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The purpose of this paper is to investigate the combined effects of slip and rheological parameters on the flow and heat transfer of the Herschel-Bulkley fluid.

The combinative dimensionless parameter method is introduced into the equations of the slip flow and heat transfer to make the discussion more comprehensive. More specifically, the slip and rheological parameters are transformed into the dimensionless slip number as well as Herschel-Bulkley number. We solve the dimensionless equations and then focus on the effects of these parameters on the slip flow and heat transfer.

The results show that, for a given value of Herschel-Bulkley number, there is a finite critical value of slip number at which the pressure gradient reaches the lowest value and both the dimensionless yield radius and slip velocity become 1. Meanwhile, the Nusselt number tends to be infinite at this critical value of slip number. For the case of slip, the Nusselt number also approaches infinity at a finite critical value of Herschel-Bulkley number. Furthermore, the dimensionless velocity as well as temperature of the yield pseudoplastic fluid with higher slip number is lower within a small radius but becomes higher near the wall. Meanwhile, from the velocity and temperature profiles, the effect of Herschel-Bulkley number on these two parameters of the Bingham fluid at the smaller radius is opposite.

These associated expressions can be generalized to the flow and heat transfer of a Herschel-Bulkley fluid under slip boundary condition. It can provide a reference for the engineering application relating to the heat transfer and flow of a Herschel-Bulkley fluid. Meanwhile, it also suggests some revelations for dealing with this similar problem.

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 screw extruder is applied in cement-three-dimensional (3D) printing. The cement paste flow in 3D printing is the typical Herschel–Bulkley fluid. To understand the flow in the channel, the improved lattice Boltzmann method (LBM) is proposed.

For Herschel–Bulkley flow, an improved LBM is presented to avoid the poor stability and accuracy. The non-Newtonian effect is regard as a special forcing term. The Poiseuille flow is taken to discuss the detailed process of the method. With the method, the analytical solution and numerical solution are obtained and compared. Then, the effect of the initial yield stress on the numerical solution is both explored by the shear-thickening fluid and the shear-thinning fluid. Moreover, the variations of the relative errors under different lattice nodes and different power-law indexes are analyzed. Finally, the method is applied into the simulation of the flow in the extruder of cement-3D printing.

The results show that the improved method is effective for Herschel–Bulkley fluids, which can simulate the flow in the extruder stably and accurately.

The simulation can contribute to understand the cement paste flow in the screw extruder, which helps to optimize the structure of the extruder in the following periods.

The improve method provide a new way to analyze the flow in the extruder of cement-3D printing. Also, in the past research, LBM for Herschel–Bulkley fluid is ignored, whereas the study can provide the reference for the numerical simulation.

This paper is concerned with the peristaltic transport of an incompressible non-Newtonian fluid in a porous elastic tube. The impacts of slip and heat transfer on the Herschel-Bulkley fluid are considered. The impacts of relevant parameters on flow rate and temperature are examined graphically. The examination incorporates Newtonian, Power-law and Bingham plastic fluids. The paper aims to discuss these issues.

The administering equations are solved utilizing long wavelength and low Reynolds number approximations, and exact solutions are acquired for velocity, temperature, flux and stream functions.

It is seen that the flow rate in a Newtonian fluid is high when contrasted with the Herschel-Bulkley model, and the inlet elastic radius and outlet elastic radius have opposite effects on the flow rate.

The analysis carried out in this paper is about the peristaltic transport of an incompressible non-Newtonian fluid in a porous elastic tube. The impact of slip and heat transfer on a Herschel-Bulkley fluid is taken into account. The impacts of relevant parameters on the flow rate and temperature are examined graphically. The examination incorporates Newtonian, Power-law and Bingham plastic fluids.

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.

This paper aims to investigate the flow characteristics of lubricating grease in extremely cold weather in which it is difficult to convey the grease due to a huge pressure drop.

The rheological behavior of grease at various temperatures is studied by a rotary rheometer to determine the constitutive equation of lubricating grease. Based on the Herschel–Bulkley (H–B) model, the flow pattern of grease is then simulated by computational fluid dynamics and compared with the test results.

The yield stress increased dramatically when the shear rate was less than 1s⁻¹ in the rheological experiments of continuous shear mode, and the phenomenon was more significant with the decrease in temperature. The rheological data obtained from the continuous shear mode agrees with the H–B equation after the shear thinned. In extremely cold conditions, there is a large yield stress in the lubricating grease; the numerical results show that the viscosity of lubricating grease increased with an increase in temperature, and the viscosity and velocity of lubricating grease showed uneven distribution leading to difficulty of lubricating grease delivery.

This paper focuses on the flow characteristics of lubricating grease in extremely cold area conditions which is studied rarely. In addition, the continuous shear model and oscillatory model are combined to establish the constitutive equations. Experiment and numerical simulation method are all used by establishing the H–B models.

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.

The aim of this study was to measure the apparent viscosity, flow behavior and density of melon juice as a function of temperature and juice concentration and to obtain simple equations to correlate experimental data.

Melon juice was concentrated in a rotary evaporator to 40±1, 52.5±1 and 65±1°Brix at 50°C, 80 rpm and stored at 4°C until analysis. Density of melon juice was determined with 25 ml pycnometer at 15, 25 and 35°C and was expressed as kg/m3. All experiments were conducted in triplicate. Experimental data were fitted to different models (linear, quadratic, exponential, quadratic exponential and polynomial) using Minitab 16. Significant differences in the mean values were reported at p<0.05. The flow behavior of melon juice was determined using a concentric cylinder rotational viscometer at shear rate range of 13.2-330 s−1 and temperatures of 15, 25 and 35°C. The experimental data were analyzed Slide Write V7.01 Trial Size (p<0.05) and the rheograms was plotted by Microsoft Excel 2007.

Results showed that the four-term polynomial model is the best model for computing density values from temperature and concentration (R2=0.999). The measured shear stress was within 1.69-780 Pa, corresponding to viscosity range of 0.016-0.237 Pa · s. Within the tested conditions, the concentrate exhibited a pseudo plastic behavior. Temperature had an inverse effect on shear stress and apparent viscosity.

No research had been done on production of melon juice concentrate.

The purpose of this study is to develop nonlinear and linearized models of DW printing dynamics that capture the complexity of DW while remaining integrable into control schemes. Control of material metering in extrusion-based additive manufacturing modalities, such as positive displacement direct-write (DW), is critical for manufacturing accuracy. However, in DW, transient flows are poorly controlled due to capacitive pressure dynamics – pressure is stored and slowly released over time from the build material and other compliant system elements, adversely impacting flow rate start-ups and stops. Thus far, modeling of these dynamics has ranged from simplistic, potentially omitting key contributors to the observed phenomena, to highly complex, making usage in control schemes difficult.

The authors present nonlinear and linearized models that seek to both capture the capacitive and nonlinear resistive fluid elements of DW systems and to pose them as ordinary differential equations for integration into control schemes. The authors validate the theoretical study with experimental flow rate and material measurements across a range of extrusion nozzle sizes and materials. The authors explore the contribution of the system and build material bulk modulus to these dynamics.

The authors show that all tested models accurately describe the measured dynamics, facilitating ease of integration into future control systems. Additionally, the authors show that system bulk modulus may be substantially reduced through appropriate system design. However, the remaining build material bulk modulus is sufficient to require feedback control for accurate material delivery.

This study presents new nonlinear and linear models for DW printing dynamics. The authors show that linear models are sufficient to describe the dynamics, with small errors between nonlinear and linear models. The authors demonstrate control is necessary for accurate material delivery in DW.

The purpose of this paper was to examine the rheological characterisation of thickened water under different temperature and pH conditions and thickened milk with different fat contents.

Beverages thickened with powdered thickeners are used in the medical management of individuals who suffer swallowing difficulties (dysphagia). Each individual requires a specific level of thickness to best meet the needs of their dysphagia. Although the level of thickness is defined, obtaining the correct consistency of thickened fluids is difficult. This is due to fluctuations associated with temperature and type of fluids to be thickened. Rheological characterisation of commercially available xanthan gum-based thickener was performed under different conditions of temperature, pH and fat contents.

The viscosity and the yield stress of thickened water was found to be unaffected by pH. Similarly, temperature did not affect the viscosity at a high thickener concentration, although it did at lower concentration levels. Conversely, viscosity and yield stress increased as fat levels increased in thickened milk. Furthermore, thickened water took less than 2 minutes to reach equilibrium viscosity, while thickened milk required approximately 15 minutes to reach equilibrium viscosity.

These findings have implications for the standing time required for different beverages before they are thickened to a consistency that has been deemed safe for the patient’s physiological needs. Additionally, it highlights that different liquid base substances required different amounts of thickener to achieve the same level of thickness.

Findings from this study confirms and explores the variability of thickened fluids under different conditions of temperature, pH and fat content for the medical management of dysphagia.