An improved analytical solution on viscous dissipation effect in extended Stokes' second problem in microchannel with isothermal boundaries.

In this analytical study, the fluid motion within a microchannel is induced by the oscillation of one surface parallel to the other stationary surface, termed the extended Stokes' problem. The novelty and research gap are acquiring the thermal effect of such motion due to the viscous dissipation or fluid friction, subject to symmetric isothermal boundary conditions. The study may shed light on the role of viscous dissipation in temperature rise in the synovial fluid of an artificial hip joint, or in the fluid layer of a mechanical bearing. The full exact analytical temperature field, until now, has been unsolved, as it involves unsteady flow with manipulation of a complicated velocity field. The assumptions in the model are one-dimensional, incompressible, laminar, Newtonian flow with constant properties in a microchannel. Through the methodology of partial differential equation analysis, the temperature field is obtained in terms of Brinkman number, Prandtl number and a dimensionless angular frequency, and results are verified with a reported numerical solution, for specified range of the variables. Results complement recent approximate solutions which are valid only for the limited condition of the dimensionless angular frequency being less than or equal to unity, whereby suggesting a new Stokes number.

Biomechanical Analysis of Age-Dependent Changes in Fontan Power Loss.

The hemodynamics in Fontan patients with single ventricles rely on favorable flow and energetics, especially in the absence of a subpulmonary ventricle. Age-related changes in energetics for extracardiac and lateral tunnel Fontan procedures are not well understood. Vorticity (VOR) and viscous dissipation rate (VDR) are two descriptors that can provide insights into flow dynamics and dissipative areas in Fontan pathways, potentially contributing to power loss. This study examined power loss and its correlation with spatio-temporal flow descriptors (vorticity and VDR). Data from 414 Fontan patients were used to establish a relationship between the superior vena cava (SVC) to inferior vena cava (IVC) flow ratio and age. Computational flow modeling was conducted for both extracardiac conduits (ECC, n = 16) and lateral tunnels (LT, n = 25) at different caval inflow ratios of 2, 1, and 0.5 that corresponded with ages 3, 8, and 15+. In both cohorts, vorticity and VDR correlated well with PL, but ECC cohort exhibited a slightly stronger correlation for PL-VOR (>0.83) and PL-VDR (>0.89) than that for LT cohort (>0.76 and > 0.77, respectively) at all ages. Our data also suggested that absolute and indexed PL increase (p < 0.02) non-linearly as caval inflow changes with age and are highly patient-specific. Comparison of indexed power loss between our ECC and LT cohort showed that while ECC had a slightly higher median PL for all 3 caval inflow ratio examined (3.3, 8.3, 15.3) as opposed to (2.7, 7.6, 14.8), these differences were statistically non-significant. Lastly, there was a consistent rise in pressure gradient across the TCPC with age-related increase in IVC flows for both ECC and LT Fontan patient cohort. Our study provided hemodynamic insights into Fontan energetics and how they are impacted by age-dependent change in caval inflow. This workflow may help assess the long-term sustainability of the Fontan circulation and inform the design of more efficient Fontan conduits.

A finite difference study of radiative mixed convection MHD heat propagating Casson fluid past an accelerating porous plate including viscous dissipation and Joule heating effects.

A finite difference numerical simulation scrutiny is executed to evaluate the combined impacts of heat generation, buoyancy forces, viscous dissipation and Joule heating in unsteady hydro-magnetic mixed convective chemically reactive and radiative Casson fluid flowing along an exponentially accelerating permeable vertical plate engrossed in a porous media by considering ramp surface concentration and temperature. The dimensionless non-linear coupled PDEs describing the flow model are dealt numerically by adopting the competent implicit Crank-Nicolson finite difference procedure. The variance of velocity, temperature, and concentration distributions are exposed via graphical representations due to the dissimilarity of the flow restrained parameters. Computational outcomes of the skin-friction, Nusselt and the Sherwood numbers are portrayed in the tabular pattern. The final outcomes of the research exposed that the impacts of thermal radiation, viscous dissipation, and heat production parameters enlarges the temperature and velocity distributions. The fluid motion deflates for growing Casson parameter and magnetic field intensity. The rising chemical reaction parameter suppresses the concentration and velocity distributions. Very importantly it is distinguished that fluid momentum, temperature, and concentration are quicker in the instance of isothermal plate temperature than ramp wall temperature. This kind of research may find specific industrial and medical utilizations such as glass manufacturing, crude oil purification, lubrication, paper production, blood transport study in cardiovascular design, etc.

Cross-diffusive flow of MHD micropolar nanofluid past a slip stretching plate.

As a novel fluid of functional material, magnetohydrodynamic (MHD) micropolar fluid has the special properties of light, heat, magnetic and so on. It is of highly practical significance. The characteristics of flow, heat and mass transfer in MHD micropolar nanofluid boundary layer past a stretching plate are investigated based on the micropolar fluid theory in the present numerical work. In the presence of magnetic field, viscous dissipation and the cross-diffusion caused by Dufour effect and Soret effect are considered. First order slip velocity condition is employed. Mathematical models are built based on the assumptions. Collocation spectral method (CSM) via matrix multiplication is adopted to solve the two-dimensional dimensionless nonlinear partial governing equations. The program codes based on CSM is developed, validated and employed. The coupled effects of microrotation, Dufour effect, Soret effect, magnetic field as well as first order slip velocity boundary condition on the flow, heat and mass transfer are revealed. Besides, the variation trends of local Nusselt number and Sherwood number are analyzed in detail. The numerical results indicate that the fluid flow can be suppressed obviously in the consideration n of slip condition and magnetic field. As slip parameter δ and magnetic parameter M rise, the velocity in the boundary layer becomes lower gradually; further, both temperature and concentration increase. On the other hand, the opposite trend can be noticed with the effect of material parameter K. Moreover, Ec and Df augment the temperature; while, Sr leads to an upsurge in concentration. The temperature rises by about 79.73% with Dufour effect and Sh enlarges by a factor of about 38.15% with Soret effect. The concentration boundary layer decreases by about 37.50% is when K=5.0.

Computational analysis of bio-convective eyring-powell nanofluid flow with magneto-hydrodynamic effects over an isothermal cone surface with convective boundary condition.

Non-Newtonian fluids are essential in situations where heat and mass transfer are involved. Heat and mass transfer processes increase efficiency when nanoparticles (0.01≤φ≤0.03) are added to these fluids. The present study implements a computational approach to investigate the behavior of non-Newtonian nanofluids on the surface of an upright cone. Viscous dissipation (0.3≤Ec≤0.9) and magnetohydrodynamics (MHD) (1≤M≤3) are also taken into account. Furthermore, we explore how microorganisms impact the fluid's mass and heat transfer. The physical model's governing equations are transformed into ordinary differential equations (ODEs) using a similarity transformation to make the analysis easier. The ODEs are solved numerically using the Bvp4c solver in MATLAB. The momentum, thermal, concentration, and microbe diffusion profiles are graphically represented in the current research. MHD (1≤M≤3) effects improve the diffusion of microbes, resulting in increased heat and mass transfer rates of 18 % and 19 %, respectively, based on our results. Furthermore, a comparison of our findings with existing literature demonstrates promising agreement.

Entropy generation for exact irreversibility analysis in the MHD channel flow of Williamson fluid with combined convective-radiative boundary conditions.

The scrutinization of entropy optimization in the various flow mechanisms of non-Newtonian fluids with heat transfer has been incredibly enhanced. Through the investigation of irreversibility sources in the steady flow of a non-Newtonian Willaimson fluid, an analysis of entropy generation is carried out in this current work. The current study has an essential aspect of investigating the heat transfer mechanism with flow phenomenon by considering convective-radiative boundary conditions. A horizontal MHD channel is assumed with two parallel plates to develop a mathematical model for the flow phenomenon by considering the variable viscosity of the fluid. The contribution of physical impacts of thermal radiation, Joule heating, and viscous dissipation is interpolated in the constitutive energy equation. The complete flow of the current analysis is established in the form of ordinary differential equations which further take the form of the dimensionless system through the contribution of the similarity variables. A graphical scrutinization of the physical features of the flow phenomenon in relation to the pertinent parameters is proposed. This study reveals that the higher magnitude of radiation parameter and Brinkman number dominates the system's entropy. Moreover, the temperature distribution experiences an increasing mechanism with improved conduction-radiation parameter at the lower plate.

A general analytical solution for fluid flow and heat convection through arbitrary-shaped triangular ducts: A variational analysis.

This paper presents an analytical solution for fluid flow and heat transfer inside arbitrarily-shaped triangular ducts for the first time. The former analytical solutions are limited to the special case of isosceles triangular ducts. The literature has no report about the analytical solution for the general case of arbitrarily-shaped triangular ducts. Due to the significant role of fluid flow through non-circular channels in industry and the large number of triangular shapes, a method for solving the heat transfer problem for all triangular shapes is needed. The heat transfer of a fluid flow through a channel with an arbitrary triangular cross-section for the case of constant heat flux at the walls is solved in this work for the first time, considering viscous dissipation. Here, the functionals of flow and heat transfer equations are derived, and the resulting Euler-Lagrange equations are solved using the Ritz method. The effect of the duct geometry on the velocity profile and friction coefficient is studied in detail. The effect of the Brinkman number on the temperature distribution and Nusselt number is investigated for both cooling and heating cases. The results reveal that the critical Brinkman Number distinguishes between the cooling and heating cases and represents the critical point at which the Nusselt number approaches infinity. The value of the Nusselt number decreases with the increase of the Brinkman number in both the wall cooling and heating modes. It is also found that the equilateral triangle exhibits the minimum friction coefficient and the maximum value of the Poiseuille number.

Unsteady magneto porous convective transport by micropolar binary fluid due to inclined plate: An inclusive analogy.

In this investigation , the consequence of viscous dissipation on the unstable magneto porous convective transport by a micropolar binary fluid due to an inclined surface with viscous dissipation and thermal radiation is examined. Viscous dissipation plays a noteworthy role in industrial applications. The governing PDEs are converted to combined ODEs with the Boussinesq approximation using a similarity analysis. The obtained non-linear ODEs are resolved using the shooting method with "ODE45 MATLAB" coding assistance. The numerical outcomes are revealed graphically for various dimensionless parameters and numbers, including temperature, concentration, velocity, and micro-rotation. The temperature, micro-rotation, and velocity fields escalate with increasing Eckert numbers. The radiation parameter and variable viscosity parameter increase the flow rate of the fluid. Increasing radiation parameters, suction parameters, and Prandtl numbers lessen the fluid temperature. The buoyancy parameters have symmetrical impacts on the velocity and microrotation of fluid particles in the cooling and heating modes. Improving Eckert number, inclined angle, Schmidt number, Prandtl number, and magnetic parameter reduces skin friction. The heat transmission rate escalates in quantity due to larger Prandtl number values. Rising Prandtl, Eckert, and Schmidt numbers accelerate the mass transfer rate. The current research result is compared to previously published article's result with good agreement.

Extracellular matrix viscoelasticity regulates TGFß1-induced epithelial-mesenchymal transition and apoptosis via integrin linked kinase.

Transforming growth factor (TGF)-ß1 is a multifunctional cytokine that plays important roles in health and disease. Previous studies have revealed that TGFß1 activation, signaling, and downstream cell responses including epithelial-mesenchymal transition (EMT) and apoptosis are regulated by the elasticity or stiffness of the extracellular matrix. However, tissues within the body are not purely elastic, rather they are viscoelastic. How matrix viscoelasticity impacts cell fate decisions downstream of TGFß1 remains unknown. Here, we synthesized polyacrylamide hydrogels that mimic the viscoelastic properties of breast tumor tissue. We found that increasing matrix viscous dissipation reduces TGFß1-induced cell spreading, F-actin stress fiber formation, and EMT-associated gene expression changes, and promotes TGFß1-induced apoptosis in mammary epithelial cells. Furthermore, TGFß1-induced expression of integrin linked kinase (ILK) and colocalization of ILK with vinculin at cell adhesions is attenuated in mammary epithelial cells cultured on viscoelastic substrata in comparison to cells cultured on nearly elastic substrata. Overexpression of ILK promotes TGFß1-induced EMT and reduces apoptosis in cells cultured on viscoelastic substrata, suggesting that ILK plays an important role in regulating cell fate downstream of TGFß1 in response to matrix viscoelasticity.

Thermal Characterization of Rarefied Flows in Rhombic Microchannels.

This work aimed to numerically investigate the dynamic and thermal behavior of a fully developed, laminar, gaseous flow in a microchannel featuring a rhombic cross-section. Due to new fabrication techniques, microducts with rhombic cross-sections have recently received more attention. The momentum and energy balance equations were solved by using a commercial CDF code and assuming the slip and the H2 boundary conditions. The temperature jump between the wall and the adjacent fluid was also taken into account. The accuracy of the numerical results was checked by using the data available in the literature in terms of velocity profiles in the slip flow regime and the Nusselt number in the continuum flow regime. To also investigate the geometry effects on the fluid behavior, several values of the side angle of the rhombus were considered. The numerical results revealed that the rarefaction degree and geometrical properties significantly affected the Nusselt number.

Numerical simulation of variable density and magnetohydrodynamics effects on heat generating and dissipating Williamson Sakiadis flow in a porous space: Impact of solar radiation and Joule heating.

This study is confined to the numerical evaluation of variable density and magnetohydrodynamics influence on Williamson Sakiadis flow in a porous space. In this study, Joule heating, dissipation, heat generation effect on optically dense gray fluid is encountered. The inclined moving surface as flow geometry is considered to induce the fluid flow. A proposed phenomenon is given a mathematical structure in partial differential equations form. These partial differential equations are then made dimensionless using dimensionless variables. The obtained dimensionless model in partial differential equations is then changed to ordinary differential equations via stream function formulation. A set of transformed equations has been solved with bvp4c solver. The numerical fallout of velocity field, temperature field, skin friction, and heat transfer rate are illustrated in graphs and tables with flow parametric variations. Conclusion is drawn that mounting values of density variation parameter confirm the reduction in velocity field and augmentation in temperature of the fluid. When Williamson fluid parameter enhances, both fluid velocity and temperature are rising correspondingly. Growing magnitudes of the magnetic number, radiation parameter, heat generation, and Eckert number rise the temperature of the fluid. A rise in a porous medium parameter weakens the fluid velocity. Skin friction is reducing as radiation parameter and density variation parameter are increased. The present solutions are compared to those that have already been published in order to validate the current model. The comparison leads to the conclusion that the two outcomes are in excellent agreement, endorsing the veracity of the current answers.

Existence of dual solution for MHD boundary layer flow over a stretching/shrinking surface in the presence of thermal radiation and porous media: KKL nanofluid model.

Present study is dedicated to analyze the closed form solution of nanofluid flow over a stretching/shrinking sheet with dual availability. Flow is developed through two-dimensional boundary layer theory. Appropriate tensor is used to generate the continuity, energy, and momentum equations. Converted governing partial differential equations (PDEs) into dimensionless non-linear ordinary differential equations (ODEs) by adoption of favorable similarity variables. The dimensionless ODEs of energy and momentum produced a dual nature solution in closed form under certain conditions. To deal with the nanofluid, the Koo-Kleinstreuer and Li (KKL) model is used, and the equations are solved using well-known software Maple. The effect of porosity Φ, suction/injection fw, stretching/shrinking λ, and magnetic effect M on skin friction, velocity, temperature, and streamlines are well explored and showcased. The results for the stable solutions have been showed that the upper branch's fluid velocity is increasing as the magnetic parameter M rises whereas the lower branch's fluid velocity is decreasing as M rises. Additionally, the CuO-nanofluid's velocity is impacted by the volume fraction of nanoparticles, with an increase in volume fraction causing a decrease in velocity. On both the lower and upper branches, the temperature profile is seen to improve as the Biot number increases. On the other hand, as the magnetic parameter varies and the magnetic field increases, the local Nusselt number against suction/injection decreases, as well as the rate of heat transfer in the upper branch decreases.

Viscous dissipation effects on hybrid nanofluid flow over a non-linearly shrinking sheet with power-law velocity.

This research intends to investigate the effect of the nonlinearity of the surface velocity on the hybrid nanofluid flow behavior. Here, the total composition of Al2O3 (alumina) as well as Cu (copper) volume fractions, are implemented in a one-to-one ratio and then dispersed in water. The similarity equations are gained employing a similarity transformation, which is programmed in MATLAB software. The dual solutions are attainable for certain ranges with respect to the mass flux parameter S and the power-law index n. Also, the turning point occurs in the region of S<0 and n>1. Besides, the rise of n led to reduce the skin friction as well as the heat transfer coefficients with 39.44 % and 11.71 % reduction, respectively. Moreover, 14.39 % reduction of the heat transfer rate is observed in the presence of viscous dissipation (Eckert number). It is found that only the first solution is stable as time progresses. Generally, this study gives scientists and engineers a starting point for predicting how to control the parameters to achieve the best results for relevant practical applications.

Investigation on the Effective Measures for Improving the Performance of Calorimetric Microflow Sensor.

The performance of the calorimetric microflow sensor is closely related to the thermal sensing part design, including structure parameter, heater temperature, and operation environment. In this paper, several measures to enhance the performance of the calorimetric microflow sensor were proposed and further verified by numerical simulations. The results demonstrate that it is more favorable to reduce the negative impact of flow separation as the space between detectors and heater is set to be 1.6 µm so as to improve the accuracy of the sensor. With an appropriate gap, the front arranged obstacle of the upstream detector can effectively widen the measure range of the sensor, benefiting from the decrease in upstream viscous dissipation. Compared to a cantilever structure, the resonances can be effectively suppressed when the heater and detectors are designed as bridge structures. In particular, the maximum amplitude of the bridge structure is only 0.022 µm at 70 sccm, which is 53% lower than that of the cantilever structure. The optimized sensor widens the range by 14.3% and significantly increases the sensitivity at high flow rates. Moreover, the feasibility of the improved measures is also illustrated via the consistency of the trend between the simulation results and experimental ones.

Analysis of the Time-Dependent magnetohydrodynamic Newtonian fluid flow over a rotating sphere with thermal radiation and chemical reaction.

This article presents the magnetohydrodynamic (MHD) flow of a nanoliquid due to a rotating sphere at a stagnation point. The flow is considered to be influenced by the magnetic field, dissipative, thermally radiative, and chemically reactive. Also, the thermophoretic and Brownian motion influences are taken into consideration. Some restrictions in the present analysis are taken: like there is no-slip and convective conditions, joule heating, Hall effects and buoyancy-driven. The solution of the present analysis is derived through the homotopy analysis method (HAM). The significance of several physical parameters on velocities, thermal and concentration profiles are shown with the help of Figures. Also, the significance of different physical factors on skin frictions, local Nusselt number and Sherwood number are demonstrated with the help of Tables. The outcomes show that the Nusselt number is lower for the larger Brownian motion parameter, Eckert number, and thermophoretic parameter, while the increment in the thermal radiation parameter augmented the Nusselt number. It is established that the increasing rotation, magnetic and positive constant parameters have increased the velocity profiles along the x-direction while reducing the velocity profiles along the z-direction of the nanoliquid flow. The increasing positive constant parameter reduces the thermal graph of the nanoliquid flow. Furthermore, the intensifying Eckert number, thermophoresis, Brownian motion, and thermal radiation factor have escalated the thermal profiles of the nanoliquid flow.

Analysis of blood flow of unsteady Carreau-Yasuda nanofluid with viscous dissipation and chemical reaction under variable magnetic field.

Blood flow analysis through arterial walls depicts unsteady non-Newtonian fluid flow behavior. Arterial walls are impacted by various chemical reactions and magnetohydrodynamic effects during treatment of malign and tumors, cancers, drug targeting and endoscopy. In this regard, current manuscript focuses on modeling and analysis of unsteady non-Newtonian Carreau-Yasuda fluid with chemical reaction, Brownian motion and thermophoresis under variable magnetic field. The main objective is to simulate the effect of different fluid parameters, especially variable magnetic field, chemical reaction and viscous dissipation on the blood flow to help medical practitioners in predicting the changes in blood to make diagnosis and treatment more efficient. Suitable similarity transformations are used for the conversion of partial differential equations into a coupled system of ordinary differential equations. Homotopy analysis method is used to solve the system and convergent results are drawn. Effect of different dimensionless parameters on the velocity, temperature and concentration profiles of blood flow are analyzed in shear thinning and thickening cases graphically. Analysis reveals that chemical reaction increases blood concentration which enhance the drug transportation. It is also observed that magnetic field elevates the blood flow in shear thinning and thickening scenarios. Furthermore, Brownian motion and thermophoresis increases temperature profile.

Unsteady nanofluid flow over a cone featuring mixed convection and variable viscosity.

This article addresses unsteady nanofluid flow over a cone with MHD and mixed convection effects. Effects of variable viscosity and viscous dissipation are also considered. The resulting system of equations is tackled through the Homotopy Analysis Method (HAM). The impact of different influential variables on skin friction coefficient, heat and mass flux are discovered through numerical tables and graphs. It is noted that the surface drag force in x and y directions increases against the buoyancy force parameter. Also, it is observed that the tangential and azimuthal velocity decrease against the variable viscosity parameter. Furthermore, the temperature of fluid is observed to decay against the unsteady parameter but it increases against the Eckert number.

Heat transfer characteristics of magnetized hybrid ferrofluid flow over a permeable moving surface with viscous dissipation effect.

Hybrid ferrofluid is a unique heat transfer fluid because it can be magnetically controlled and ideal in various applications. Further exploration to unleash its potential through studying heat transfer and boundary layer flow is crucial, especially in solving the thermal efficiency problem. Hence, this research focuses on the numerical examination of flow behaviour and heat transfer attributes of magnetized hybrid ferrofluid Fe3O4-CoFe2O4/water across a permeable moving surface considering the mutual effects of magnetohydrodynamic (MHD), viscous dissipation, and suction/injection. The problem was represented by the Tiwari and Das model with duo magnetic nanoparticle hybridization; magnetite Fe3O4 and cobalt ferrite CoFe2O4 immersed in water. The governing equations were transformed into ordinary differential equations using appropriate similarity variables and solved with bvp4c MATLAB. A dual solution is obtained, and via stability analysis, the first solution is stable and physically reliable. The significant influence of governing effects on the temperature and velocity profiles, the local skin friction coefficient and the local Nusselt number are analyzed and visually shown. The surge-up value of suction and CoFe2O4 ferroparticle volume concentration enhances the local skin friction coefficient and heat transfer rate. Additionally, the magnetic parameter and Eckert number reduced the heat transfer. Using a 1% volume fraction of Fe3O4 and CoFe2O4; the hybrid ferrofluid's convective heat transfer rate was shown to be superior to mono-ferrofluid and water by enhancing 2.75% and 6.91%, respectively. This present study also suggests implying a greater volume concentration of CoFe2O4 and lessening the magnetic intensity to maintain the laminar flow phase.

MHD flow of nanofluid over moving slender needle with nanoparticles aggregation and viscous dissipation effects.

The study of boundary layer flows over an irregularly shaped needle with small horizontal and vertical dimensions is popular among academics because it seems to have a lot of uses in fields as different as bioinformatics, medicine, engineering, and aerodynamics. With nanoparticle aggregation, magnetohydrodynamics, and viscous dissipation all playing a role in the flow and heat transmission of an axisymmetric TiO2-C2H6O2 nanofluid via a moving thin needle, this article provides guidance on how to employ a boundary layer for this purpose. In this case, we utilized the similarity transformation to change the dimensional partial differential equation into the dimensionless ordinary differential equation. We utilize MATHEMATICA to include shooting using RK-IV methods after identifying the numerical issue. Several characteristics were measured, leading to the discovery of a broad variety of values for things like skin friction coefficients, Nusselt numbers, velocity profiles, and temperature distributions. Velocity profile decreases with increasing values of ϕ,M,e and increases against ε. Temperature profiles enhances with increasing values of ϕ,M,e,ε, and Ec. The reduction in skin friction between a needle and a fluid can be observed when the values of M and ϕ are boosted. Furthermore, it was also noticed an increase in heat transfer on needle surface dramatically when ϕ,e, and M were raised, whereas Ec displayed the opposite effect. The findings of the current study are compared with prior findings for a particular instance in order to confirm the findings. Excellent agreement between the two sets of results is found.

Numerical Modeling of the Mixing of Highly Viscous Polymer Suspensions in Partially Filled Sigma Blade Mixers.

This paper presents a non-isothermal, non-Newtonian Computational Fluid Dynamics (CFD) model for the mixing of a highly viscous polymer suspension in a partially filled sigma blade mixer. The model accounts for viscous heating and the free surface of the suspension. The rheological model is found by calibration with experimental temperature measurements. Subsequently, the model is exploited to study the effect of applying heat both before and during mixing on the suspension's mixing quality. Two mixing indexes are used to evaluate the mixing condition, namely, the Ica Manas-Zlaczower dispersive index and Kramer's distributive index. Some fluctuations are observed in the predictions of the dispersive mixing index, which could be associated with the free surface of the suspension, thus indicating that this index might not be ideal for partially filled mixers. The Kramer index results are stable and indicate that the particles in the suspension can be well distributed. Interestingly, the results highlight that the speed at which the suspension becomes well distributed is almost independent of applying heat both before and during the process.