Showing papers on "Herschel–Bulkley fluid published in 2015"
TL;DR: In this article, the Cattaneo-Christov heat flux model is used to investigate the rotating flow of viscoelastic fluid bounded by a stretching surface and the boundary layer equations are first modeled and then reduced to self-similar forms via similarity approach.
Abstract: In this paper Cattaneo-Christov heat flux model is used to investigate the rotating flow of viscoelastic fluid bounded by a stretching surface. This model is a modified version of the classical Fourier’s law that takes into account the interesting aspect of thermal relaxation time. The boundary layer equations are first modeled and then reduced to self-similar forms via similarity approach. Both analytical and numerical solutions are obtained and found in excellent agreement. Our computations reveal that velocity is inversely proportional to the viscoelastic fluid parameter. Further fluid temperature has inverse relationship with the relaxation time for heat flux and with the Prandtl number. Present consideration even in the case of Newtonian fluid does not yet exist in the literature.
217 citations
TL;DR: This work deals with the flow and heat transfer in upper-convected Maxwell fluid above an exponentially stretching surface and reveals that fluid temperature has inverse relationship with the thermal relaxation time.
Abstract: This work deals with the flow and heat transfer in upper-convected Maxwell fluid above an exponentially stretching surface. Cattaneo-Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. Similarity approach is utilized to normalize the governing boundary layer equations. Local similarity solutions are achieved by shooting approach together with fourth-fifth-order Runge-Kutta integration technique and Newton’s method. Our computations reveal that fluid temperature has inverse relationship with the thermal relaxation time. Further the fluid velocity is a decreasing function of the fluid relaxation time. A comparison of Fourier’s law and the Cattaneo-Christov’s law is also presented. Present attempt even in the case of Newtonian fluid is not yet available in the literature.
117 citations
TL;DR: In this paper, the influence of Newtonian heating on heat and mass transfer in unsteady hydromagnetic flow of a Casson fluid past a vertical plate in the presence of thermal radiation and chemical reaction is studied.
Abstract: The influence of Newtonian heating on heat and mass transfer in unsteady hydromagnetic flow of a Casson fluid past a vertical plate in the presence of thermal radiation and chemical reaction is studied The Casson fluid model is used to distinguish the non-Newtonian fluid behavior The fluid flow is induced due to periodic oscillations of the plate along its length and a uniform transverse magnetic field is applied in a direction which is normal to the direction of fluid flow The partial differential equations governing the flow, heat, and mass transfer are transformed to non-dimensional form using suitable non-dimensional variables which are then solved analytically by using Laplace transform technique The numerical values of the fluid velocity, fluid temperature, and species concentration are depicted graphically whereas the values of skin-friction, Nusselt number, and Sherwood number are presented in tabular form It is noticed that the fluid velocity and temperature decrease with increasing values of Casson parameter while concentration decreases with increasing values of chemical reaction parameter and Schmidt number Such a fluid flow model has several industrial and medical applications such as in glass manufacturing, paper production, purification of crude oil and study of blood flow in the cardiovascular system
84 citations
TL;DR: In this article, the influence of melting heat transfer and thermal radiation on MHD stagnation point flow of an electrically conducting non-Newtonian fluid (Jeffrey fluid) over a stretching sheet with partial surface slip was investigated numerically.
Abstract: The present paper investigates numerically the influence of melting heat transfer and thermal radiation on MHD stagnation point flow of an electrically conducting non-Newtonian fluid (Jeffrey fluid) over a stretching sheet with partial surface slip. The governing equations are reduced to non-linear ordinary differential equations by using a similarity transformation and then solved numerically by using Runge–Kutta–Fehlberg method. The effects of pertinent parameters on the flow and heat transfer fields are presented through tables and graphs, and are discussed from the physical point of view. Our analysis revealed that the fluid temperature is higher in case of Jeffrey fluid than that in the case of Newtonian fluid. It is also observed that the wall stress increases with increasing the values of slip parameter but the effect is opposite for the rate of heat transfer at the wall.
75 citations
TL;DR: In this article, a more detailed 2D numerical model was developed using a laser scanner system with a spacing grid of 0.1mm, and the results of the procedure for shear displacement simulation illustrate the distribution of the absolute velocity and pressure drop under the constant pressure gradient.
Abstract: Extensive research has shown that fluid flow through rock fractures is greatly influenced by surface roughness. For a single rock fracture, the roughness of the upper and bottom surfaces is the same in the initial condition and then its deformation occurs with normal stress and shear stress imposed on the natural rock. Previous researchers have paid considerable attention to describing the roughness of the single fracture and its effects on fluid flow. However, few studies have explained the fluid flow with shear displacement and the direction of the fluid flow velocity field. In this work, a more detailed 2D numerical model was developed using a laser scanner system with a spacing grid of 0.1 mm. To investigate the influence of shear displacement accurately, the COMSOL multiphase codes were applied. By applying the Navier–Stokes equations, the results of the procedure for shear displacement simulation illustrate the distribution of the absolute velocity and pressure drop under the constant pressure gradient. The velocities predicted at the vertical profiles of the inlet were similar to the parabolic velocity curve defined by the cubic laws. The mean mechanical aperture was usually larger than the hydraulic aperture from the measured flow rates, and a devised empirical equation was proposed to describe the relationship between the mechanical aperture and the hydraulic aperture values. The recirculation zones observed in directional fluid flow during shear explain the anisotropy of roughness of a single fracture, and the phenomenon argues the applicability of local cubic laws which overestimate the total fluid flow rate.
68 citations
TL;DR: In this paper, the influence of gap between parallel plates, surface texture of the bottom plate, and mixing intensity on the yield stress and plastic viscosity of cementitious suspensions extracted using the Bingham model was investigated.
Abstract: This paper investigates the influence of gap between parallel plates, surface texture of the bottom plate, and mixing intensity on the yield stress and plastic viscosity of cementitious suspensions extracted using the Bingham model. Special emphasis is paid toward understanding the effects of shear rate range and different rheological models on the flow parameters. It is shown that the use of a wider shear rate range (0.1–100/s), can be beneficial in obtaining a reasonable portion of the stress plateau in the shear stress–shear rate relationship, which facilitates a model-less, yet accurate extraction of yield stress. The Bingham model that considers only the linear region (i.e. ∼5–100/s) overestimates the yield stress as indicated by the stress asymptote while the Herschel–Bulkley (H–B) equation applied in the 0.1–100/s shear rate range underestimates the yield stress. Further lowering the evaluated shear rate range (i.e. 0.005–100/s) does substantially improve the H–B prediction of yield stress.
54 citations
TL;DR: In this paper, the effect of concentration of the three main components of a novel environmentally friendly lightweight CGA based drilling fluid, i.e., xanthan gum biopolymer, starch, and biosurfactant, to the Herschel-Bulkley rheological model parameters was investigated.
Abstract: The proper understanding of rheological characteristics of CGA based fluids is of crucial importance in determining the performance of the fluid, in order to maintain the most effective fluid properties for safe, efficient, and economical drilling operation. This paper presents a concise investigation on the effect of concentration of the three main components of a novel environmentally friendly lightweight CGA based drilling fluid, i.e., xanthan gum biopolymer, starch, and biosurfactant, to the Herschel–Bulkley rheological model parameters. The three parameters of Herschel–Bulkley model, i.e., yield stress, fluid consistency, and fluid flow index were calculated by fitting the experimental data of shear stress as a function of rate of shear to the model. Results of data fitting analysis show that Herschel–Bulkley model performs satisfactorily well in describing the rheological behavior of CGA based fluids with R2 greater than 0.99. Moreover, experimental results indicate that the increment of the amount of three main components increase the yield stress of the final CGA based fluid as the flow resistance is increased. Furthermore, the result also showed that the calculated fluid consistency of the drilling fluid appears to be strongly dependent on the presence of xanthan gum and starch. However, the fluid consistency appears not to be affected by the presence of salt. It is also concluded that the formulated CGA based fluids have shear-thinning behaviors with values of fluid flow indices (n) 0.2–0.3. The results of this study can be helpful in determining the appropriate procedure for utilizing the CGA based fluids in oilfield operations.
51 citations
TL;DR: In this article, the entropy generation rate in the flow and heat transfer of hydromagnetic third grade fluid between horizontal parallel plates saturated with porous materials was studied, and the effect of various flow parameters on the fluid flow was presented graphically and discussed.
Abstract: In this work, analysis has been carried out to study the entropy generation rate in the flow and heat transfer of hydromagnetic third grade fluid between horizontal parallel plates saturated with porous materials. The flow is induced by a constant pressure gradient applied in the flow direction and also influenced by a uniform magnetic field that is applied across the flow channel. The equations governing the fluid flow are modeled, non-dimensionalized and solved analytically using regular perturbation method. The effect of various flow parameters on the fluid flow is presented graphically and discussed.
50 citations
TL;DR: In this paper, the rheological properties of suspensions of bubbles in yield stress fluids are investigated through experiments on model systems made of monodisperse bubbles dispersed in concentrated emulsions.
Abstract: The rheological properties of suspensions of bubbles in yield stress fluids are investigated through experiments on model systems made of monodisperse bubbles dispersed in concentrated emulsions. Thanks to this highly tunable system, the bubble size and the rheological properties of the suspending yield stress fluid are varied over a wide range. We show that the macroscopic response under shear of the suspensions depends on the gas volume fraction and the bubble stiffness in the suspending fluid. This relative stiffness can be quantified through capillary numbers comparing the capillary pressure to stress scales associated with the rheological properties of the suspending fluid. We demonstrate that those capillary numbers govern the decrease of the elastic and loss moduli, the absence of variation of the yield stress and the increase of the consistency with the gas volume fraction, for the investigated range of capillary numbers. Micro-mechanical estimates are consistent with the experimental data and provide insight on the experimental results.
47 citations
TL;DR: In this article, published values of rheological properties of fruit and vegetable-based products are presented, concerning shear stress, consistency coefficient, flow behavior index, Bingham plastic viscosity, and activation energy as function of soluble solids content and temperature.
Abstract: Recently, published values of rheological properties of fruit- and vegetable-based products are presented, concerning shear stress, consistency coefficient, flow behaviour index, Bingham plastic viscosity, and activation energy as function of soluble solids content and temperature. The Herschel–Bulkley model was used to describe most of the products showing a pseudoplastic behaviour, whilst the Power law and the Bingham model were successfully fitted to the others. The clarified and depectinated fruit juices as well as carrot juice showed a Newtonian behaviour.
46 citations
TL;DR: The steady two-dimensional flow of Powell-Eyring fluid is investigated in this article, where the governing nonlinear differential equations are reduced to the ordinary differential equations by similarity transformations.
Abstract: The steady two-dimensional flow of Powell-Eyring fluid is investigated. The flow is caused by a stretching surface with homogeneous-heterogeneous reactions. The governing nonlinear differential equations are reduced to the ordinary differential equations by similarity transformations. The analytic solutions are presented in series forms by homotopy analysis method (HAM). Convergence of the obtained series solutions is explicitly discussed. The physical significance of different parameters on the velocity and concentration profiles is discussed through graphical illustrations. It is noticed that the boundary layer thickness increases by increasing the Powell-Eyring fluid material parameter (e) whereas it decreases by increasing the fluid material parameter (δ). Further, the concentration profile increases when Powell-Eyring fluid material parameters increase. The concentration is also an increasing function of Schmidt number and decreasing function of strength of homogeneous reaction. Also mass transfer rate increases for larger rate of heterogeneous reaction.
TL;DR: In this paper, the authors investigated Rayleigh-Benard convection in a viscoplastic fluid prepared from Carbopol (Ultrez 20) gel using temperature-dependent rheological properties.
Abstract: The intent of the present work is to investigate Rayleigh–Benard convection in a viscoplastic fluid prepared from Carbopol (Ultrez 20) gel. Thermorheological characterization of the test fluid has been presented and rheological properties are represented by Herschel–Bulkley model. Further, temperature dependency of rheological parameters is described by Arrhenius model. Rayleigh–Benard convection phenomenon in a square enclosure filled with viscoplastic fluid has been investigated numerically as well as experimentally. The proposed computational model uses the temperature-dependent rheological properties. Results of the proposed model show a fair agreement with our own experimental data. Use of temperature-dependent rheological properties has improved the predictions significantly. With the increase in yield stress, there is a phenomenal change in diminishing convective flow patterns. Critical Rayleigh number representing the onset of convection has been determined for different concentrations of the gel. Nusselt number correlations as a function of Rayleigh number and yield number have been developed for two different values of Prandtl number.
TL;DR: The results suggest that the Newtonian approximation can accurately model wall shear stress in the aortic flow of blood; however, for other variables (e.g. mean velocity) the shear-thinning model is more appropriate.
Abstract: The effects of percentage stenosis and Reynolds number (Re) on steady flow, and Womersley number (Wo) on pulsatile flow, of blood through a two-dimensional channel with stenosis are investigated, and the results are compared with the Newtonian case. We model blood using the shear-thinning relation proposed by Yeleswarapu, while the stenosis is approximated using a cosine-shaped taper. The vorticity–streamfunction formulation of the flow equations is solved using a finite difference scheme in conjunction with a full-multigrid algorithm that reduces computational time. The presence of stenosis leads to a recirculation zone immediately downstream of the stenosis. In steady flow, the shear-thinning fluid predicts higher peak wall shear stress than the Newtonian fluid: the difference between the predictions, expressed as a percentage of the Newtonian wall shear stress, decreases as percentage stenosis and Reynolds number increase. For a given percentage stenosis and Reynolds number, the percentage difference between the shear-thinning fluid and Newtonian fluid decreases, and remains negligible, as the Womersley number increases (corresponding to increasing pulsatile nature of the flow). This suggests that the Newtonian approximation can accurately model wall shear stress in the aortic flow of blood; however, for other variables (e.g. mean velocity) the shear-thinning model is more appropriate.
01 Mar 2015
TL;DR: In this paper, a more realistic model for the carbon nanotube conveying viscous fluid which is embedded in a visco-elastic medium, the effect of viscosity of the medium surrounding the CNT has been investigated.
Abstract: In this paper, considering a more realistic model for the carbon nanotube (CNT) conveying viscous fluid which is embedded in a visco-elastic medium, the effect of viscosity of the medium surrounding the CNT has been investigated. By taking into account the influence of the fluid viscosity and using the Navier-Stokes equations, the governing equation of motion has been derived and a new analytical technique based on the power series is presented for its vibration analysis. The frequency equation of the system is obtained by applying the boundary conditions. The influence of the medium parameters and the fluid viscosity on the natural frequencies of the CNT has been studied. The results show that the medium damping has a marked effect on the natural frequencies and the critical fluid velocity. Furthermore, by increasing the fluid viscosity, the natural frequencies and the critical fluid velocity increase. There is a good agreement between the results obtained through the proposed method and the data reporte...
TL;DR: In this paper, a multiphase lattice Boltzmann method was used to model the pressure-driven displacement of a non-Newtonian fluid by a Newtonian fluid in a two-dimensional channel.
Abstract: The pressure-driven displacement of a non-Newtonian fluid by a Newtonian fluid in a two-dimensional channel is investigated via a multiphase lattice Boltzmann method using a non-ideal gas equation of state well-suited for two incompressible fluids. The code has been validated by comparing the results obtained using different regularized models, proposed in the literature, to model the viscoplasticity of the displaced material. Then, the effects of the Bingham number, which characterizes the behaviour of the yield-stress of the fluid and the flow index, which reflects the shear-thinning/thickening tendency of the fluid, are studied. It was found that increasing the Bingham number and increasing the flow index increases the size of the unyielded region of the fluid in the downstream portion of the channel and increases the thickness of the residual layer of the fluid resident initially in the channel; the latter is left behind on the channel walls by the propagating ‘finger’ of the displacing fluid. This, in turn, reduces the growth rate of interfacial instabilities and the speed of finger propagation.
TL;DR: An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids.
Abstract: An analysis of blood flow through a tapered artery with stenosis and dilatation has been carried out where the blood is treated as incompressible Herschel-Bulkley fluid. A comparison between numerical values and analytical values of pressure gradient at the midpoint of stenotic region shows that the analytical expression for pressure gradient works well for the values of yield stress till 2.4. The wall shear stress and flow resistance increase significantly with axial distance and the increase is more in the case of converging tapered artery. A comparison study of velocity profiles, wall shear stress, and flow resistance for Newtonian, power law, Bingham-plastic, and Herschel-Bulkley fluids shows that the variation is greater for Herschel-Bulkley fluid than the other fluids. The obtained velocity profiles have been compared with the experimental data and it is observed that blood behaves like a Herschel-Bulkley fluid rather than power law, Bingham, and Newtonian fluids. It is observed that, in the case of a tapered stenosed tube, the streamline pattern follows a convex pattern when we move from r/R = 0 to r/R = 1 and it follows a concave pattern when we move from r/R = 0 to r/R = -1. Further, it is of opposite behaviour in the case of a tapered dilatation tube which forms new information that is, for the first time, added to the literature.
TL;DR: In this article, the effect of the xanthan gum concentration on the flow nonideality in a continuous-flow mixer was investigated using the Herschel-Bulkley model, and the results revealed that the mixing effectiveness of the mixer was enhanced by decreasing the consistency index, decreasing the fluid yield stress, enhancing the residence time of the fluid in the tank, and reducing the solution mass concentration.
Abstract: A novel study on exploring the effect of the rheological parameters of the yield-pseudoplastic fluids on the non-ideal flows in a continuous-flow mixer was performed The rheological behavior of the xanthan gum solution, a yield-pseudoplastic fluid, was modeled by the Herschel–Bulkley model In fact, varying the xanthan gum concentration changes the values of all rheological parameters (ie consistency index (K), power law index (n) and fluid yield stress (τy)) simultaneously Thus, merely studying the effect of the xanthan gum concentration on the flow nonideality represents the combined effect of all Herschel–Bulkley model parameters The core objective of this research was to investigate the effects of K (3–33 Pa sn), n (011–099), τy (17–206 Pa), xanthan gum mass concentration (05–15 w/v%), and feed flow rate (Q) (0320–1417 L min−1) on the percentage of channeling (f) and fully mixed volume (Vfully mixed/Vtotal) in the continuous-flow reactor through computational fluid dynamics (CFD) The validated CFD model predicted that the percentage of the parameter f increased and Vfully mixed/Vtotal decreased as n was increased from 011 to 099 This result revealed that the mixing was improved when the extent of the shear thinning was increased Moreover, the mixing effectiveness of the continuous-flow mixer was enhanced by decreasing the consistency index, decreasing the fluid yield stress, enhancing the residence time of the fluid in the tank (TR), and the reducing the solution mass concentration
TL;DR: In this paper, a numerical scheme for fluid-particle coupled discrete element method (DEM), which is based on poro-elasticity, is presented, and the numerical results showed very good agreement with the analytical solutions, which show the correctness of this algorithm.
Abstract: Summary
This paper presents a numerical scheme for fluid-particle coupled discrete element method (DEM), which is based on poro-elasticity. The motion of the particles is resolved by means of DEM. While within the proposition of Darcian regime, the fluid is assumed as a continuum phase on a Eulerian mesh, and the continuity equation on the fluid mesh for a compressible fluid is solved using the FEM. Analytical solutions of traditional soil mechanics examples, such as the isotropic compression and one-dimensional upward seepage flow, were used to validate the proposed algorithm quantitatively. The numerical results showed very good agreement with the analytical solutions, which show the correctness of this algorithm. Sensitivity studies on the effect of some influential factors of the coupling scheme such as pore fluid bulk modulus, volumetric strain calculation, and fluid mesh size were performed to display the accuracy, efficiency, and robustness of the numerical algorithm. It is revealed that the pore fluid bulk modulus is a critical parameter that can affect the accuracy of the results. Because of the iterative coupling scheme of these algorithms, high value of fluid bulk modulus can result in instability and consequently reduction in the maximum possible time-step. Furthermore, the increase of the fluid mesh size reduces the accuracy of the calculated pore pressure. This study enhances our current understanding of the capacity of fluid-particle coupled DEM to simulate the mechanical behavior of saturated granular materials. Copyright © 2014 John Wiley & Sons, Ltd.
TL;DR: In this paper, a simple, reliable, and cost-effective artificial neural network (ANN) method was used to predict pressure losses for non-Newtonian drilling fluids inside annulus, and the average relative error was less than 5% with correlation coefficient (R) of 0.999.
Abstract: Accurate estimation of the pressure losses for non-Newtonian drilling fluids inside annulus is quite important to determine pump rates and select mud pump systems during drilling operations. Therefore, in this study, pressure losses of Herschel–Bulkley drilling fluids in concentric and eccentric annulus are predicted using simple, reliable, and cost-effective artificial neural network (ANN) method. The average relative error was less than 5% with correlation coefficient (R) of 0.999 for the prediction of pressure loss (ΔP) taking the ratio of pipe diameter to casing diameter (D i /D o ), eccentricity of annulus (ϵ), and properties of the non-Newtonian liquid, that is, flow behavior index (n), consistency index (K), yield stress (τ y ), and liquid flow rate (Q) as inputs to an ANN for Herschel–Bulkley fluids. Experimental data from the literature were used to train the ANN for predicting pressure losses in eccentric annuli.
TL;DR: In this paper, the peristaltic transport of a non-Newtonian viscous fluid in an elastic tube was investigated using the assumptions of long wavelength and low Reynolds number approximations.
Abstract: In this paper, we investigate the peristaltic transport of a non-Newtonian viscous fluid in an elastic tube. The governing equations are solved using the assumptions of long wavelength and low Reynolds number approximations. The constitution of blood has a non-Newtonian fluid model and it demands the yield stress fluid model: The blood transport in small blood vessels is done under peristalsis. Among the available yield stress fluid models for blood flow, the non-Newtonian Herschel–Bulkley fluid is preferred (because Bingham, power-law and Newtonian models can be obtained as its special cases). The Herschel–Bulkley model has two parameters namely the yield stress and the power-law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flow rate are derived. The flux is determined as a function of inlet, outlet, external pressures, yield stress, amplitude ratio, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress and in the absence of peristalsis, our results agree with Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress, peristaltic wave, and the elastic parameters have strong effects on the flux of the non-Newtonian fluid flow. Effects of various wave forms (namely, sinusoidal, trapezoidal and square) on the flow are discussed. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.
TL;DR: In this article, a model is developed for suspensions of rigid fibers in a non-Newtonian fluid exhibiting a yield stress by taking into account hydrodynamic and fiber-fiber interactions.
Abstract: A model is developed for suspensions of rigid fibers in a non-Newtonian fluid exhibiting a yield stress by taking into account hydrodynamic and fiber–fiber interactions. To be applied to fiber-reinforced viscoplastic fluids such as cementitious pastes or mortars, the matrix behavior is described by a Herschel–Bulkley law. The model is able to predict shear thinning and shear thickening behaviors as well as anisotropic yield stress depending on the fiber orientation. The extra stress term involves structural tensors, where exact analytical solutions have been proposed for an isotropic fiber orientation in simple shear flow. The model predictions show a good agreement with the yield stress values of steel fibers dispersed in kaolin pastes.
TL;DR: In this article, peristaltic mechanisms in a two dimensional nonuniform channel filled with Herschel-Bulkley fluid were investigated under the assumptions of long-wavelength and low-Reynolds-number approximation.
Abstract: Abstract In this article, we have investigated peristaltic mechanisms in a two dimensional nonuniform channel filled with Herschel–Bulkley fluid. Problem is studied under the assumptions of long-wavelength and low-Reynolds-number approximation. The fluid flow is investigated in the wave frame of reference moving with the velocity of the peristaltic wave in a channel. Exact solutions for the velocity field, temperature profile, stream functions, and pressure gradient are obtained and illustrated graphically for different parameters of interest such as α (angle of inclination), τ (the ratio of yield stress), φ (amplitude ratio), Pr (Prandtl number), and Q (mean flow rate) etc.
TL;DR: In this paper, a frequency-dependent dynamic fluid modulus (DFM) was developed to understand the velocity dispersion and wave attenuation due to wave-induced fluid flow.
Abstract: Based on poroelasticity analysis, we developed a new concept of frequency-dependent dynamic fluid modulus (DFM) to understand the velocity dispersion and wave attenuation due to wave-induced fluid flow. Conventional applications of Gassmann’s equation require a complete homogeneity inside the porous media (or equivalently, at zero frequency) and closed boundary condition. We first analyzed the fluid effect on the bulk modulus in homogeneous porous media with a nonclosed condition. The partial drainage of pore fluid causes additional pore volume change under applied stress. An incoming fluid flow stiffens the porous system, and an outgoing flow softens it. Such a phenomenon can still be effectively formulated as a closed system with Gassmann’s equation, by introducing a DFM, which adds a flow term into the original fluid modulus. We further proved that in heterogeneous porous media, the wave-induced internal fluid flow caused additional bulk volume deformation. It equals the amount of the fluid flo...
TL;DR: In this paper, the radiation and chemical reaction effects on non-Newtonian fluid towards a porous stretching surface in the presence of thermal and hydrodynamic slip conditions were investigated, and the governing boundary layer conservation equations were normalized into nonsimilar form using similarity transformations.
Abstract: This paper investigates the radiation and chemical reaction effects on Casson non-Newtonian fluid towards a porous stretching surface in the presence of thermal and hydrodynamic slip conditions. The governing boundary layer conservation equations are normalized into nonsimilar form using similarity transformations. A numerical approach is applied to the resultant equations. The behavior of the velocity, temperature, concentration, as well as the skin friction coefficient, Nusselt number, and Sherwood number for various governing physical are discussed. Increasing the radiation parameter decreases the temperature. An increase in the rheological parameter (Casson parameter) induces an elevation in the skin friction coefficient, the heat and mass transfer rates. The larger the β values the closer the fluid is in behavior to a Newtonian fluid and further departs from plastic flow. Temperature of the fluid was found to decrease with increasing values of the Casson rheological parameter. The most important non-Newtonian fluid possessing a yield value is the rheological Casson fluid, which finds significant applications in polymer processing industries, biomechanics, and chocolate food processing.
TL;DR: In this article, the authors investigate core annular flow (CAF) using computational techniques for the case in which the core fluid is non-Newtonian and the annular fluid is Newtonian.
TL;DR: In this paper, the simultaneous effects of heat and mass transfer on the peristaltic transport of an electrically conducting couple-stress fluid in a compliant walls channel were analyzed.
Abstract: Analysis is performed for the simultaneous effects of heat and mass transfer on the peristaltic transport of an electrically conducting couple-stress fluid in a compliant walls channel. The study may be useful in understanding the physiological flow of blood through micro-circulatory system in the presence of particle-size effect. Long wavelength and low Reynolds number aspects are taken into consideration. Exact solutions for stream function, temperature and concentration are derived. Impact of pertinent parameters like the couple-stress fluid parameter (γ), Hartman number (M), amplitude ratio (ϵ), elastic parameters (E1, E2, E3, E4, E5), Brinkman number (Br) and Schmidt number (Sc). It is observed that velocity and temperature distributions are greater for couple stress fluid when compared with the Newtonian fluid.
TL;DR: Adopting the lubrication theory, highly nonlinear coupled governing equations involving power law index as an exponent have been linearized and perturbation solutions are obtained about the Sisko fluid parameter.
Abstract: This paper looks at the effects of radiative heat transfer on the peristaltic transport of a Sisko fluid in an asymmetric channel with nonuniform wall temperatures. Adopting the lubrication theory, highly nonlinear coupled governing equations involving power law index as an exponent have been linearized and perturbation solutions are obtained about the Sisko fluid parameter. Analytical solutions for the stream function, axial pressure gradient, axial velocity, skin friction, and Nusselt number are derived for three different cases (i.e., shear thinning fluid, viscous fluid, and shear thickening fluid). The effects of Grashof number, radiation parameter, and other configuration parameters on pumping, trapping, temperature, Nusselt number, and skin friction have been examined in detail. A good agreement has been found for the case of viscous fluid with existing results.
TL;DR: In this article, the estimation of wall shear rates for yield stress fluids using rotating coaxial-cylinder viscometer readings is presented, based on the generalized difference equation for rotating narrow gap coaxial cylinder Fann Viscometer under purely steady, laminar and isothermal tangential fluid flow condition.
TL;DR: In this article, numerical analysis of non-Newtonian effects on the vortex flow mechanism was presented, where the authors used Reynolds stress turbulence model (RSM) and mixed multiphase flow model (Mixture) of FLUENT (fluid calculation software) and combined with the constitutive equation of apparent viscosity of nonnewtonian fluid.
TL;DR: The fractional calculus approach is employed in the constitutive relationship of the fluid model and the Darcy's law, and an exact solution of the model is obtained in term of Fox’s H -function.
Abstract: In this paper, the fractional calculus approach is employed in the constitutive relationship of the fluid model and the Darcy’s law. The flow of the fractional Jeffreys’ fluid induced by the impulsive motion of a flat plate in a porous half space is studied in form of an initial and boundary value problem with fractional derivatives. Using the Laplace transform method, we obtain an exact solution of the model in term of Fox’s H -function. As a byproduct, the solutions of the analogous flow for the generalized second grade fluid, the fractional Maxwell fluid and the Newtonian fluid in the porous half space are also deduced. In addition, the influence of the material parameters and the fractional parameters on the fluid motion is investigated, as well as a comparison among the fractional Jeffreys’ fluid, the fractional Maxwell fluid and the Newtonian fluid in porous medium is also analyzed by graphical illustrations.