Search Results (64)

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

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

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

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

This study presents numerical work to investigate the Falkner–Skan flow of a bio-convective Casson fluid over a wedge using an Evolutionary Padé Approximation (EPA) scheme. The governing partial differential equations and boundary conditions of a Falkner–Skan flow model are transformed to a system of ordinary differential equations involving ten dimensionless parameters by using similarity transformations. In the proposed EPA framework, an equivalent constrained optimization problem is formed. The solution of the resulting optimization problem is analogous to the solution of the dimensionless system of ordinary differential equations. The solutions produced in this work, with respect to various combinations of the physical parameters, are found to be in good agreement with those reported in the previously published literature. The effects of a non-dimensional physical-parameter wedge, Casson fluid, fluid phase effective heat capacity, Brownian motion, thermophoresis, radiation, and magnetic field on velocity profile, temperature profile, fluid concentration profile, and the density of motile microorganisms are discussed and presented graphically. It is observed that the fluid velocity rises with a rise in the Casson fluid viscosity force parameter, and an increase in the Prandtl number causes a decrease in the heat transfer rate. Another significant observation is that the temperature and fluid concentration fields are greatly increased by an increase in the thermophoresis parameter. An increase in the Péclet number suppresses the microorganism density. Moreover, the increased values of the Prandtl number increase the local Nusslet number, whereas the skin friction is increased when an increase in the Prandtl number occurs. Full article

The aim of this work was to prepare a new hydrogel based on nanohydroxyapatite (nFAP, 10% w/w) and fluorides (4% w/w), both of which are used as sources of fluoride ions in the treatment of dentin hypersensitivity, and to characterize its physicochemical properties. The release of fluoride ions from 3 gels (G-F, G-F-nFAP, and G-nFAP gel) was controlled in Fusayama–Meyer artificial saliva at pH 4.5, 6.6, and 8.0. The properties of the formulations were determined by an analysis of viscosity, a shear rate test, a swelling study, and gel aging. Various methods, i.e., FT-IR spectroscopy, UV-VIS spectroscopy, and thermogravimetric, electrochemical, and rheological analysis, were used for the experiment. The profiles of fluoride release indicate that the amount of fluoride ions released increases with a decrease in the pH value. The low pH value facilitated water absorption by the hydrogel, which was also confirmed by the swelling test, and it promoted the exchange of ions with the surrounding environment. Under conditions similar to physiological conditions (at pH 6.6), the amounts of fluorides released into artificial saliva were approximately 250 µg/cm² and 300 µg/cm² for the G-F-nFAP hydrogel and G-F hydrogel, respectively. The aging study and properties of the gels showed a loosening of the gel network structure. The Casson rheological model was used to assess the rheological properties of the non-Newtonian fluids. Hydrogels consisting of nanohydroxyapatite and sodium fluoride are promising biomaterials in the prevention and management of the dentin hypersensitivity. Full article

A non-Newtonian stagnation point fluid flow towards two different inclined heated surfaces is mathematically formulated with pertinent effects, namely mixed convection, viscous dissipation, thermal radiations, heat generation, and temperature-dependent thermal conductivity. Mass transfer is additionally considered by the use of a concentration equation. The flow narrating equations are solved numerically by using the shooting method along with the Runge–Kutta scheme. A total of 80 samples are considered for five different inputs, namely the velocities ratio parameter, temperature Grashof number, Casson fluid parameter, solutal Grashof number, and magnetic field parameter. A total of 70% of the data are used for training the network; 15% of the data are used for validation; and 15% of the data are used for testing. The skin friction coefficient (SFC) is the targeted output. Ten neurons are considered in the hidden layer. The artificial networking models are trained by using the Levenberg–Marquardt algorithm. The SFC values are predicted for cylindrical and flat surfaces by using developed artificial neural networking (ANN) models. SFC shows decline values for the velocity ratio parameter, concentration Grashof number, Casson fluid parameter, and solutal Grashof number. In an absolute sense, owning to a prediction by ANN models, we have seen that the SFC values are high in magnitude for the case of an inclined cylindrical surface in comparison with a flat surface. The present results will serve as a helpful source for future studies on the prediction of surface quantities by using artificial intelligence. Full article

In this work, the objective is to get the exact analytical solution of a generalized Casson fluid model with heat generation and chemical reaction described by the Caputo fractional operator, using the approach that the Laplace transform method includes the Laplace transform of the Caputo derivative. After the exact solution, it will be studied the impact of the order of the fractional derivative and the most essential parameters included in the modeling like the Prandtl number, the thermal Grashof number, the mass Grashof number, the Schmidt number, the heat generation parameter, and the chemical reaction parameter. The physical points of view of the influence will be discussed and analyzed. The findings of the paper will be illustrated by several graphics. The development in industry and engineering science, it makes important to study the flow behavior of non-Newtonian fluids. The domains of applications of the flow behavior of non-Newtonian fluids are diverse such as geophysics, biorheology, and chemical and petroleum industries. Full article

This work examines the non-Newtonian Cassonnanofluid’s three-dimensional flow and heat and mass transmission properties over a Riga plate. The Buongiorno nanofluid model, which is included in the present model, includes thermo-migration and random movement of nanoparticles. It also took into account the Cattaneo–Christov double flux processes in the mass and heat equations. The non-Newtonian Casson fluid model and the boundary layer approximation are included in the modeling of nonlinear partial differential systems. The homotopy technique was used to analytically solve the system’s governing equations. To examine the impact of dimensionless parameters on velocities, concentrations, temperatures, local Nusselt number, skin friction, and local Sherwood number, a parametric analysis was carried out. The velocity profile is augmented in this study as the size of the modified Hartmann number increases. The greater thermal radiative enhances the heat transport rate. When the mass relaxation parameter is used, the mass flux values start to decrease. Full article

Stochastic simulations enable researchers to incorporate uncertainties beyond numerical discretization errors in computational fluid dynamics (CFD). Here, the authors provide examples of stochastic simulations of incompressible flows and numerical solutions for validating these newly emerging stochastic modeling methods. A numerical scheme is constructed for finding solutions to stochastic parabolic equations. The scheme is second-order accurate in time for the constant coefficient of the Wiener process term. The stability analysis of the scheme is also provided. The scheme is applied to the dimensionless heat and mass transfer model of mixed convective non-Newtonian nanofluid flow over oscillatory sheets. Both the deterministic and stochastic energy equations use temperature-dependent thermal conductivity. The stochastic model is more general than the deterministic model. The results are calculated for both flat and oscillatory plates. Casson parameter, mixed convective parameter, thermophoresis, Brownian motion parameter, Prandtl number, Schmidt number, and reaction rate parameter all impact the velocities, temperatures, and concentrations shown in the graphs. Under the influence of the oscillating plate, the results reveal that the concentration profile decreases with increasing Brownian motion parameters and increases with increasing thermophoresis parameters. The behavior of the velocity profile for the deterministic and stochastic models is provided, and contour plots for the stochastic model are also displayed. This article aims to provide a state-of-the-art overview of recent achievements in the field of stochastic computational fluid dynamics (SCFD) while also pointing out potential future avenues and unresolved challenges for the computational mathematics community to investigate. Full article

A novel analysis of the electromagnetohydrodynamic (EMHD) non-Newtonian nanofluid blood flow incorporating CuO and Al${}_2$O${}_3$ nanoparticles through a permeable walled diseased artery having irregular stenosis and an aneurysm is analyzed in this paper. The non-Newtonian behavior of blood flow is addressed by the Casson fluid model. The effective viscosity and thermal conductivity of nanofluids are calculated using the Koo-Kleinstreuer-Li model, which takes into account the Brownian motion of nanoparticles. The mild stenosis approximation is employed to reduce the bi-directional flow of blood to uni-directional. The blood flow is influenced by an electric field along with a magnetic field perpendicular to the blood flow. The governing mathematical equations are solved using Crank-Nicolson finite difference approach. The model has been developed and validated by comparing the current results to previously published benchmarks that are peculiar to this study. The results are utilized to investigate the impact of physical factors on momentum diffusion and heat transfer. The Nusselt number escalates with increasing CuO nanoparticle diameter and diminishing the diameter of Al${}_2$O${}_3$ nanoparticles. The relative % variation in Nusselt number enhances with Magnetic number, whereas a declining trend is obtained for the electric field parameter. The present study’s findings may be helpful in the diagnosis of hemodynamic abnormalities and the fields of nano-hemodynamics, nano-pharmacology, drug delivery, tissue regeneration, wound healing, and blood purification systems. Full article