Casson Model Research Articles

Impact of velocity slip and radiative magnetized Casson nanofluid with chemical reaction towards a nonlinear stretching sheet: Three-stage Lobatto collocation scheme

This paper examines the influence of magnetized Casson nanofluid flow and heat transport phenomena towards a boundary layer flow over a nonlinear stretchable surface. The characteristics of the nanofluid are illustrated by considering Brownian motion and thermophoresis effects due to which the fluid is electrically conducting. The nonlinear Casson model is very useful to describe the fluid behavior and the flow curves of suspensions of pigments in lithographic varnishes intended for the preparation of printing inks. A uniform magnetic field, along with suction and chemical reaction are taken into account. Similarity transformations are employed to convert the PDEs into ODEs, and then solved numerically (Bvp4c) using MATLAB. This scheme consists of a finite difference scheme that implements three-stage Lobatto IIIa collocation formula which provides continuous solution upto fifth-order accuracy. Excellent correctness of the present results has been acquired which is compared with the previous one. The outcomes of various parameters on heat transfer rate, skin friction coefficient, nanoparticle concentration, Sherwood number, velocity and temperature profiles are demonstrated via tabular forms and pictorially. The most important fact is that an increase in the thermophoresis parameter, radiation and magnetic parameter boosts up the fluid temperature, resulting in an improvement in the thermal boundary layer.

Implementing the spectral relaxation method for MHD Casson and Williamson model under the effects of heat generation and viscous dissipation

The nonlinear system of ordinary differential equations (ODEs) that represents the model of non‐Newtonian Casson and Williamson fluid flow and heat mass transfer on the slendering stretched surface immersed in a porous medium is solved and successfully treated by using the spectral relaxation method (SRM). In this physical model, which is dependent linearly on temperature, we investigate the impact of thermal conductivity viscous dissipation. The primary purpose of this research is to look at how the physical elements affecting the problem affect velocity, temperature, and concentration profiles. The Gauss–Seidel principle is also used in the SRM to break down the resulting nonlinear system of ODEs into smaller linear systems. We utilize this approach because it solves the problem accurately, quickly, and with little programming effort. We give particular focus on demonstrating the SRM's stability and convergence rate. The findings reveal that the skin friction coefficient grows as the magnetic number increases, whereas the Casson and local Williamson parameters behave oppositely. Additionally, the Nusselt number is further enhanced by improving the local Williamson parameter contrary to the decreasing trend with the thermal conductivity parameter and Eckert number. The numerical results show that the suggested methodology enhances the method's computing speed and gives improved accuracy, which we can confirm. Additionally, the SRM speeds up convergence to the necessary solution.

Convective Heat and Mass Transport in Casson Fluid Flow in Curved Corrugated Cavity with Inclined Magnetic Field.

Convection in fluids produced by temperature and solute concentration differences is known as thermosolutal convection. It has valuable utilization in wide industrial and technological procedures such as electronic cooling, cleaning, and dying processes, oxidation of surface materials, storage components, heat exchangers, and thermal storage systems. In view of such prominent physical significance, focus is made to explicate double (thermal and solutal)-diffusive transport in viscoelastic fluid characterized by the Casson model enclosed in a curved enclosure with corrugations. An incliningly directed magnetic field is employed to the flow domain. A uniformly thermalized and concentrated circular cylinder is installed at the center of the enclosure to measure transport changes. Dimensionally balanced governing equations are formulated in 2D, representing governed phenomenon. Finite element-based open-sourced software known as COMSOL is utilized. The domain of the problem is distributed in the form of triangular and quadrilateral elements. Transport distributions are interpolated by linear and quadratic polynomials. The attained non-linear system is solved by a less time and computation cost consuming package known as PARDISO. Convergence tests for grid generation and validation of results are executed to assure credibility of work. The influence of involved physical parameters on concerned fields are revealed in graphical and tabular manner. Additionally, heat and mass fluxes, along with, kinetic energy variation are also evaluated.

Forced convection of non-darcy flow of ethylene glycol conveying copper(II) oxide and titanium dioxide nanoparticles subject to lorentz force on wedges: Non-newtonian casson model.

The topic of two-dimensional steady laminar MHD boundary layer flow across a wedge with non-Newtonian hybrid nanoliquid (CuO-TiO2/C2H6O2) with viscous dissipation and radiation is taken into consideration. The controlling partial differential equations have been converted to non-linear higher-order ordinary differential equations using the appropriate similarity transformations. It is demonstrated that a number of thermo-physical characteristics govern the transmuted model. The issue is then mathematically resolved. When the method’s accuracy is compared to results that have already been published, an excellent agreement is found. While the thermal distribution increases with an increase in Eckert number, radiation and porosity parameters, the velocity distribution decreases as porosity increases.

Hall device-controlled ciliated flow of viscoplastic material due to the non-uniform complex ciliated pump subject to inclined magnetic force

In the last two decades, the applications of peristaltic and ciliated pumps in diverse domains of engineering and medicine are increasing because of their efficiency and easy operation with fewer errors in performing a task than the other biological pumps. The current study describes a mathematical formulation of the ciliated flow of viscoplastic material through an infinite length under the impact of heat transfer. The rheological impact of viscoplastic material is inspected using the robust Casson model. The motion is also controlled by the two external simulated powers: one is an inclined magnetic field and the other is the Hall device. The governing equations are simplified using the two biological approximations: one is the creeping phenomena and the other is the long wavelength. Analytical solutions of the flow equations are obtained by the integration method. The impact of rheological and thermo-physical parameters is physically incorporated. The Cilia-length parameter and the Brinkman number are vibrant in the enhancement of the heat phenomena and the heat transfer rate at the upper wall (HTRUW). Applications of the current formulation include the chemical industry, magnetic material processing, and the medical domain under the creeping phenomenon.

The influence of formulation and packaging material on the rheological properties of milk chocolate

Fiber is a substitute for sugar in chocolates but changes its hygroscopicity and rheological characteristics if their packaging doesn't avoid its moisture gain. The objective of this study was to evaluate the water vapor permeability of different packaging materials (BOPP/metBOPP (biaxial oriented polypropylene /metallized) BOPP/BOPP white and Cellophane) and the effect of the permeability on the rheological properties (by Casson model) of three types of milk chocolate: standard, with the addition of Inulin and Fructooligosaccharides during storage at 20 °C /75% RH. Due to the high hygroscopicity of the fibers, the initial moisture content of the chocolates with fibers was higher than that of standard chocolate. No increase in viscosity were observed at standard and with Inulin chocolates during 270 days at 20 °C/75% RH, regardless of the packaging material used. However, chocolate with FOS packed in cellophane showed changes in their viscosity, with values ranging from 4.63 Pa.s to 7.5 Pa.s after 210 days of storage. In addition, the Inulin chocolate in Cellophane package showed an increase at flow limit from 3 Pa to 6 Pa after 270 days. Therefore, the results indicated that chocolates with fibers should be packed in materials with medium or high barrier to water vapor, such as BOPP/metBOPP and BOPP/BOPP, to avoid rheological changes during storage.

Pickering emulsion polymerized Fe3O4@graphene oxide-polystyrene composite particles and their electro/magnetorheological responses

In this study, magnetic and semiconducting Fe3O4@graphene oxide (GO)-polystyrene (PS) composite particles were fabricated using the Pickering emulsion polymerization technique. The Fe3O4@GO composite particles were initially synthesized via a co-precipitation method and then used as a Pickering emulsifier. The basic properties, such as the morphology, chemical properties, and the magnetic properties of the Fe3O4@GO-PS composite particles, were characterized using transmission electron microscopy, Fourier-transform infrared spectroscopy, and VSM. The Fe3O4@GO-PS composite particles were then dispersed in silicone oil to obtain electrorheological (ER) and magnetorheological (MR) fluids. The ER and MR properties were tested using a rheometer with two different geometries under electric and magnetic fields. The ER dynamic yield stresses were obtained using the Bingham model fitting method, whereas the MR dynamic yield stresses were obtained using the Casson model fitting method. Furthermore, the yield stress was obtained by fitting the complex viscosity using the Carreau model. All three yield stresses were also fitted with respect to the electric or magnetic field strengths, and a slope of 1.5 was determined.

Fluid structure interaction study of non-Newtonian Casson fluid in a bifurcated channel having stenosis with elastic walls

Fluid–structure interaction (FSI) gained a huge attention of scientists and researchers due to its applications in biomedical and mechanical engineering. One of the most important applications of FSI is to study the elastic wall behavior of stenotic arteries. Blood is the suspension of various cells characterized by shear thinning, yield stress, and viscoelastic qualities that can be assessed by using non-Newtonian models. In this study we explored non-Newtonian, incompressible Casson fluid flow in a bifurcated artery with a stenosis. The two-dimensional Casson model is used to study the hemodynamics of the flow. The walls of the artery are supposed to be elastic and the stenosis region is constructed in both walls. Suitable scales are used to transform the nonlinear differential equations into a dimensionless form. The problem is formulated and discretized using Arbitrary Lagrangian–Eulerian (ALE) approach. The finite element method (FEM) technique is used to solve the system of equations, together with appropriate boundary conditions. The analysis is carried out for the Bingham number, Hartmann number, and Reynolds number. The graphical results of pressure field, velocity profile, and load on the walls are assessed and used to study the influence of hemodynamic effects on stenotic arteries, bifurcation region, and elastic walls. This study shows that there is an increase in wall shear stresses (WSS) with increasing values of Bingham number and Hartmann number. Also, for different values of the Bingham number, the load on the upper wall is computed against the Hartmann number. The result indicate that load at the walls increases as the values of Bingham number and Hartmann number increase.

A proof-of-concept study for the simulation of blood flow in a post arterial segment for different blood rheology models.

Cardiovascular disease (CVD) and especially atherosclerosis are chronic inflammatory diseases which cause the atherosclerotic plaque growth in the arterial vessels and the blood flow reduction. Stents have revolutionized the treatment of this disease to a great extent by restoring the blood flow in the vessel. The present study investigates the performance of the blood flow after stent implantation in patient-specific coronary artery and demonstrates the effect of using Newtonian vs. non-Newtonian blood fluid models in the distribution of endothelial shear stress. In particular, the Navier-Stokes and continuity equations were employed, and three non-Newtonian fluid models were investigated (Carreau, Carreau-Yasuda and the Casson model). Computational finite elements models were used for the simulation of blood flow. The comparison of the results demonstrates that the Newtonian fluid model underestimates the calculation of Endothelial Shear Stress, while the three non-Newtonian fluids present similar distribution of shear stress. Keywords: Blood flow dynamics, stented artery, non-Newtonian fluid. Clinical Relevance- This work demonstrates that when blood flow modeling is performed at stented arteries and predictive models are developed, the non-Newtonian nature of blood must be considered.

MHD Casson nanofluid flow over a stretching surface with melting heat transfer condition

AbstractIn this current communication thermal characteristics of non‐Newtonian fluid flow over a stretching surface with a melting heat transfer effect are discussed. Casson's rheological model is adapted to explain non‐Newtonian fluid flow characteristics. The boundary value problem comprising momentum, energy, and concentration equations is turned into a system of ordinary differential equations and then solved by applying the shooting method. Detailed analysis of important engineering quantities such as skin friction and Nusselt number are computed for the non‐Newtonian (Casson) model and Newtonian model. Some of the important outcomes are: melting parameter increases velocity and decreases temperature. Thermophoresis and Brownian motion parameters increase temperature profiles.

Analytical approach on the free convection of Buongiorno model nanofluid over a shrinking surface

This article focuses on the two-dimensional unsteady flow of an incompressible Casson nanofluid over a shrinking horizontal sheet under the influence of inclined magnetic field and in an advance dissipative heat due to Joule heating. The proposed Buongiorno model for the inclusion of Brownian and thermophoresis enriches the flow profiles. Casson model constituents a plastic fluid model that exhibits shear thinning characteristics and high shear viscosity. The proposed fluid model also approximates the rheological behavior of other liquids like physiological suspensions, cosmetics, syrups, etc. The governing partial differential equations (PDEs) that account for effect of Buongiorno model are converted in to nonlinear ordinary differential equations (ODEs) through suitable similarity variables. Further, approximate analytical technique such as Adomian Decomposition Method is beneficial to carry out the solution of the transformed governing equations and the significant nature of the contributing parameter for both the steady and unsteady case is presented via graphs. Moreover, the major contribution is; the Casson parameter along with suction/injection favors in the smooth enhancement in the velocity profiles and the fluid temperature also encouraged by the augmentation in Brownian and thermophoresis parameter.

Flow of Blood in Asymmetric Stenosed Artery with Velocity Slip at the Interface: A Two–Layered Casson Model

Flow of Blood in Asymmetric Stenosed Artery with Velocity Slip at the Interface: A Two–Layered Casson Model

The effect of pharmaceutical nanoparticles and atherosclerosis in aorta artery on the instable blood velocity based on numerical method.

In medicine field, dynamic investigation of aorta artery has received attention due to its notable functions and significance upon performance of heart and individual health. Because, aortic injuries cause lethal occurrences having numerous mortality rates. Therefore, more probes, in particular, dynamic response of aorta arteries conveying blood flow containing pharmaceutical nanoparticles is essential. In present research, we attempt to model biomechanically the dynamic instability assessment of aorta arteries with atherosclerosis in tissue matrix conveying blood including pharmaceutical magnetic nanoparticles. Thus, according to classical cylindrical shell theory, the aorta arteries will be considered as elastic cylindrical vessels and symmetric lipid tissue is utilized in order to model atherosclerosis in the artery. Applying magnetic field to nanoparticles results in attraction of lipid tissue in artery. Moreover, the nature of blood flow is regarded non-Newtonian based on Casson, Carreau, and power law models. Using Hamilton's principle, the motion equations are derived and based on differential quadrature method, the dynamic instability region of aorta artery is obtained. The influences of different variables such as magnetic field, magnetic nanoparticle's volume percent, combined effects of the tissue, lipid's height and length, and non-Newtonian models upon dynamic behavior of aorta artery are investigated. According to the results, increase in lipid's height leads to increase in resonance frequency of aorta arteries.

Examination of thermal and velocity slip effects on the flow of blood suspended with aluminum alloys over a bi-directional stretching sheet: the ternary nanofluid model

The flow of a ternary nanofluid through a bi-directionally distending sheet has been analyzed by employing the Casson model. The ternary nanofluid is formed by suspending the aluminum alloys namely and along with the oxide into blood. The nanoparticles that are suspended in the base fluid are assumed to be in the shape of a blade so that the maximum surface of the nanoparticle will be intact with the base fluid and thus will absorb more heat from the surface. Also, the shape of the nanoparticle helps in faster movement within the nanofluid. The flow is further subjected to velocity and thermal slips. With these assumptions, the mathematical model is framed with the help of partial differential equations considering thermal radiation and heat source/sink to achieve realistic results. These equations are further transformed into non-linear differential equations that are solved using the technique. The results of this study are interpreted graphically for various parameters concerning fluid flow. It is observed that the fluid flow velocity is ebbed considerably with the increase in Casson parameter and the slips at the boundary have enhanced the corresponding fluid profiles.

Application of Novel Fruit Extract for Flow Assurance of Indian Field Waxy Crude Oil

Summary This research article deals with the application of shikakai fruit (Senegalia rugata) extract (SE) used as a novel bio-additive for improving flow properties of waxy crude oil (WCO) to reduce pumping cost during pipeline transportation. SE was synthesized using solvent extraction method, which is one of the most common economic extraction processes. Bio-additive was characterized by Fourier transform infrared spectroscopy (FTIR) spectroscopy, carbon, hydrogen, nitrogen, sulfur (CHNS) analysis, gas chromatography-mass gas chromatography-mass spectroscopy (GC-MS), differential light scattering, and thermogravimetric analysis (TGA). Pour point of WCO was decreased by 12°C due to addition of 1,000 ppm of SE on crude oil. Viscosity of WCO reduced significantly after addition of a bio-additive. It was found that viscosity of SE beneficiated crude oil (1,000 ppm dosage) at 30°C is less than that of pure crude at 50°C. So, addition of SE may be an alternative of heating during flow of WCO. Microscopic studies confirm that wax and other solid particles become smaller and more dispersive so that the particles are not able to come closer and form a three-dimensional network. Consequently, flow becomes easier and pumping cost gets reduced. Experimental data related to viscosity better fitted with Casson model and Bingham model before addition of SE depict that significant yield stress is required to restart the flow of crude oil. Due to the addition of SE, yield stress was deceased significantly and crude oil beneficiated with bio-additive tends to behave like a Newtonian fluid. This article also investigates wax deposition through laboratory-designed wax depositional setup. The wax deposition of crude oil after addition of 1,000 ppm SE was comparatively 56 and 75% lower than untreated crude oil when deposition studies were performed for 2 and 4 hours, respectively, at 25°C. Wax crystals of SE-treated crude oil decreased in diameter and disoriented the particles, preventing the formation of three-dimensional networks so that crude oil can easily flow through pipelines. Considering the efficacy of extracted bio-additive and its cost effectiveness, the same can be applied for flow assurance of WCO through pipelines even at very low temperatures.

Studying Massive Suction Impact on Magneto-Flow of a Hybridized Casson Nanofluid on a Porous Continuous Moving or Fixed Surface

Non-Newtonian nanofluids flow due to the augmented thermal performances of nanoparticles, and their importance in various sectors plays a vital role in medicine, cosmetics, manufacturing, and engineering processes. In this regard, the present theoretical investigation explores the magneto-flow of Casson hybrid nanofluid through a continuous moving/fixed surface with significant suction. The nature of spherical copper and alumina dispersed in water was assessed as the conventional heat transfer in Casson fluid with impacts of viscous dissipation and Ohmic heating. Two states are addressed regarding symmetry, one corresponding to a surface moving in parallel with a free stream and the other a surface moving in the opposite direction to the free stream. In the momentum equation, the Casson model with magnetic field effect is exploited. The governing equations are transformed into the necessary equations using transformations invoking symmetric property of the independent variables. The numerical outputs of the nonlinear governing equations are collected using an efficient improved shooting method with fast convergence and low computational cost. Graphical demonstrations of the influence of relevant parameters on symmetrical behavior for velocity, skin friction, Nusselt number, and temperature are shown.

Modelling of rheological behaviour of macaíba pulp at different temperatures

ABSTRACT Fruit pulps undergo temperature variations during processing, leading to viscosity changes. This study aimed to analyse the rheological behaviour of macaíba pulp at different temperatures (10 to 50 ºC, with 5 ºC increments) and speeds (2.5 to 200 rpm, totalling 17 speeds). Experimental measurements were performed in a Brookfield viscometer, fitting the Ostwald-de-Waele, Mizrahi-Berk, Herschel-Bulkley, and Casson models to the experimental data of shear stress as a function of shear rate. Among the models used, the Mizrahi-Berk model (R² > 0.9656 and average percentage deviation - P ≤ 4.1%) was found to best fit the rheogram data. Macaíba pulp exhibited a non-newtonian behaviour and was characterised as pseudoplastic. It showed fluid behaviour indexes below unity under the studied conditions, with decreases in apparent viscosity as temperature and shear rate increased. Such behaviour could be described by the Arrhenius equation. The Mizrahi-Berk and Falguera-Ibarz models (R² > 0.99 and P ≤ 10%) best fitted the data and were used to represent the viscosity behaviour of macaíba pulp. The activation energy values of macaíba pulp ranged between 17.53 and 25.37 kJ mol-1, showing a rheological behaviour like other fruit pulps.

Dynamical behaviour of magneto-copper-titania/water-ethylene glycol stream inside a gyrating channel

Inspired by the latest deeds of nanomaterials and their novel features in science and engineering sectors, a detailed mathematical model is presented to investigate an unsteady magneto-buoyancy-driven flow of a non-Newtonian (Casson model) chemically bonded hybrid nano liquid (copper-titania/water-ethylene glycol mixture) streaming through a gyrating channel with fluctuating wall temperature and concentration confined by the porous regime. Hybridized nanoparticles (copper-titania) are dispersed into the water-ethylene glycol mixture (vol.60–40%) hybrid base Casson liquid. Hall currents, porous resistance, thermal radiation, and Dufour impacts are hypothesized in the flow system. This model’s governing partial differential equations are derived from the generic laws of conservation of momentum, energy, and mass. These derived equations are rendered dimensionless by incorporating the normalization variables and parameters. The solutions of the dimensionless transport equations are realized in the closed-form followed by an analytical approach. The stipulated graphs and tables are designed to scrutinize the physical and theoretical upshots of a variety of essential system parameters on the critical dynamical functions or variables. Our simulation results based on set parameters disclose that Hall currents have a propensity to accelerate the fluid flow in the vertical direction and lessen the magnitude of the fluid velocity along the cross-flow direction. Amplifying frequency parameter recommends a diminution in the temperature and concentration profiles. The pattern of streamlines, heatlines, and masslines is drawn to envisage the flow and transport features in the gyrating channel. The novelty of this thermal model is that significance of rotating hybrid suspension and dominating magnetic field along with Hall currents is identified. Due to the rotation of the system, the flow is noticeably amended by the centrifugal and Coriolis forces. The present model is, of course, of great practical and technological importance, for example, chemical engineering, material science, mineral and cleaning oils manufacturing, and plastic and polymer industries.

Numerical Study of Thermal Radiation Phenomenon and Its Influence on Amelioration of the Heat Transfer Mechanism through MHD Non-Newtonian Casson Model

The present study’s main focus is regarding the physical properties of a two-dimensional (2D) magneto-hydrodynamic boundary layer non-Newtonian Casson fluid flow that moves due to an exponentially expanding surface with a mixed convection heat transfer mechanism. In the hydrodynamic flow and heat transmission process, the combined impact of thermal radiation and magnetic field influence is explored. The internal heat generation owing to the fluid motion or a very fluid viscosity is not taken into account. The Chebyshev spectral method (CSM) is employed in this work due to its ability, accuracy, and ease of obtaining the solution for non-linear system of ordinary differential equations (ODEs). This method is an approximate method that can usually obtain the solution in a series form. The mixed convection impact is incorporated in our problem. The results are graphed to help comprehend the many physical parameters that arise in the problem. Graphical results uncover that the speed liquid stream is lessened when reinforcing both the Casson boundary and the Hartmann number, while converse attributes are applied for the Grashof number and the radiation boundary. Finally, a comparison of our current results with previously published work on several particular situations of the problem reveals that they are in excellent agreement.

MHD dissipative Casson nanofluid liquid film flow due to an unsteady stretching sheet with radiation influence and slip velocity phenomenon

Abstract The problem of non-Newtonian Casson thin film flow of an electrically conducting fluid on a horizontal elastic sheet was studied using suitable dimensionless transformations on equations representing the problem. The thin film flow and heat mechanism coupled with mass transfer characteristics are basically governed by the slip velocity, magnetic field, and the dissipation phenomenon. The present numerical analysis by the shooting method was carried out to study the detailed, fully developed heat and mass transfer techniques in the laminar thin film layer by solving the competent controlling equations with eight dominant parameters for the thin liquid film. Additionally, the predicted drag force via skin-friction coefficient and Nusselt and Sherwood numbers were correlated. In view of the present study, a smaller magnetic parameter or a smaller slip velocity parameter exerts very good influence on the development of the liquid film thickness for the non-Newtonian Casson model. Furthermore, a boost in the parameter of unsteadiness causes an increase in both velocity distribution and concentration distribution in thin film layer while an increase in the same parameter causes a reduction in the film thickness. Likewise, the present results are observed to be in an excellent agreement with those offered previously by other authors. Finally, some of the physical parameters in this study, which can serve as improvement factors for heat mass transfer and thermophysical characteristics, make nanofluids premium candidates for important future engineering applications.