non-Newtonian Fluid Saturated Porous Medium Research Articles

A Study on Mixed Convective, MHD Flow from a Vertical Plate Embedded in Non-Newtonian Fluid Saturated Non- Darcy Porous Medium with Melting Effect

We analyzed in this paper the problem of mixed convection along a vertical plate in a non-Newtonian fluid saturated non-Darcy porous medium in the presence of melting and thermal dispersion-radiation effects for aiding and opposing external flows. Similarity solution for the governing equations is obtained for the flow equations in steady state. The equations are numerically solved by using Runge-kutta fourth order method coupled with shooting technique. The effects of melting (M), thermal dispersion (D), radiation (R), magnetic field (MH), viscosity index (n) and mixed convection (Ra/Pe) on fluid velocity and temperature are examined for aiding and opposing external flows.

MHD and Thermal Dispersion-Radiation Effects on Non-Newtonian Fluid Saturated Non-Darcy Mixed Convective Flow with Melting Effect

The problem of mixed convection along a vertical plate in a non-Newtonian fluid saturated non-Darcy porous medium in the presence of melting, thermal dispersion-radiation effects for aiding and opposing external flows is analyzed. Similarity solution for the governing equations is obtained for the flow equations in steady state. The equations are numerically solved by using Runge-kutta fourth order method coupled with shooting technique. The effects of melting (M), thermal dispersion (D)-radiation (R), inertia (F) and mixed convection (Ra/Pe) on velocity and temperature distributions are examined in the presence of magnetic parameter MH.

Effect of Melting on Mixed Convection Heat and Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

In this paper, we investigate the influence of melting on mixed convection heat and mass transfer from vertical flat plate in a non-Newtonian fluid-saturated non-Darcy porous medium including the prominent Soret effect. The wall and the ambient medium are maintained at constant but different levels of temperature and concentration such that the heat and mass transfer occurs from the wall to the medium. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. A similarity solution for the transformed governing equations is obtained. The numerical computation is carried out for various values of the nondimensional physical parameters. The variation of temperature, concentration, and heat and mass transfer coefficients with the power law index, mixed convection parameter, inertia parameter, melting parameter, Soret number, buoyancy ratio, and Lewis number is discussed for a wide range of values of these parameters.

Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.

Viscosity and dispersion effects on natural convection from a vertical cone in a nonnewtonian fluid saturated porous medium

This paper investigates the influence of double dispersion and viscosity on natural convection heat and mass transfer from vertical cone in a non-Darcy porous medium saturated with non- Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. A similarity solution for the transformed governing equations is obtained. The numerical computation is carried out for various values of the non-dimensional physical parameters. The effect of non-Darcy parameter, viscosity parameter, thermal and solutal dispersion, buoyancy ratio, Lewis number and power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.

Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium

The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves, pseudo-Rayleigh waves, flexural waves, and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot–Tsiklauri model by calculating their velocity dispersion and attenuation coefficients. The corresponding acoustic waveforms illustrate their properties in time domain. The results are also compared with those based on generalized Biot's theory. The results show that the influence of non-Newtonian effect on acoustic guided wave, especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.

Melting and radiation effects on mixed convection from a vertical surface embedded in a non-Newtonian fluid saturated non-Darcy porous medium for aiding and opposing eternal flows

Continuum equations governing mixed convection from a vertical surface embedded in a non-Darcy porous medium with aiding and opposing external flows in the presence of melting, radiation and heat generation or absorption effects for non-Newtonian fluids are developed. Similarity variables are employed for the partial differential equations governing the flow and heat transfer characteristics and the resulting ordinary differential equations are solved numerically by an implicit, iterative, finite-difference method. The accuracy of the numerical method is tested by performing various comparisons with previously published work and the results are found to be in excellent agreement. Representative Flow and heat transfer results are obtained for various combinations of physical parameters. These results are presented graphically to illustrate interesting features of the physics of the problem. Key words: Melting effect, non-Newtonian fluid, non-Darcy flow, thermal radiation, heat generation or absorption.

Elastic waves in Maxwell fluid-saturated porous media with the squirt flow mechanism

Based on Biot-Tsiklauri model and the combined Biot/squirt model, a universal acoustic model for non-Newtonian fluid (Maxwell fluid) saturated porous medium with an arbitrary pore size distribution is presented, in which the squirt-flow mechanism has been taken into account. The influences of non-Newtonian effect of Maxwell fluid on the attenuation and the dispersion characteristics of elastic waves propagating in such a porous medium are investigated. It shows that the non-Newtonian effect and the squirt-flow effect are the important factors for elastic wave dispersion and attenuation. When the squirt flow mechanism occurs, the squirt flow mechanism dominates the contribution to the energy loss of compressional waves at low frequencies. It shows that the squirt flow only affects the dispersion and the attenuation characteristics of two compressional waves, while the non-Newtonian effect of Maxwell fluid not only affects the dispersion and the attenuation characteristics of the compressional waves, but also influences the dispersion and the attenuation characteristics of shear waves.

Double diffusion from a vertical truncated cone in a non-Newtonian fluid saturated porous medium with variable heat and mass fluxes

This paper studies the double diffusion flow over a vertical truncated cone with variable heat and mass fluxes in a porous medium saturated with non-Newtonian power-law fluids. A coordinate transformation is used to obtain the nonsimilar governing equations, and the transformed boundary layer equations are then solved by the cubic spline collocation method. Results for local surface temperature and concentration are presented as functions of power-law indexes, exponents for variable heat and mass fluxes, buoyancy ratios, and Lewis numbers. The local surface temperature and concentration of the truncated cone decrease as the exponents for variable heat and mass fluxes are increased. Moreover, a decrease in the power-law index of fluids tends to decrease the local surface temperature and concentration of the truncated cone.

Effect of Melting and Thermo-Diffusion on Natural Convection Heat Mass Transfer in a Non-Newtonian Fluid Saturated Non-Darcy Porous Medium

This paper investigates the influence of melting and thermo-diffusion effect on natural convection heat and mass transfer from vertical flat plate in a non-Newtonian fluid saturated non-Darcy porous medium. The wall and the ambient medium are maintained at constant but different levels of temperature and concentration such that the heat and mass transfer occurs from the wall to the medium. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. A similarity solution for the transformed governing equations is obtained, computation is carried out for various values of the non-dimensional physical parameters. The variation in velocity, temperature, concentration, heat and mass transfer coefficients with the power law index, inertia parameter, melting parameter, thermo- diffusion parameter, buoyancy ratio and Lewis number is discussed for a wide range of values of these parameters.

Effect of thermophoretic particle deposition in non-Newtonian free convection flow over a vertical plate with magnetic field effect

The present contribution deals with the effects of thermophoretic particle deposition on the free convective flow over a vertical flat plate embedded in a non-Newtonian fluid-saturated porous medium in the presence of a magnetic field. The governing partial differential equations are transformed into ordinary differential equations by using special transformations. The resulting similarity equations are solved numerically by an efficient implicit finite-difference method. For various values of the problem parameters, graphs of the profile concentration in the boundary layer and of thermophoretic deposition velocity are presented.

Combined heat and mass transfer in natural convection flow from a vertical wavy surface in a power-law fluid saturated porous medium with thermal and mass stratification

This work studies the coupled heat and mass transfer by natural convection near a vertical wavy surface in a non-Newtonian fluid saturated porous medium with thermal and mass stratification. The surface of the vertical wavy plate is kept at constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary layer equations are then solved by the cubic spline collocation method. Effects of thermal and concentration stratification parameters, Lewis number, buoyancy ratio, power-law index, and wavy geometry on the important heat and mass transfer characteristics are studied. Results show that an increase in the thermal and concentration stratification parameter decreases the buoyancy force and retards the flow, thus decreasing the heat and mass transfer rates between the fluid and the vertical wavy surface. It is shown that an increase in the power-law index, the thermal stratification parameter, or the concentration stratification parameter leads to a smaller fluctuation of the local Nusselt and Sherwood numbers with the streamwise coordinate. Moreover, the total heat transfer rate and the total mass transfer rate of vertical wavy surfaces are higher than those of the corresponding smooth surfaces.

Double-diffusive natural convection along a vertical wavy truncated cone in non-Newtonian fluid saturated porous media with thermal and mass stratification

This paper studies the double-diffusive natural convection near a vertical wavy truncated cone in a non-Newtonian fluid saturated porous medium with thermal and mass stratification. The surface of the truncated cone is kept at constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary-layer equations are then solved by the cubic spline collocation method. Effects of thermal and concentration stratification parameters, Lewis number, buoyancy ratio, power-law index, and wavy geometry on the heat and mass transfer characteristics are studied. Results show that the streamwise distributions of the local Nusselt number and the local Sherwood number are harmonic curves with a wave number twice the wave number of the surface of the vertical wavy truncated cone. An increase in the power-law index leads to a smaller fluctuation of the local Nusselt and Sherwood numbers. Moreover, increasing the thermal and concentration stratification parameter decreases the buoyancy force and retards the flow, thus decreasing the heat and mass transfer rates between the fluid and the wavy surface of the vertical truncated cone.

Effect of variable viscosity on non-Darcy free or mixed convection flow on a vertical surface in a non-Newtonian fluid saturated porous medium

The effect of variable viscosity on non-Darcy free or mixed convective heat transfer along a vertical surface embedded in a porous medium saturated with a non-Newtonian fluid has been analysed. The viscosity of the fluid is assumed to be an inverse linear function of temperature. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions which are compared with the existing results, for a few particular cases. The results show that the variable viscosity parameter, viscosity index, mixed convection parameter, Ergun number, Peclet number, Rayleigh number and temperature variation parameter have significant influence on the velocity and heat transfer rate at the surface.

An implicit-Chebyshev pseudospectral method for the effect of radiation on power-law fluid past a vertical plate immersed in a porous medium

An implicit-Chebyshev collocation spectral method is employed in this study. This method was used to compute the problem of unsteady free convection with heat transfer from an isothermal vertical flat plate to a non-Newtonian fluid saturated porous medium, which is modeled as a power-law fluid. Boundary layer and Boussinesq approximations have been incorporated. The Darcy–Brinkman–Forchheimer model is applied to describe the flow field, where the magnetic field and the radiation effects are taken into account. Because of the non-Newtonian rheology, these problems are non-linear and must be solved numerically. The domain of the problem is discretized according to the implicit-Chebyshev spectral collocation scheme. In this study, the spatial derivatives are computed with a differentiation matrix and the time derivatives are computed with Crank–Nicolson implicit finite-difference method. Numerical calculations are carried out for the various parameters entering into the problem. Velocity and temperature profiles are shown in tables and graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficients approach the steady state values.

Rayleigh wave propagation along the boundary of a non-Newtonian fluid-saturated porous medium

The Frenkel-Biot theory is used to study the reflection of elastic waves from the boundary of a non-Newtonian (Maxwell) fluid-saturated porous medium. The velocity and attenuation of a Rayleigh surface wave propagating along the boundary of the medium are determined. Two models of a fluid-saturated porous medium are used for calculation: with pore channels of a fixed diameter and with a lognormal distribution of pore channels in size. The results of calculations show that, when the fluid in the porous medium is characterized by a small Deborah number (i.e., exhibits non-Newtonian properties), the velocity of Rayleigh waves exhibits a considerable frequency dispersion. The results also suggest that, in principle, it is possible to estimate the Deborah number from the measured frequency dispersion of the Rayleigh wave velocity.

Non-Darcy Non-Newtonian Free Convection Flow Over a Horizontal Cylinder in a Saturated Porous Medium

Steady state solutions are obtained for non-Darcy free convection flow along a horizontal cylinder in a non-Newtonian fluid saturated porous medium. The boundary-layer equations governing the flow are solved numerically by using an implicit finite-difference method developed by Keller. Numerical results are obtained for the velocity and heat transfer at the wall for various values of the parameters namely, the Ergun number, Rayleigh number, power-law index and transpiration parameter.

Effects of viscous dissipation on a power-law fluid over plate embedded in a porous medium

The present study is devoted to investigate the influences of viscous dissipation on buoyancy induced flow over a horizontal or a vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained with prescribed variable surface temperature (PT) or with prescribed variable surface heat flux (PHF) for the horizontal plate case. While, the similarity solutions are obtained with prescribed variable surface heat flux for the vertical plate case. Different similar transformations, for each case, are used. Numerical results for the details of the velocity and temperature profiles are shown on graphs. Nusselt number associated with temperature distributions and excess surface temperature associated with heat flux distributions which are entered in tables have been presented for different values of the power-law index n and the exponent λ as well as Eckert number.

Combined effect of magnetic field and viscous dissipation on a power-law fluid over plate with variable surface heat flux embedded in a porous medium

An analysis is presented to investigate the influences of viscous dissipation on buoyancy-induced flow over (a horizontal or a vertical flat plate) embedded in a non-Newtonian fluid saturated porous medium under the action of a transverse magnetic field. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solutions for the transformed governing equations are obtained with prescribed variable surface heat flux, for each position of the plate. Numerical results for the details of the velocity and temperature profiles are shown on graphs, for the two cases horizontal and vertical plate, for different values of the magnetic field parameter, power-law index n and the exponent λ as well as the Eckert number. Values of the excess surface temperature which are entered in tables or plotted in figures have been presented for different values of the different parameters, for the two cases, horizontal and vertical plate.

Properties of Elastic Waves in a Non-Newtonian (Maxwell) Fluid-Saturated Porous Medium

The present study investigates novelties brought into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Based on our previous results (Tsiklauri and Beresnev, 2001), we investigated the propagation of rotational and dilatational elastic waves by calculating their phase velocities and attenuation coefficients as a function of frequency. We found that the replacement of an ordinary Newtonian fluid by a Maxwell fluid in the fluid-saturated porous solid results in: (a) an overall increase of the phase velocities of both the rotational and dilatational waves. With the increase of frequency these quantities tend to a fixed, higher level, as compared to the Newtonian limiting case, which does not change with the decrease of the Deborah number α. (b) The overall decrease of the attenuation coefficients of both the rotational and dilatational waves. With the increase of frequency these quantities tend to a progressively lower level, as compared to the Newtonian limiting case, as α decreases. (c) Appearance of oscillations in all physical quantities in the deeply non-Newtonian regime.