermediate times and good at large times under the realistic sedimentary basin conditions. The simplicity of the asymptotic solution obtained makes it possible to vary the problem parameters and determine the porosity, pressure, and velocities for particular geological conditions by means of simple calculations.     

A Numerical Study of Oscillating Peristaltic Flow of Generalized Maxwell Viscoelastic Fluids Through a Porous Medium

This article presents a numerical study on oscillating peristaltic flow of generalized Maxwell fluids through a porous medium. A sinusoidal model is employed for the oscillating flow regime. A modified Darcy-Brinkman model is utilized to simulate the flow of a generalized Maxwell fluid in a homogenous, isotropic porous medium. The governing equations are simplified by assuming long wavelength and low Reynolds number approximations. The numerical and approximate analytical solutions of the problem are obtained by a semi-numerical technique, namely the homotopy perturbation method. The influence of the dominating physical parameters such as fractional Maxwell parameter, relaxation time, amplitude ratio, and permeability parameter on the flow characteristics are depicted graphically. The size of the trapped bolus is slightly enhanced by increasing the magnitude of permeability parameter whereas it is decreased with increasing amplitude ratio. Furthermore, it is shown that in the entire pumping region and the free pumping region, both volumetric flow rate and pressure decrease with increasing relaxation time, whereas in the co-pumping region, the volumetric flow rate is elevated with rising magnitude of relaxation time.     

Effect of Variable Viscosity on Free Convective Heat Transfer over a Non-isothermal Body of Arbitrary Shape in a Non-Newtonian Fluid Saturated Porous Medium with Internal Heat Generation

Similarity solutions are proposed for the analysis of free convection flow over a non-isothermal body of arbitrary shape embedded in porous media in the presence of internal heat generation. The porous medium is saturated with non-Newtonian power law fluid. The effect of temperature dependent viscosity on heat transfer rates is investigated. The linearized version of the Arrhenius law for temperature dependent viscosity is considered and it is shown that the heat transferred is more for a less viscous fluid.     

Analysis of Laminar Flow and Forced Convection Heat Transfer in a Porous Medium

The flow of an incompressible Newtonian fluid confined in a planar geometry with different wall temperatures filled with a homogenous and isotropic porous medium is analyzed in terms of determining the unsteady state and steady state velocities, the temperature and the entropy generation rate as function of the pressure drop, the Darcy number, and the Brinkman number. The one-dimensional approximate equation in the rectangular Cartesian coordinates governing the flow of a Newtonian fluid through porous medium is derived by accounting for the order of magnitude of terms as well as accompanying approximations to the full-blown three-dimensional equations by using scaling arguments. The one-dimensional approximate energy and the entropy equations with the viscous dissipation consisting of the velocity gradient and the square of velocity are derived by following the same procedure used in the derivation of velocity expressions. The one-dimensional approximate equations for the velocity, the temperature, and the entropy generation rate are analytically solved to determine the velocity, the temperature, and the entropy distributions in the saturated porous medium as functions of the effective process parameters. It is found that the pressure drop, the Darcy number, and the Brinkman number affect the temperature distribution in the similar way, and besides the above parameters, the irreversibility distribution ratio also affects the entropy generation rate in the similar way.     

Casson Fluid Flow Due to Non-Coaxial Rotation of a Porous Disk and the Fluid at Infinity Through a Porous Medium

The flow of the Casson fluid due to non-coaxial rotation of a disk and the fluid at infinity is investigated. Partial differential equations are made dimensionless and coupled. The exact solution of the resultant nonlinear initial-boundary-value problem is solved by applying the Laplace transform. The shear stresses at the disk surface and the steady state stresses are computed. The effects of dimensionless parameters on the dimensionless primary and secondary velocities are analyzed.     

Features of High-Viscosity Fluid Flow Through a Porous Medium Heated by Electromagnetic Radiation

Models describing the process of flow of a high- viscosity fluid through a porous medium heated by electromagnetic radiation are investigated analytically and numerically with allowance for the temperature dependence of the fluid viscosity and density. In addition to ordinary heating, the nonlinear electromagnetic heating regime associated with variation of the radiation absorption coefficient with temperature is considered.     

Analysis of Heat and Mass Transfer in a Vertical Annular Porous Cylinder Using FEM

The present study is intended to study heat and mass transfer in a vertical annular cylinder embedded with saturated porous medium. The inner surface of cylinder is maintained at uniform wall temperature and uniform wall concentration. The governing partial differential equations are non-dimensionalised and solved by using finite element method (FEM). The porous medium is discritised using triangular elements with uneven element size. Large number of smaller-sized elements are placed near the walls of the annulus to capture the smallest variation in solution parameters. The results are reported for both aiding and opposing flows. The effects of various non-dimensional numbers such as buoyancy ratio, Lewis number, Rayleigh number, aspect ratio, etc on heat and mass transfer are discussed. The temperature and concentration profiles are presented.     

Thermal Dispersion Effects on Combined Convection in Non-Newtonian Fluids Along a Nonisothermal Vertical Plate in a Porous Medium

The method of non-similarity solution is used to study the influence of thermal dispersion on combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid. The coefficient of thermal diffusivity has been assumed to be the sum of molecular diffusivity and the dispersion thermal diffusivity due to mechanical dispersion. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented.