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This paper aims to investigate the aspect ratio (AR; ratio of enclosure height:length) dependence of steady-state Rayleigh–Bénard convection of Bingham fluids within rectangular enclosures for both constant wall temperature and constant wall heat flux boundary conditions. A nominal Rayleigh number range 103 ≤ Ra ≤ 10⁵ (Ra defined based on the height) for a single representative value of nominal Prandtl number (i.e. Pr = 500) has been considered for 1/4 ≤ AR ≤ 4.

The bi-viscosity Bingham model is used to mimic Bingham fluids for Rayleigh–Bénard convection of Bingham fluids in rectangular enclosures. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.

It has been found that buoyancy-driven flow strengthens with increasing nominal Rayleigh number Ra, but the convective transport weakens with increasing Bingham number Bn, because of additional flow resistance arising from yield stress in Bingham fluids. The relative contribution of thermal conduction (advection) to the total thermal transport strengthens (diminishes) with increasing AR for a given set of values of Ra and Pr for both Newtonian and Bingham fluids for both boundary conditions, and the thermal transport takes place purely because of conduction for tall enclosures.

Correlations for the mean Nusselt number Nu ¯ have been proposed for both boundary conditions for both Newtonian and Bingham fluids using scaling arguments, and the correlations have been demonstrated to predict Nu ¯ obtained from simulation data for 1/4 ≤ AR ≤ 4, 10³ ≤ Ra ≤ 10⁵ and Pr = 500.

The purpose of this paper is to analyze two-dimensional steady-state Rayleigh–Bénard convection within rectangular enclosures in different aspect ratios filled with yield stress fluids obeying the Herschel–Bulkley model.

In this study, a numerical method based on the finite element has been developed for analyzing two-dimensional natural convection of a Herschel–Bulkley fluid. The effects of Bingham number Bn and power law index n on heat and momentum transport have been investigated for a nominal Rayleigh number range (5 × 10³ < Ra < 10⁵), three different aspect ratios (ratio of enclosure length:height AR = 1, 2, 3) and a single representative value of nominal Prandtl number (Pr = 10).

Results show that the mean Nusselt number Nu¯ increases with increasing Rayleigh number due to strengthening of convective transport. However, with the same nominal value of Ra, the values of Nu¯ for shear thinning fluids n < 1 are greater than shear thickening fluids n > 1. The values of Nu¯ decrease with Bingham number and for large values of Bn, Nu¯ rapidly approaches unity, which indicates that heat transfer takes place principally by thermal conduction. The effects of aspect ratios have also been investigated and results show that Nu¯ increases with increasing AR due to stronger convection effects.

This paper presents a numerical study of Rayleigh–Bérnard flows involving Herschel–Bulkley fluids for a wide range of Rayleigh numbers, Bingham numbers and power law index based on finite element method. The effects of aspect ratio on flow and heat transfer of Herschel–Bulkley fluids are also studied.

The purpose of this paper is to analyze the natural convection of a yield stress fluid in a square enclosure with differentially heated side walls. In particular, the Casson model is considered which is a commonly used model.

The coupled conservation equations of mass, momentum and energy related to the two-dimensional steady-state natural convection within square enclosures are solved numerically by using the Galerkin's weighted residual finite element method with quadrilateral, eight nodes elements.

Results highlight a small degree of the shear-thinning in the Casson fluids. It is shown that the yield stress has a stabilizing effect since the convection can stop for yield stress fluids while this is not the case for Newtonian fluids. The heat transfer rate, velocity and Yc obtained with the Casson model have the smallest values compared to other viscoplastic models. Results highlight a weak dependence of Yc with the Rayleigh number: Yc∼Ra0.07. A supercritical bifurcation at the transition between the convective and the conductive regimes is found.

The originality of the present study concerns the comprehensive and detailed solutions of the natural convection of Casson fluids in square enclosures with differentially heated side walls. It is shown that there exists a major difference between the cases of Casson and Bingham models, and hence using the Bingham model for analyzing the viscoplastic behavior of the fluids which follow the Casson model (such as blood) may not be accurate. Finally, a correlation is proposed for the mean Nusselt number Nu¯.

This work is concerned with computational modelling of viscoplastic fluids. The flows considered are assumed to be incompressible, while the viscoplastic laws are obtained by incorporating a yield stress below which the fluid is assumed to remain non‐deformable. The Bingham fluid is chosen as a model problem and is considered in detail in the text. The finite element formulation adopted in this work is based on a version of the stabilised finite element method, known as the Galerkin/least‐squares method, originally developed by Hughes and co‐workers. This methodology allows use of low and equal order interpolation of the pressure and velocity fields, thus providing an efficient finite element framework. The Newton‐Raphson method has been chosen for solution of the incremental non‐linear problem arising through the temporal discretisation of the evolution problem. Numerical examples are provided to illustrate the main features of the described methodology.

This study aims on a broad review of Concrete's Rheological Properties. The Concrete is a commonly used engineering material because of its exquisite mechanical interpretation, but the addition of constituent amounts has significant effects on the concrete’s fresh properties. The workability of the concrete mixture is a short-term property, but it is anticipated to affect the concrete’s long-term property.

In this review, the concrete and workability definition; concrete’s rheology models like Bingham model, thixotropy model, H-B model and modified Bingham model; obtained rheological parameters of concrete; the effect of constituent’s rheological properties, which includes cement and aggregates; and the concrete’s rheological properties such as consistency, mobility, compatibility, workability and stability were studied in detail.

Also, this review study has detailed the constituents and concrete’s rheological properties effects. Moreover, it exhibits the relationship between yield stress and plastic viscosity in concrete’s rheological behavior. Hence, several methods have been reviewed, and performance has been noted. In that, the abrasion resistance concrete has attained the maximum compressive strength of 73.6 Mpa; the thixotropy approach has gained the lowest plastic viscosity at 22 Pa.s; and the model coaxial cylinder has recorded the lowest stress rate at 8 Pa.

This paper especially describes the possible strategies to constrain improper prediction of concrete’s rheological properties that make the workability and rheological behavior prediction simpler and more accurate. From this, future guidelines can afford for prediction of concrete rheological behavior by implementing novel enhancing numerical techniques and exploring the finest process to evaluate the workability.

The purpose of this study is to solve convective diffusion equation analytically by considering appropriate boundary conditions and using the Taylor-Aris method to determine the solute concentration, the effective and relative axial diffusivities.

>An analysis has been conducted on how body acceleration affects the dispersion of a solute in blood flow, which is known as a Bingham fluid, within an artery. To solve the system of differential equations analytically while validating the target boundary conditions, the blood velocity is obtained.

The blood velocity is impacted by the presence of body acceleration, as well as the yield stress associated with Casson fluid and as such, the process of dispersing the solute is distracted. It graphically illustrates how the blood velocity and the process of solute dispersion are affected by various factors, including the amplitude and lead angle of body acceleration, the yield stress, the gradient of pressure and the Peclet number.

It is witnessed that the blood velocity, the solute concentration and also the effective and relative axial diffusivities experience a drop when either of the amplitude, lead angle or the yield stress rises.

The purpose of this paper is to present experimental research on the behaviour of a new electrorheological fluid (ETSERF).

The ETSERF is a suspension based on diatomite powders dispersed in silicon oil with a surfactant. A design of experiments is conducted to investigate the effects of electric field strength, particle concentration, surfactant percentage, particle size and shear rate on the efficiency of ETSERFs. The influence of the interactions on shear stresses is analyzed by varying all the combinations of the independent variables. The dielectric properties of the ETSERF are investigated in order to explain the interactions between these independent variables. Furthermore, a quantitative relationship between the dynamic shear stresses and the independent variables is developed.

The relationship provides a very useful explanation for the contributions of each independent variable to the viscosity and yield stress.

A new empirical model is proposed to explain the rheological behaviour of the ER fluids with a shear‐thinning behaviour.

This paper sets out to present a fully explicit smoothed particle hydrodynamics (SPH) method to solve non‐Newtonian fluid flow problems.

The governing equations are momentum equations along with the continuity equation which are described in a Lagrangian framework. A new treatment similar to that used in Eulerian formulations is applied to viscous terms, which facilitates the implementation of various inelastic non‐Newtonian models. This approach utilizes the exact forms of the shear strain rate tensor and its second principal invariant to calculate the shear stress tensor. Three constitutive laws including power‐law, Bingham‐plastic and Herschel‐Bulkley models are studied in this work. The imposition of the incompressibility is fulfilled using a penalty‐like formulation which creates a trade‐off between the pressure and density variations. Solid walls are simulated by the boundary particles whose positions are fixed but contribute to the field variables in the same way as the fluid particles in flow field.

The performance of the proposed algorithm is assessed by solving three test cases including a non‐Newtonian dam‐break problem, flow in an annular viscometer using the aforementioned models and a mud fluid flow on a sloping bed under an overlying water. The results obtained by the proposed SPH algorithm are in close agreement with the available experimental and/or numerical data.

In this work, only inelastic non‐Newtonian models are studied. This paper deals with 2D problems, although extension of the proposed scheme to 3D is straightforward.

This study shows that various types of flow problems involving fluid‐solid and fluid‐fluid interfaces can be solved using the proposed SPH method.

Using the proposed numerical treatment of viscous terms, a unified and consistent approach was devised to study various non‐Newtonian flow models.

According to the research, viscoplastic fluids are sensitive to slipping. The purpose of this study is to determine whether slip affects the Rayleigh–Bénard convection of viscoplastic fluids in cavities and, if so, under what conditions.

The wall slip was evaluated using a model created for viscoplastic (Bingham) fluids. The coupled conservation equations were solved numerically using the finite element method. Simulations were performed for various parameters: the Rayleigh number, yield number, slip yield number and friction number.

Wall slip determines two essential yield stresses: a specific yield stress value beyond which wall slippage is impossible (S_Yc); and a maximum yield stress beyond which convective flow is impossible (Y_c). At low Rayleigh numbers, Y_c is smaller than S_Yc. Hence, the flow attained a stable (conduction) condition before achieving the no-slip condition. However, for more significant Rayleigh numbers Y_c exceeded S_Yc. Thus, the flow will slip at low yield numbers while remaining no-slip at high yield numbers. The possibility of slipping on the wall increases the buoyancy force, facilitating the onset of Rayleigh–Bénard convection.

An essential aspect of this study lies in its comprehensive examination of the effect of slippage on the natural convection flow of viscoplastic materials within a cavity, which has not been previously investigated. This research contributes to a new understanding of the viscoplastic fluid behavior resulting from slipping.

The purpose of this paper is to obtain a constitutive model of cement-based material in the rheological stage, which owns the different water-cement ratio (w/c) and temperature and have a significant impact on the workability of concrete materials.

It is introduced a modified Arrhenius equation into the Herschel–Bulkley model, which is widely applied in rheological analysis and constructed an ordinary differential equation (ODE) of w/c from the Navier–Stokes equation. By solving the ODE, an approximate constitutive relation of cement-based materials included w/c and temperature is derived. Compared with the experimental results, the present model is validated.

The shear stress and shear rate curves with different w/c and temperature are simulated by the present method, and the present model can be applied to analyze the changes of apparent viscosity in cement-based material slurry as the w/c and temperature varying.

This work gives a mathematical model, which can effectively approximate the shear stress–shear rate relation with different w/c and temperature in the rheological stage of cement-based material.