Search Results (107)

This study presents a novel framework for uncertainty propagation in power-law, Bingham, and Casson fluids through rectangular ducts under stochastic viscosity (Case I) and pressure gradient conditions (Case II). Using the computationally efficient Stochastic Finite Difference Method with Homogeneous Chaos (SFDHC), validated via comparison with quasi-Monte Carlo simulations, we demonstrate significantly lower computational costs across varying Coefficients of Variation (COVs). For viscosity uncertainty (Case I), results show a 0.54–2.8% increase in mean maximum velocity with standard deviations reaching 75.3–82.5% of the COV, where the power-law model exhibits the greatest sensitivity (velocity variations spanning 71.2–177.3% of the mean at COV = 20%). Pressure gradient uncertainty (Case II) preserves mean velocities but produces narrower and symmetric distributions. We systematically evaluate the effects of aspect ratio, yield stress, and flow behavior index on the stochastic velocity response of each fluid. Moreover, our analysis pioneers a performance hierarchy: Herschel–Bulkley fluids show the highest mean and standard deviation of maximum velocity, followed by power-law, Robertson–Stiff, Bingham, and Casson models. A key finding is the extreme fluctuation of the Robertson–Stiff model, which exhibits the most drastic deviations, reaching up to 177% of the average velocity. The significance of fluid-specific stochastic analysis in duct system design is underscored by these results. This is especially critical for non-Newtonian flows, where system performance and reliability are greatly impacted by uncertainties in viscosity and pressure gradient, which reflect actual operational variations. Full article

The physical and rheological properties of mucilage hydrogels derived from the cladodes of Opuntia ficus-indica (L. Mill) were compared with those of commercial pectin for potential applications in the food industry. All hydrogels—formulated by incorporating sucrose and either calcium chloride or calcium carbonate to promote favorable gel network formation—exhibited pseudoplastic (shear-thinning) behavior. The flow characteristics of the hydrogels prepared with mucilage or pectin conformed to the Casson fluid model. Moreover, all samples consistently displayed loss modulus (G″) values exceeding their corresponding storage modulus (G′) values, indicating a dominant viscous behavior over elastic properties. The ζ-potential of all samples was negative across the pH range studied. Mucilage-based samples exhibited lower ionizability per unit mass and reduced phase stability compared to those containing pectin. Principal component analysis (PCA) revealed that mucilage hydrogels exhibited multivariate profiles similar to pectin hydrogels containing calcium carbonate, though the latter demonstrated greater polydispersity than standard pectic gels. Infrared spectroscopy further highlighted distinct spectral differences between pectins and mucilages, offering valuable insights into their respective functional characteristics. Collectively, these findings underscore the potential of Opuntia ficus-indica mucilages as viable additives in food formulations. Full article

This paper explores the complex dynamics of mixed convective flow in a Casson fluid saturated in a non-Darcy porous medium, focusing on the influence of gyrotactic microorganisms, internal heat generation, and multiple convective mechanisms. Casson fluids, known for their non-Newtonian behavior, are relevant in various industrial and biological contexts where traditional fluid models are insufficient. This study addresses the limitations of the standard Darcy’s law by examining non-Darcy flow, which accounts for nonlinear inertial effects in porous media. The governing equations, derived from conservation laws, are transformed into a system of no linear ordinary differential equations (ODEs) using similarity transformations. These ODEs are solved numerically using a finite differencing method that incorporates central differencing, tridiagonal matrix manipulation, and iterative procedures to ensure accuracy across various convective regimes. The reliability of this method is confirmed through validation with the MATLAB (R2024b) bvp4c scheme. The investigation analyzes the impact of key parameters (such as the Casson fluid parameter, Darcy number, Biot numbers, and heat generation) on velocity, temperature, and microorganism concentration profiles. This study reveals that the Casson fluid parameter significantly improves the velocity, concentration, and motile microorganism profiles while decreasing the temperature profile. Additionally, the Biot number is shown to considerably increase the concentration and dispersion of motile microorganisms, as well as the heat transfer rate. The findings provide valuable insights into non-Newtonian fluid behavior in porous environments, with applications in bioengineering, environmental remediation, and energy systems, such as bioreactor design and geothermal energy extraction. Full article

Cardiovascular diseases represent one of the leading causes of mortality worldwide, underscoring the need for accurate simulations of blood flow to improve diagnosis and treatment. This study examines blood flow dynamics in two different vascular structures—the aorta and the right coronary artery (RCA)—using Computational Fluid Dynamics (CFD). Utilizing COMSOL Multiphysics^®, various mathematical models were applied to simulate blood flow under physiological conditions, assuming a steady-flow regime. These models include both Newtonian and non-Newtonian approaches, such as the Carreau and Casson models, as well as viscoelastic frameworks like Oldroyd-B, Giesekus, and FENE-P. Key metrics—such as velocity fields, pressure distributions, and error analysis—were evaluated to determine which model most accurately describes hemodynamic behavior in large vessels like the aorta and in smaller and more complex vessels like the RCA. The results highlight the importance of shear-thinning and viscoelastic properties in small vessels like the RCA, which contrasts with the predominantly Newtonian behavior observed in the aorta. While computational challenges remain, this study contributes to a deeper understanding of blood rheology, enhancing the accuracy of cardiovascular simulations and offering valuable insights for diagnosing and managing vascular diseases. Full article

The study examines the onset of magnetoconvection in a Casson fluid-saturated inclined porous layer. Oberbeck–Boussinesq approximation and Darcy law employed to characterize the fluid motion. The stability of the system is examined using both linear and nonlinear stability theories. A basic solution of the governing equation is determined. The linear instability is studied by employing disturbances to the basic flow. The nonlinear instability is analyzed utilizing the energy method. The solution to the eigenvalue problem is derived using the bvp4c routine in MATLAB R2023a. This study evaluates the influence of nondimensional parameters specifically, the Hartmann number, Casson parameter, and inclination angle on both linear and nonlinear instability. The Casson parameter destabilizes the system, whereas the Hartmann number and inclination angle stabilize it. Transverse rolls exhibit greater stability compared to longitudinal rolls. Changes in the Casson parameter significantly affect the presence or absence of transverse rolls; as its value changes, so does the disappearance of transverse rolls. Full article

Fluid flow along an inclined channel phenomenon is crucial in several geophysical, environmental, engineering, biological, and industrial processes, and in aerodynamics and hemodynamics. This present study examines the effect of a constant magnetic field on the entropy production rate in a steady flow of Casson fluid along an inclined heated channel. The governing equations for the flow of velocity, temperature, and entropy generation are formulated based on the Casson constitutive relations and thermodynamics’ first and second laws. The exact solutions are constructed for the dimensionless equations and validated with previous results in the literature. The effects of various fluid parameters on the flow, heat transfer, and entropy production rate are conducted and reported graphically with adequate discussion. The impact of the Hartmann number parameter reveals a decrease in both flow velocity and entropy generation rate, meanwhile it also enhances the fluid temperature distribution across the inclined channel. An opposite trend is, however, observed with the Casson fluid parameter. Full article

In this study, five different time-dependent incompressible non-Newtonian boundary layer models in two dimensions are investigated with the self-similar Ansatz, including external magnetic field effects. The power-law, the Casson fluid, the Oldroyd-B model, the Walter fluid B model, and the Williamson fluid are analyzed. For the first two models, analytical results are given for the velocity and pressure distributions, which can be expressed by different types of hypergeometric functions. Depending on the parameters involved in the analytical solutions of the nonlinear ordinary differential equation obtained by the similarity transformation, a vast range of solution types is presented. It turned out that the last three models lack self-similar symmetry; therefore, no analytic solutions can be derived. Full article

This study investigates the steady, two-dimensional boundary layer flow of a Casson fluid over an inclined nonlinear stretching surface embedded within a Forchheimer porous medium. The governing partial differential equations are transformed into a set of ordinary differential equations through similarity transformations. The analysis incorporates the effects of an external uniform magnetic field, gravitational forces, thermal radiation modeled by the Rosseland approximation, and first-order homogeneous chemical reactions. We consider several dimensionless parameters, including the Casson fluid parameter, magnetic parameter, Darcy and Forchheimer numbers, Prandtl and Schmidt numbers, and the Eckert number to characterize the flow, heat, and mass transfer phenomena. Analytical solutions for the velocity, temperature, and concentration profiles are derived under simplifying assumptions, and expressions for critical physical quantities such as the skin friction coefficient, Nusselt number, and Sherwood number are obtained. Full article

This analysis emphasizes the significance of radiation and chemical reaction effects on the boundary layer flow (BLF) of Casson liquid over a linearly elongating surface, as well as the properties of momentum, entropy production, species, and thermal dispersion. The mass diffusion coefficient and temperature-dependent models of thermal conductivity and species are used to provide thermal transportation. Nonlinear partial differential equations (NPDEs) that go against the conservation laws of mass, momentum, heat, and species transportation are the form arising problems take on. A set of coupled dimensionless partial differential equations (PDEs) are obtained from a set of convective differential equations by applying the proper non-similar transformations. Local non-similarity approaches provide an analytical approximation of the dimensionless non-similar system up to two degrees of truncations. The built-in Matlab (Version: 7.10.0.499 (R2010a)) solver bvp4c is used to perform numerical simulations of the local non-similar (LNS) truncations. Full article

In this study, numerical simulations are conducted with the goal of exploring the impact of the direction of the moving wall, solute and thermal transport, and entropy production on doubly diffusive convection in a chamber occupied by a Casson liquid. Wall movement has a significant impact on convective flow, which, in turn, affects the rate of mass and heat transfer; this sparked our interest in conducting further analysis. The left and right (upright) walls are preserved with constant (but different) thermal and solutal distributions, while the horizontal boundaries are impermeable to mass transfer and insulated from heat transfer. Numerical solutions are acquired using the control volume technique. Outcomes under a variety of Casson fluid parameters, including Ri, Gr, buoyancy ratio, and direction of the moving wall(s), are explored, and the influences of entropy generation are comprehensively investigated. While the flow field consists of a single cell in case I, it is dual-cellular in case III for all values of the considered parameters. Comparing the three cases, the average heat and mass transport presented lower values in case III due to the movement of an isothermal (left) wall against the buoyant force, while these values are enhanced in case I. The obtained results are expected to be useful in thermal engineering, material, food, and chemical processing applications. Full article

Many studies on magnetorheological fluid (MRF) have been carried out over the last three decades, highlighting several salient advantages, such as a fast phase change, easy control of the yield stress, and so forth. In particular, several review articles of MRF technology have been reported over the last two decades, summarizing the development of MRFs and their applications. As specific examples, review articles have been published that include the optimization of the particles and carrier liquid to achieve minimum off-state viscosity and maximum yield stress at on-state, the formulation of many constitutive models including the Casson model and the Herschel–Bulkley (H–B) model, sedimentation enhancement using additives and nanosized particles, many types of dampers for automotive suspension and civil structures, medical and rehabilitation devices, MRF polishing technology, the methods of magnetic circuit design, and the synthesis of various controllers. More recently, the effect of the temperature and thermal conductivity on the properties of MRFs and application systems are actively being investigated by several works. However, there is no review article on this issue so far, despite the fact that the thermal problem is one of the most crucial factors to be seriously considered for the development of advanced MRFs and commercial products of application systems. In this work, studies on the thermal conductivity and temperature in MRFs themselves and their temperature-dependent application systems are reviewed, respectively, and principal results are summarized, emphasizing the following: how to reduce the temperature effect on the field-dependent properties of MRFs and how to design an application system that minimizes the thermal effect. It is noted here that the review summary is organized in a chronological format using tables. Full article

The primary goal of this research is to present a novel computational intelligence approach of the AI-based Levenberg–Marquardt scheme under the influence of backpropagated neural network (LMS-BPNN) for optimizing MHD ternary hybrid nanofluid using Casson fluid over a porous shrinking sheet in the existence of thermal radiation ($Rd$) effects. The governing partial differential equations (PDEs) showing the Casson ternary hybrid nanofluid are converted into a system of ordinary differential equations (ODEs) with suitable transformations. The numerical data is constructed as a reference with bvp4c (MATLAB built-in function used to solve a system of ODEs) by varying Casson fluid parameters ($\beta$), magnetic field ($M$), porosity ($S$), nanoparticle concentrations (${\varphi }_1={\varphi }_2={\varphi }_3$), and thermal radiation ($Rd$) effects across all LMS-BPNN scenarios. The numerical data-sheet is divided into 80% of training, 10% of testing, and 10% of validation for LMS-BPNN are used to analyze the estimated solution and its assessment with a numerical solution using bvp4c is discussed. The efficiency and consistency of LMS-BPNN are confirmed via mean squared error (MSE) based fitness curves, regression analysis, correlation index ($R$) and error histogram. The results show that velocity decreases as $\beta$ grows, whereas velocity increase as $M$ increases. The concentrations of nanoparticles and thermal radiations have increasing effects on $\theta \left(0\right)$. To comprehend the dependability and correctness of the data gained from numerical simulations, error analysis is a key stage in every scientific inquiry. Error analysis is presented in terms of absolute error and it is noticed that the error between the numerical values and predicted values with AI is approximately ${10}^{-6}$. The error analysis reveals that the developed AI algorithm is consistent and reliable. Full article

Nanofluids are extremely beneficial to scientists because of their excellent heat transfer rates, which have numerous medical and industrial applications. The current study deals with the peristaltic flow of nanofluid (i.e., Casson nanofluid) in a symmetric elastic/compliant channel. Buongiorno’s framework of nanofluids was utilized to create the equations for flow and thermal/mass transfer along with the features of Brownian motion and thermophoresis. Slip conditions were applied to the compliant channel walls. The thermal field incorporated the attributes of viscous dissipation, ohmic heating, and thermal radiation. First-order chemical-reaction impacts were inserted in the mass transport. The influences of the Hall current and mixed convection were also presented within the momentum equations. Lubricant approximations were exploited to make the system of equations more simplified for the proposed framework. The solution of a nonlinear system of ODEs was accomplished via a numerical method. The influence of pertinent variables was examined by constructing graphs of fluid velocity, temperature profile, and rate of heat transfer. The concentration field was scrutinized via table. The velocity of the fluid declined with the increment of the Hartman number. The effects of thermal radiation and thermal Grashof number on temperature showed opposite behavior. Heat transfer rate was improved by raising the Casson fluid parameter and the Brownian motion parameter. Full article

In this article, we present a finite element method for studying the dynamic behavior of deformable vesicles, which mimic red blood cells, in a non-Newtonian Casson fluid. The fluid membrane, represented by an implicit level-set function, adheres to the Canham–Helfrich model and maintains surface inextensibility constraint through penalty. We propose a two-step time integration scheme that incorporates higher-order accuracy by using an asymmetric composition of discrete flow based on the second-order backward difference formula, followed by a projection onto the real axis. Our framework incorporates variable time steps generated by an appropriate adaptation criterion. We validate our model through numerical simulations against existing experimental and numerical results in the case of purely Newtonian flow. Furthermore, we provide preliminary results demonstrating the influence of the non-Newtonian fluid model on membrane regimes. Full article

The rapid development of nanotechnology in our emerging industries has drawn the interest of numerous researchers and scientists, especially in experimental and numerical studies. Therefore, the present analytical study will help reduce time and costs and validate the numerical study. However, the analytical research of carbon nanotubes with Casson fluid in a channel is still limited. Therefore, the current analytical study inspected the consequences of carbon nanotubes (CNTs) nanoparticles on the heat and mass transfer of magnetohydrodynamics (MHD) Casson nanofluid flow induced by a moving vertical plate with a porous region inside an asymmetrical channel. Dimensional governing equations are used for the modelling, which is then expressed in a dimensionless form by employing dimensionless variables. The analytical solutions for the velocity, temperature, and concentration are tackled using the Laplace transform technique. The temperature and velocity are significantly enhanced when increasing the nanoparticle volume fraction. This is due to the outstanding characteristic of nanofluid thermal conductivity, which results in an efficient heat transfer. This result has the potential to be applied to various nanofluid cooling technologies. Since the solutions are determined in an analytical form, this study could be used as a reference for other numerical and experimental works and a guide for several industries. Full article