Search Results (67)

The non-Newtonian Carreau fluid model is a suitable model for pseudoplastic fluids and can be used to characterize fluids not so different from biological fluids, such as the blood, and fluids involved in geological processes, such as lava and magma. These fluids are frequently conveyed by complex flow structures, which consist of a network of channels that allow the fluid to flow from one place (source or sink) to a variety of locations or vice versa. These flow networks are not randomly arranged but show self-similarity at different spatial scales. Our work focuses on the design of self-similar branched flow networks that look the same on any scale. The flow is incompressible and stationary with a viscosity following the Carreau model, which is important for the study of complex flow systems. The flow division ratios, the flow resistances at different scales, and the geometric size ratios for maximum flow access are studied, based on Computational Fluid Dynamics (CFD). A special emphasis is placed on investigating the possible incidence of flow asymmetry in these symmetric networks. Our results show that asymmetries may occur for both Newtonian and non-Newtonian fluids and shear-thinning fluids most affect performance results. The lowest flow resistance occurs when the diameters of the parent and daughter ducts are equal, and the more uniform distribution of flow resistance occurs for a ratio between the diameters of the parent and daughter ducts equal to 0.75. Resistances for non-Newtonian fluids are 4.8 to 5.6 times greater than for Newtonian fluids at Reynolds numbers of 100 and 250, respectively. For the design of engineering systems and the assessment of biological systems, it is recommended that the findings presented are taken into account. Full article

Radical or partial nephrectomy, commonly used for the treatment of kidney tumors, is a surgical procedure with a risk of high blood loss. The primary aim of this study is to quantify blood loss and elucidate the redistribution of blood flux and pressure between the two kidneys and the abdominal aorta during renal resection. We have developed a robust research methodology that introduces a new lumped-parameter mathematical model, specifically focusing on the vasculature of both kidneys using a non-Newtonian Carreau fluid. This model, a first-order approximation, accounts for the variation in the total impedance of the vasculature when various vessels are severed in the diseased kidney (assumed to be the left in this work). The model offers near real-time estimations of the flow–pressure redistribution within the vascular network of the two kidneys and the downstream aorta for several radical or partial nephrectomy scenarios. Notably, our findings indicate that the downstream aorta receives an approximately 1.27 times higher percentage of the redistributed flow from the diseased kidney compared to that received by the healthy kidney, in nearly all examined cases. The implications of this study are significant, as they can inform the development of surgical protocols to minimize blood loss and can assist surgeons in evaluating the adequacy of the remaining kidney vasculature. Full article

Peristaltic flow in a straight rectangular duct is examined imposed by contraction pulses implemented by pairs of horizontal cylindrical segments with their axes perpendicular to the flow direction. The wave propagation speed is considered in such a range that triggers a laminar fluid motion. The setting is analyzed over a set of variables which includes the propagation speed, the relative occlusion, the modality of the squeezing pulse profile and the Carreau power index. The numerical solution of the equations of motion on Cartesian meshes is grounded in the immersed boundary method. An increase in the peristaltic pulse modality leads to the reduction in the shear rate levels on the central tube axis and to the movement of the peristaltic characteristics to higher pressure values. The effect of the no slip side walls (NSSWs) is elucidated by the collation with relevant results for the flow field produced under the same assumptions though with slip side walls (SSWs). Shear thinning behavior exhibits a significantly larger effect on transport efficiency for the NSSWs duct than on the SSWs duct. Full article

Drilled shafts are cylindrical, cast-in-place concrete deep foundation elements. During construction, anomalies in drilled shafts can occur due to the kinematics of concrete, flowing radially from the center of the shaft to the concrete cover region at the peripheral edge. This radial component of concrete flow develops veins or creases of poorly cemented or high water-cement ratio material, as the concrete flows around the reinforcement cage of rebars and ties, jeopardizing the shaft integrity. This manuscript presents a three-dimensional computational fluid dynamics (CFD) model of the non-Newtonian concrete flow in drilled shaft construction developed using the finite volume method with interface tracking based on the volume of fluid (VOF) method. The non-Newtonian behavior of the concrete is represented via the Carreau constitutive model. The model results are encouraging as the flow obtained from the simulations shows patterns of both horizontal and vertical creases in the concrete cover region, consistent with previously reported field and laboratory experiments. Moreover, the flow exhibits the concrete head differential developed between the inside and the outside of the reinforcement cage, as exhibited in the physical experiments. This head differential induces the radial component of the concrete flow responsible for the creases that develop in the concrete cover region. Results show that the head differential depends on the flowability of the concrete, consistent with field observations. Less viscous concrete tends to reduce the head differential and the formation of creases of poorly cemented material. The model is unique, making use of state-of-the-art numerical techniques and demonstrating the capability of CFD to model industrially relevant concrete flows. Full article

In 2021, approximately 51% of patients diagnosed with kidney tumors underwent surgical resections. One possible way to reduce complications from surgery is to minimise the associated blood loss, which, in the case of partial nephrectomy, is caused by the inadequate repair of branching arteries within the kidney cut during the tumor resection. The kidney vasculature is particularly complicated in nature, consisting of various interconnecting blood vessels and numerous bifurcation, trifurcation, tetrafurcation, and pentafurcation points. In this study, we present a mathematical lumped-parameter model of a whole kidney, assuming a non-Newtonian Carreau fluid, as a first approximation of estimating the blood loss arising from the cutting of single or multiple vessels. It shows that severing one or more blood vessels from the kidney vasculature results in a redistribution of the blood flow rates and pressures to the unaltered section of the kidney. The model can account for the change in the total impedance of the vascular network and considers a variety of multiple cuts. Calculating the blood loss for numerous combinations of arterial cuts allows us to identify the appropriate surgical protocols required to minimise blood loss during partial nephrectomy as well as enhance our understanding of perfusion and account for the possibility of cellular necrosis. This model may help renal surgeons during partial organ resection in assessing whether the remaining vascularisation is sufficient to support organ viability. Full article

The use of coat-hanger dies is prevalent in the plastic film and sheet extrusion industry. The product quality and the power of the extrusion machine depend on the uniformities of the fluid velocity at the exit and the pressure drop. Die manufacturers face the challenge of producing coat-hanger dies that can extrude materials uniformly and with a minimal pressure drop. Previous studies have analyzed the die outlet’s flow homogeneity and pressure drop using various numerical simulations. However, the combination of the scheme programming language together with the Adjoint Method of Optimization has yet to be attempted. The adjoint optimization method has been demonstrated to be beneficial in addressing issues related to shape optimization problems and it may also be beneficial in optimizing the design of dies used in polymer melt extrusion. In this study, the proposed innovations involve incorporating both the Scheme programming language and Adjoint solver to examine and optimize the coat hanger’s flow homogeneity and pressure drop. Before optimization, the outlet velocity was almost 10 times higher at the die center than at the edges but after optimization, it became more uniform. The proposed optimized coat-hanger die geometry results in more uniform melt flow as demonstrated by the velocity contour plot and the outlet velocity graph in the die slit area, reducing the deviation value from 0.097 to 0.015. Additionally, the mass flux variance across the die outlet decreased by 71.6% from 0.015069 kg m⁻² s⁻¹ to 0.004281 kg m⁻² s⁻¹. Therefore, using this method reduces the amount of time wasted on trial and error or other optimization techniques that may be limited by design constraints. Full article

Injection molding is a multiphase process that requires accurate simulation of the filling phase. This is a key element in predicting the complete injection molding cycle. The filling phase presents a complex set of challenges, including migrating melt fronts, multi-phase flow, non-Newtonian fluid dynamics, and intertwined heat transfer. Evolving from 1D to 2D, 2.5D, and 3D techniques, filling simulation research has adapted to capture the intricacies of injection-molded parts. However, the need for accuracy in the characterization of the rheological properties of polymers during filling is still of paramount importance. In order to systematically categorize the numerical methods used to simulate the filling phase of injection molding, this review paper provides a comprehensive summary. Particular emphasis is given to the complex interaction of multiple geometric parameters that significantly influence the dynamic evolution of the filling process. In addition, a spectrum of rheological models is thoroughly and exhaustively explored in the manuscript. These models serve as basic mathematical constructs to help describe the complex viscous behavior of polymers during the filling phase. These models cover a spectrum of complexity and include widely recognized formulations such as the Power-Law, second-order, Herschel–Bulkley, Carreau, Bird–Carreau, and Cross models. The paper presents their implementation to include the temperature-dependent influence on viscosity. In this context, the extensions of these models are explained in detail. These extensions are designed to take into account the dynamic viscosity changes caused by the different thermal conditions during the filling process. An important contribution of this study is the systematic classification of these models. This categorization encompasses both academic research and practical integration into commercial software frameworks. In addition to the theoretical importance of these models, their practical value in overcoming challenges in the field of injection molding is emphasized. By systematically outlining these models within a structured framework, this classification promotes a comprehensive understanding of their intrinsic characteristics and relevance in different scenarios. Full article

This investigation is related to this study of entropy generation during Carreau nanofluid flow under variable thermal conductivity conditions. The heat and mass transfer phenomena are observed in the presence of thermal radiation and activation energy. The flow is induced by a porous stretching surface. Appropriate variables are used in order to simplify the problem into dimensionless form. The numerical simulations are performed by using the shooting technique. The physical aspects of the problem in view of different flow parameters are reported. It is observed that consideration of variable fluid thermal conductivity enhances heat transfer. An enhancement in heat and mass transfer phenomena is observed with increasing the Weissenberg number. Moreover, entropy generation increases with Weissenberg and Brinkman numbers. Current results present applications in thermal processes, heat exchangers, energy systems, combustion and engine design, chemical processes, refrigeration systems, etc. Full article

This current investigation aims to explore the significance of induced magnetic fields and double-diffusive convection in the radiative flow of Carreau nanofluid through three distinct geometries. To simplify the fluid transport equations, appropriate self-similarity variables were employed, converting them into ordinary differential equations. These equations were subsequently solved using the Runge–Kutta–Fehlberg (RKF) method. Through graphical representations like graphs and tables, the study demonstrates how various dynamic factors influence the fluid’s transport characteristics. Additionally, the artificial neural network (ANN) approach is considered an alternative method to handle fluid flow issues, significantly reducing processing time. In this study, a novel intelligent numerical computing approach was adopted, implementing a Levenberg–Marquardt algorithm-based MLP feed-forward back-propagation ANN. Data collection was conducted to evaluate, validate, and guide the artificial neural network model. Throughout all the investigated geometries, both velocity and induced magnetic profiles exhibit a declining trend for higher values of the magnetic parameter. An increase in the Dufour number corresponds to a rise in the nanofluid temperature. The concentration of nanofluid increases with higher values of the Soret number. Similarly, the nanofluid velocity increases with higher velocity slip parameter values, while the fluid temperature exhibits opposite behavior, decreasing with increasing velocity slip parameter values. Full article

This mainly theoretical work is devoted to the study of the contribution of the cell-free layer (CFL) near the vessel wall to hemodynamics in a large coronary artery with stenosis to assess the relevance of CFL modeling to the needs of interventional cardiology. An Euler–Euler model considering blood as a two-component fluid with a discrete phase of erythrocytes and a liquid plasma phase was applied to a simple 2d vessel with 65% stenosis. It was found that both the CFL thickness and the local contribution of the CFL thickness to hemodynamics are inhomogeneous along the vessel. The effects of CFL on the velocity profiles, vortex formation, hematocrit, viscosity, and wall shear stresses in the area of stenosis were determined. To demonstrate the significance of CFL modeling for prognostic purposes, the same hemodynamic conditions, analyzed using a one-component model, were also considered. A comparison analysis showed that the existence of CFL resulted in a significant overestimation (up to over 100%) of the main hemodynamic characteristics of the flow obtained using the model based on the Carreau equation. Full article

Despite the wide application of combustion in reactive materials, one of the challenges faced globally is the auto-ignition of such materials, resulting in fire and explosion hazards. To avoid this unfortunate occurrence, a mathematical model describing the thermal decomposition of combustible polymer material in a rectangular stockpile is formulated. A nonlinear momentum equation is provided with the assumption that the combustible polymer follows a Carreau constitutive relation. The chemical reaction of the polymer material is assumed to be exothermic; therefore, Arrhenius’s kinetic theory is considered in the energy balance equation. The bivariate spectral local linearization scheme (BSLLS) is utilized to provide a numerical solution for the dimensionless equations governing the problem. The obtained results are validated by the collocation weighted residual method (CWRM), and a good agreement is achieved. Dimensionless velocity, temperature, and thermal stability results are presented and explained comprehensively with suitable applications. Some of the obtained results show that thermal criticality increases with increasing power law index (n) and radiation (Ra) values and decreases with increasing variable viscosity (β1) and material parameter (We) values. Full article

Activation energy can be elaborated as the minimal energy required to start a certain chemical reaction. The concept of this energy was first presented by Arrhenius in the year 1889 and was later used in the oil reservoir industry, emulsion of water, geothermal as well as chemical engineering and food processing. This study relates to the impacts of mass transfer caused by temperature differences (Soret) and heat transport due to concentration gradient (Dufour) in a Carreau model with nanofluids (NFs), mixed convection and a magnetic field past a stretched sheet. Moreover, thermal radiation and activation energy with new mass flux constraints are presumed. All chemical science specifications of nanofluid are measured as constant. As a result of the motion of nanofluid particles, the fluid temperature and concentration are inspected, with some physical description. A system of coupled partial differential frameworks is used mathematically to formulate the physical model. A numerical scheme named the Runge–Kutta (R-K) approach along with the shooting technique are used to solve the obtained equations to a high degree of accuracy. The MATLAB R2022b software is used for the graphical presentation of the solution. The temperature of the nanofluid encompasses a quicker rate within the efficiency of a Dufour number. An intensifying thermal trend is observed for thermophoresis and the Brownian motion parameter. The Soret effect causes a decline in the fluid concentration, and the opposite trend is observed for rising activation energy. In addition, the local Nusselt number increases with the Prandtl number. Further, the comparative outcomes for drag force are established, with satisfying agreement with the existing literature. The results acquired here are anticipated to be applied to improving heat exchanger thermal efficiency to maintain thermal balancing control in compact heat density equipment and devices. Full article

We present a computational framework for modeling an inextensible single vesicle driven by the Helfrich force in an incompressible, non-Newtonian extracellular Carreau fluid. The vesicle membrane is captured with a level set strategy. The local inextensibility constraint is relaxed by introducing a penalty which allows computational savings and facilitates implementation. A high-order Galerkin finite element approximation allows accurate calculations of the membrane force with high-order derivatives. The time discretization is based on the double composition of the one-step backward Euler scheme, while the time step size is flexibly controlled using a time integration error estimation. Numerical examples are presented with particular attention paid to the validation and assessment of the model’s relevance in terms of physiological significance. Optimal convergence rates of the time discretization are obtained. Full article

This study focused on the analysis of two-dimensional incompressible magnetohydrodynamic Carreau nanofluid flow across a stretching cylinder containing microorganisms with the impacts of chemical reactions and multiple slip boundary conditions. Moreover, the main objective is concerned with the enhancement of thermal transportation with the effect of heat source and bioconvection. By assigning pertinent similarity transitions to the governing partial differential equations, a series of equations (ODES) is generated. An optimum computational solver, namely the bvp5c software package, is utilized for numerical estimations. The impact of distinct parameters on thermal expansion, thermophoresis, and the Nusselt number has been emphasized, employing tables, diagrams, and surface maps for both shear thinning (n < 1) and shear thickening (n > 1) instances. Motile concentration profiles decrease with Lb and the motile microorganism density slip parameter. It is observed that with increasing values of Pr, both the boundary layer thickness and temperature declined in both cases. The Weissenberg number demonstrates a different nature depending on the type of fluid; skin friction, the velocity profile and Nusselt number drop when n < 1 and increase when n > 1. The two- and three-dimensional graphs show the simultaneous effect of involving parameters with physical quantities. The accuracy of the existing observations is evidenced by the impressive resemblance between the contemporary and preceding remedies. Full article

This study compares the film thickness, lubricant temperature, and traction curves of two groups of commonly used constitutive models for lubricants in thermo-elastohydrodynamic lubrication (TEHL) modelling. The first group consists of the Tait equation of state, the Doolittle Newtonian viscosity model, and the Carreau shear thinning model. The second group includes the Dowson equation of state, the Roelands–Houpert Newtonian viscosity model, and the Eyring shear thinning model. The simulations were conducted using a Computational Fluid Dynamic and Fluid-Structure Interaction (CFD-FSI) approach, which employs a homogeneous equilibrium model for the flow simulation along with a linear elastic solver to describe the deformation of the solid materials. The simulations were conducted under a load range of 100 kN/m to 200 kN/m and a slide-to-roll-ratio (SRR) range between 0 and 2 using Squalane lubricant. The results show up to a 10% deviation in central film thickness, a 31% deviation in coefficient of friction (CoF), and a 38% deviation in maximum lubricant temperature when using the different constitutive models. This study highlights the sensitivity of TEHL simulation results to the choice of constitutive models for lubricants and the importance of carefully selecting the appropriate models for specific applications. Full article