Variable Viscosity Research Articles

A variable turbulent Schmidt number model in Jet-in-Crossflow simulation and its applications

This study proposes a variable turbulent Schmidt number (Sct) model to improve the precision of Reynolds-Averaged Navier-Stokes (RANS) simulations for Jet-in-Crossflow (JICF) scalar mixing phenomena, with a particular focus on hydrogen/air mixing characterized by strong density variations. By incorporating a correction term associated with turbulent kinetic energy based on a selected Sct value, the model aims to amplify the diffusion rate of the jet, particularly in regions where the interaction between the mainstream flow and the jet is significant. This enhancement in simulation accuracy is validated against Large Eddy Simulation (LES) results, which serve as the benchmark for analysis. Statistical analysis of LES results reveals a notable increase in the turbulent diffusion coefficient in regions characterized by strong interactions between the jet and mainstream flow. Meanwhile, minimal variation in turbulent viscosity is observed, resulting in a reduced Sct in areas with high turbulent kinetic energy. The proposed model is validated within a open-space JICF case, a micro-tube JICF case and a free jet case. In micro-tube JICF scenarios, initial simulations with a fixed Sct value were conducted. Following comparison, a value of 0.7 was identified as the basis for correction. Subsequently, the variable Sct model was implemented, thereby enhancing the accuracy of RANS simulations in micro-tubes.

MINIMIZING TEMPERATURE DEVIATIONS IN RUBBER MIXING PROCESS BY USING ARTIFICIAL NEURAL NETWORKS

ABSTRACT Rubber mixing is a complex manufacturing process that poses challenges for process control due to the high number of control variables, including mixing parameter settings, rheological behavior, compound viscosity, and batch-dependent material variations. Already small deviations from the control variables can influence the compound properties, leading to increased scrap rates. To address these challenges, this paper introduces an artificial intelligence–based approach to enhance process control in rubber mixing by predicting mixing temperatures from input variables. The proposed method uses feedforward neural networks (FFNs) to enable early identification of batch-specific temperature deviations, thereby enabling systematic improvements with each new application. The FFN was trained on a diverse dataset encompassing various rubber recipes and batches. Post-training, the FFN demonstrated remarkable accuracy, achieving a mean absolute percentage error of 1.00% on the training dataset and 1.44% on the validation dataset, thereby showcasing its efficacy in predicting temperature fluctuations within the mixing process. Consequently, the FFN can determine the relevant input variables necessary to achieve specific mixing temperatures, providing a foundation for an automated control system in rubber mixing process. This paper outlines the system architecture of the FFN tailored for rubber mixing and provides a comprehensive overview of the experimental results.

Variable viscosity characteristics of two-layered isothermal calendering phenomena with non-Newtonian fluids

Two-layer calendering using non-Newtonian fluids is used frequently in different industries to improve the working and the quality of the products. In this article, two-layer calendering of incompressible non-Newtonian fluids, that is, couple stress fluid and viscoplastic fluid in the upper and lower layer respectively is investigated. For the simplified governing equations, Lubrication approximation theory is applied. By the use of no-slip condition and non-dimensional variables, the exact solution for pressure gradient, pressure, and velocity profiles for both layers of fluid is calculated. The parameters are important from an engineering point of view like roll separating force, power delivered by rollers, torque acting by each roller, and adiabatic temperature are also calculated analytically. Additionally, the results of a couple stress parameter, viscoplastic Casson parameter, and viscosity ratios on all the parameters are also discussed and investigated in detail. Moreover, all the effects investigated are also verified with the literature results of single-layer calendering of non-Newtonian fluids by using large numeric values for the couple stress parameter and viscoplastic Casson parameter.

Modeling Subduction With Extremely Fast Trench Retreat

AbstractThe Tonga‐Kermadec subduction zone exhibits the fastest observed trench retreat and convergence near its northern end. However, a paradox exists: despite the rapid trench retreat, the Tonga slab maintains a relatively steep dip angle above 400 km depth. The slab turns flat around 400 km, then steepening again until encountering a stagnant segment near 670 km. Despite its significance for understanding slab dynamics, no existing numerical model has successfully demonstrated how such a distinct slab morphology can be generated under the fast convergence. Here we run subduction models that successfully reproduce the slab geometries while incorporating the observed subduction rate. We use a hybrid velocity boundary condition, imposing velocities on the arc and subducting plate while allowing the overriding plate to respond freely. This approach is crucial for achieving a good match between the modeled and observed Tonga slab. The results explain how the detailed slab structure is highly sensitive to physical parameters including the seafloor age and the mantle viscosity. Notably, a nonlinear rheology, where dislocation creep reduces upper mantle viscosity under strong mantle flow, is essential. The weakened upper mantle allows for a faster slab sinking rate, which explains the large dip angle. Our findings highlight the utilizing rheological parameters that lead to extreme viscosity variations within numerical models to achieve an accurate representation of complex subduction systems like the Tonga‐Kermadec zone. Our study opens new avenues for further study of ocean‐ocean subduction systems, advancing our understanding of their role in shaping regional and global tectonics.

Near-infrared hemicyanine photosensitizer for targeted mitochondrial viscosity imaging and efficient photodynamic therapy

As a severe threat to human health, cancer has always been one of the most significant challenges facing the medical field. However, there is currently no effective technology or method to diagnose and treat cancer simultaneously. Therefore, developing a new approach that integrates diagnosis and treatment holds promise as a means of achieving personalized and precise cancer therapy. In this study, we developed a novel dual-functional near-infrared mitochondrial-targeted photosensitizer, Hcy-I, which is capable of simultaneously monitoring cellular viscosity and specifically targeting mitochondria for photodynamic therapy. Compared with traditional hemicyanine dyes, the introduction of iodine atoms in Hcy-I enhanced spin–orbit coupling (SOC) and promoted the intersystem crossing (ISC) rate, thereby increasing the efficiency of singlet oxygen (1O2) generation. In vitro experiments demonstrated that Hcy-I exhibited high sensitivity to viscosity variations and efficiently generated 1O2 under 638 nm laser irradiation, with an 1O2 quantum yield of up to 48.9 %. Cell experiments further revealed that this photosensitizer could effectively target mitochondria for photodynamic therapy, disrupting mitochondrial membrane potential and inducing cell death. When treated with Hcy-I at a concentration of 0.8 µM, the survival rate of HepG-2 cells was only 13 %. These results suggested that Hcy-I had the potential to integrate cancer diagnosis and treatment. The research not only promotes the development of photodynamic thereby technology, but also opens up new avenues for the diagnosis and treatment of cancer.

Selected Soluble Dietary Fibres as Replacers of Octenyl Succinic Anhydride (OSA) Starch in Spray-Drying Production of Linseed Oil Powders Applied to Apple Juice

The aim of the study was to compare two kinds of soluble dietary fibres in a mixture with OSA-starch as wall components of linseed oil capsules. Comparison was made based on emulsion (droplet size, polydispersity index, and viscosity) and powder properties (outer structure, colour, surface oil content, and encapsulation efficiency). Additionally, linseed oil powders were applied to the food model (apple juice) and the colour, physical stability, and volatile compound profile of fortified juice were determined. Although the obtained linseed oil emulsions with different compositions of polysaccharide components showed some variation in droplet size, polydisperse index and viscosity, their encapsulation efficiency by spray-drying was very high (>98%). The powders produced had a similar structure and low surface oil content, and their 2% addition to apple juice did not change its stability and only slightly decreased its colour lightness and yellowness. However, greater differences in the volatile compounds of obtained juices were observed. Overall, the added powders reduced the volatility of aroma compounds typical of apple juice but introduced propanal and hexanal, especially the powders with the highest OSA-starch share.

Limited sensitivity of Antarctic GIA mass change estimates to lateral viscosity variations

The Gravity Recovery and Climate Experiment (GRACE) has revealed spatiotemporal mass changes in the Antarctic Ice Sheet. However, GRACE data must be corrected for the gravity changes due to glacial isostatic adjustment (GIA). Here we investigate the sensitivity of GIA-induced gravity changes in Antarctica to the lithospheric thickness and upper mantle viscosity using a one-dimensional (1-D) model that assumes a radially varying Earth structure. The sensitivity is assessed using several Antarctic ice-history models that have been widely used to correct GRACE data. The results indicate a trade-off between lithospheric thickness and upper mantle viscosity in evaluating the Antarctic GIA correction. This trade-off exists for all ice-history models; however, the reason for the trade-off differs among models. Furthermore, since there is a sharp contrast in the Earth structure between West and East Antarctica, the adopted ice histories are separated into West and East Antarctic components to examine their contributions to the Antarctic GIA correction. We consider 1-D Earth structures that are averaged from the seismically derived three-dimensional Earth structure for West and East Antarctica. These results indicate that the contributions of the East and West Antarctic loads do not significantly affect the GIA corrections for the West and East Antarctic regions, respectively, and that the trade-off between lithospheric thickness and upper mantle viscosity results in minimal divergence in the assessment of the Antarctic GIA correction between the averaged Earth models of West and East Antarctica. Therefore, the contrast in Earth structure beneath Antarctica may have a limited effect on the ice-mass change estimates for the entire Antarctic Ice Sheet.

Direct numerical simulation study on wall-modeling of turbulent water channel flows with temperature-dependent viscosity

We discuss wall-modeling of turbulent heat transfer of water channel flows with temperature-dependent viscosity via direct numerical simulations. We considered a top-cooled wall (293[K]) and a bottom-heated wall (353[K]) and varied the friction Reynolds numbers from 300 to 1000. The fluid viscosity varied depending on the local fluid temperature, whereas the other physical properties were assumed to be constant. The results show that semi-local scaling based on the local viscosity and wall friction velocity reasonably accounts for the effects of variable viscosity on turbulent flows, except in the vicinity of the wall, where wall cooling intensifies the turbulent vortical motion, leading to increased semi-locally scaled eddy diffusivities compared with those near the heated wall. In the vicinity of the cooled wall, turbulent transport is enhanced by increased viscous transport, which transfers more turbulent kinetic energy toward the cooled wall. The effectiveness of semi-local scaling for wall-modeling was validated by performing a wall-modeled large-eddy simulation at Reτ=1000, where we incorporated the semi-local viscous length scale into the classical mixing-length model. The modified mixing-length model reasonably reproduced the effects of variable viscosity on turbulent flows.

Thermal slip and variable viscosity analysis on heat rate and magnetic flux through accelerating non-conducting wedge in the presence of induced magnetic field

The focus of present study is to incorporate the variable viscosity and temperature slip impact on heating rate and induced magnetic gradient along the moving non-conducting wedge under magnetic field. In industrial and engineering procedures, the impact of induced magnetization improves the efficiency of thermal systems to main the heating rates. The similarity transformations and stream functions are applied to reduce the governing equations into ordinary form. During this transformation, the pertinent parameters such as wedge parameter, moving parameter, Prandtl factor, viscosity parameter and temperature-slip parameter is obtained. These parameters play a prominent role on the physical values of fluid velocity, induced magnetic field and temperature distributions. The skin friction, Nusselt coefficient and induced magnetic gradient are incorporated through these parameters. The numerical values are executed by using the Keller box analysis with Newton–Raphson technique. It is depicted that the maximum slip in fluid velocity and temperature distribution is obtained for each values of thermal-slip parameter. It is noticed that maximum magnitude in induced magnetic field is reported for each wedge factor. The maximum velocity slip and temperature slip is observed for each choice of moving parameter. It is reported that the maximum variation in heating rate and induced magnetic gradient is obtained for magnetic force and viscosity parameter. The enhancing behavior of skin friction is observed for maximum values of Prandtl number.

The influence of temperature-dependent variable viscosity and suction on a natural convective heat transfer in magneto generated plume

The study provides novel and valuable insights into the behavior of fluid flow and heat transfer in a generated plume under the influence of an aligned magnetic field, which is a complex and less-explored area in fluid dynamics. Incorporating variable viscosity and suction effects adds to the realism and applicability of the model, as it accounts for more realistic conditions where fluid properties change with temperature and external forces influence the flow. A mathematical model is formulated as a system of coupled partial differential equations to analyze the flow dynamics. Subsequently, a numerical solution is derived with stream function formulation for the system of coupled partial differential equations, which transmuted it into ordinary differential equations. To achieve this, the numerical properties of the problem are established through the utilization of a Shooting method in tandem with the MATLAB tool bvp4c. The graphical representations of both missing and specified boundary conditions, analyzes the influences of the viscosity parameter ε, suction parameter ξ, magnetic force parameter S, Prandtl number Pr and magnetic Prandtl number γ. The impact of these parameters on the heat transfer and fluid flow is given in detail. Inclusion of suction velocity counteracted the effects of temperature-dependent viscosity. The velocity f′, current density ϕ″, temperature θ, skin friction f″ and magnetic flux ϕ′ depicted an enhanced behavior while heat transfer rate θ′ dropped with an increment in viscosity parameter ε. However, for an increasing suction parameter ξ, the reverse trend of these properties is observed as compared to the viscosity parameter ε. The inclusion of suction counteracted to the effects of variable viscosity. Understanding how heat plumes behave under magnetic fields the study aims to provide insights that can be applied to real-world scenarios, such as improving cooling systems in industrial applications, enhancing environmental safety measures, and optimizing biomedical engineering processes.

Lithospheric Folding Controls the Intracontinental Orogen of South China: Insight from Numerical Simulation

Abstract Orogenic processes worldwide have been attributed to various deformation mechanisms. However, the significance of lithospheric folding in these processes has often been overlooked and underestimated. Within the South China Block (SCB), a region marked by notable temporal and spatial variability in intracontinental deformation, the emergence of fold-and-thrust belts during the Paleozoic and Mesozoic periods has captured a scientific interest. The mechanisms governing the genesis of these belts remain a subject of debate, with no discernible subduction interface accounting for the extensive-scale fold-thrust deformation. Moreover, the SCB presents a substantial variation in lithospheric thickness, exceeding 100 km, offering a plausible mechanism for lithospheric folding. To interrogate this mechanism, we conducted lithospheric compression simulations via two-dimensional finite element methods, incorporating variable viscosity both laterally and vertically within the SCB. Our models elucidate that disparities in lithospheric strength beget distinctive deformational manifestation within the SCB. We observe that a weaker lithosphere tends to uplift, whereas a stronger lithosphere tends to subside during compression. Lithospheric strength also influences the Xuefengshan uplift and the spatial distribution of deformational features. In addition, lithospheric folding can account for crustal shortening and the presence of deep anomaly structures. A compelling correlation emerges between lithospheric folding and fluctuations in Moho depth and lithospheric thickness, suggesting its potential influence over the prolonged topographical evolution and shifts in depositional environments within the SCB. This study sheds new light on the role of lithospheric folding in the complex geodynamic history of the SCB and highlights its importance in understanding the broader context of orogenic processes worldwide.

Energy-stable auxiliary variable viscosity splitting (AVVS) method for the incompressible Navier–Stokes equations and turbidity current system

In this work, we develop a novel energy-stable linear approach, which we name as auxiliary variable viscosity splitting (AVVS) method, to efficiently solve the incompressible fluid flows. Different from the projection-type methods with pressure correction, the AVVS method adopts the viscosity splitting strategy to split the original momentum equation into an intermediate momentum equation without divergence-free constraint and an advection-free momentum equation. A time-dependent auxiliary variable which has exact value 1 is introduced to construct a supplementary equation. The new model not only inherits the same dynamics of original incompressible Navier–Stokes equations, but also facilitates us to design linearly decoupled and energy-stable time-marching scheme. Comparing with the conventional projection-type schemes, the present method leads to an energy dissipation law with respect to kinetic energy instead of a modified energy including velocity and pressure gradient. In each time step, only two parabolic equations with constant coefficients and one Poisson equation need to be solved. Therefore, the numerical implementation is highly efficient. Moreover, the proposed AVVS method can be directly extended to construct linear, decoupled, and energy-stable scheme for the turbidity current system with slight modifications on the right-hand side of supplementary equation. Extensive numerical experiments are implemented to validate the accuracy, energy stability, and capability in complex fluid simulations.

Chemically reactive flow beyond constant thermophysical characteristics

Hydromagnetic chemically reactive flow over stretching wall is discussed. Formulation is based upon consideration of Reiner-Rivlin constitutive relation. Variable thermophysical characteristics are under consideration. Radiation, heat generation and dissipation impacts exist in thermal relation. Concentration expression subject to reaction with first order is considered. Modeling with entropy optimization is made. Appropriate transformations lead to relevant differential systems. Numerical study by ND-solve is carried out. Quantities under interest are graphically analyzed. An opposite behavior detected for magnetic parameter on entropy rate and velocity. Velocity field versus magnetic field parameter decreases whereas reverse impact witnessed for variable viscosity parameter. An enhancement in thermal distribution and entropy detected for radiation. Thermal distribution enhancement is observed for generation of heat and thermal conductivity variables. Chemical reaction for concentration has decaying impact. Results of Schmidt number for concentration are similar to that of chemical reaction. Brinkman number leads to entropy rate improvement. Entropy rate upsurges against variable viscosity and mass diffusivity parameters.

A comparative study of exact and neural network models for wave‐induced multiphase flow in nonuniform geometries: Application of Levenberg–Marquardt neural networks

AbstractMultiphase fluids exhibit immiscible, heterogeneous structures like emulsions, foams, and suspensions. Their complex rheology arises from relative phase proportions, interfacial interactions, and component properties. Consequently, they demonstrate nonlinear effects—shear‐thinning, viscoelasticity, and yield stress. Peristalsis generates fluid flow by propagating contraction waves along channel walls. This mechanism can effectively transport multiphase and non‐Newtonian fluids in microsystems. Accurate modeling requires considering evolving phase relations, variable viscosity, slip, and particle migration anomalies, using approaches like homogenization theory or volume‐averaging. Applications include peristaltic pumping of emulsified biopharmaceuticals, microscale mixing/separating of multiphase constituents, and enhancing porous media fluid flow in oil reservoirs. Analytical and computational approaches to modeling multiphase fluid flows in peristaltic conduits provide an enhanced understanding of their complex dynamics, toward innovating engineering systems. An analytical approach is taken to model non‐Newtonian Ree‐Eyring fluid flows in asymmetric, peristaltic systems. Governing differential equations incorporate key parameters and yield closed‐form solutions for velocity, flow rate, and permeability. Suitable assumptions of long wavelength, and low Reynolds number provide accuracy. In parallel, an artificial neural network (ANN) is developed using supervised learning to predict permeability. The inputs consist of channel asymmetry, Reynolds number, amplitude ratio, and other physical factors. Outcomes validate both methodologies—analytical equations derive precise relationships from first principles, while ANNs reliably learn the system patterns from input‐output data. Additionally, ANNs can tackle more complex fluid dynamics problems with speed and adaptability. Their promising role is highlighted in developing new fluid models, improving the efficiency of simulations, and designing control systems. Side‐by‐side analytical and ANN simulation plots will further highlight ANN capabilities in emulating the system characteristics. This paves the path for employing machine learning to investigate multifaceted flows in flexible, peristaltic systems at scale. Performing a graphical examination of the engineering skin friction coefficient across a range of parameters, encompassing volume fraction, first and second order slip, Ree–Eyring fluid attributes, and permeability.

Characterization, processing, and modeling of industrial recycled polyolefins

AbstractThis study aims to establish a systematic approach for characterizing recycled polyolefins of unknown composition, with a specific focus on predicting their performance in film extrusion. We explore various characterization techniques, including differential scanning calorimetry (DSC), Fourier‐transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), and rheometry to assess their effectiveness in identifying the polyethylene (PE) fractions within polypropylene (PP) recyclates. By integrating experimental data with modeling techniques, we aim to provide insights into the predictive capabilities of these techniques in determining processing behaviors. The research highlights the superior fidelity of DSC in predicting the relative fraction and type of PE in a PP recyclate. FTIR is also identified as a high‐fidelity approach, albeit requiring application‐specific calibration. TGA, capillary, and oscillatory rheometry are recognized for their ability to distinguish between grades of recycled polyolefins but provide aggregate behaviors rather than detailed constituent information. 3D flow simulation of the cast film extrusion investigated the effect of the viscosity characterization method, non‐isothermal assumption, and process settings but could not fully replicate the observed variations in the cast film processing of two industrial polyolefins with similar melt flow rates and viscosity behaviors. This underscores the practical challenge of predicting processing issues prior to actual processing, necessitating reliance on reliable instrumentation suites and human expertise for diagnosing and remedying variations.Highlights Two industrial recycled polypropylene materials having similar melt flow rates exhibit drastically different cast film processing behaviors. DSC and FTIR provide reasonable approaches for identifying constituent materials. Modeling of the melt viscosities characterized by capillary and parallel plate rheology suggests that viscosity variations relative to the power‐law behavior assumed in the coat hanger die design is a predominant driver of cast film instabilities.

Rheological behavior of the synovial fluid: a mathematical challenge

BackgroundSynovial fluid (SF) is often used for diagnostic and research purposes as it reflects the local inflammatory environment. Owing to its complex composition, especially the presence of hyaluronic acid, SF is usually viscous and non-homogeneous. The presence of high-molar-mass hyaluronan in this fluid gives it the required viscosity for its function as a lubricant. Viscosity is the greatest major hydraulic attribute of the SF in articular cartilage.MethodsEmpirical modeling of previously published results was performed. In this study, we explored the flow of a non-Newtonian fluid that could be used to model the SF flow. Analyzing the flow in a simple geometry can help explain the model’s efficacy and assess the SF models. By employing some viscosity data reported elsewhere, we summarized the dynamic viscosity values of normal human SF of the knee joints in terms of time after injecting hyaluronidase (HYAL) at 25°C. The suggested quadratic behavior was obtained through extrapolation. For accurate diagnosis or prediction, the comparison between three specific parameters (ai, t0, and ln η0) was made for normal and pathological cases under the same experimental conditions for treatment by addition of HYAL and for investigation of the rheological properties. A new model on the variation of viscosity on the SF of knee joints with time after injection of HYAL with respect to normal and postmortem samples at different velocity gradients was proposed using data previously reported elsewhere.ResultsThe rheological behavior of SF changes progressively over time from non-Newtonian to a Newtonian profile, where the viscosity has a limiting constant value (η0) independent of the gradient velocity at a unique characteristic time (t0 ≈ 8.5 h). The proposed three-parameter model with physical meaning offers insights into future pathological cases. The outcomes of this work are expected to offer new perspectives for diagnosis, criteria, and prediction of pathological case types through comparisons with new parameter values treated under the same experimental conditions as HYAL injection. This study also highlights the importance of HYAL treatment for better intra-assay precision.

Analysis of variable fluidic properties with varying magnetic influence on an unsteady radiated nanofluid flow on the stagnant point region of a spinning sphere: a numerical exploration

Abstract The purpose of this article is to invent the impact of inconstant properties of fluids on the nanofluidic stream towards the stagnation area of a revolving sphere. The motion is treated as an unsteady radiated flow with a nonlinear sort of heat radiation. It is presumed to have Brownian motion & thermophoretic impact in our flow model. Additionally, a variable magnetic influence is addressed perpendicularly on the spherical surface. A suitable alteration has been applied to make dimensionless of our prime flow profiles. The translated equations and the limiting restrictions are solved through a numerical approach. The well established method RK4 Shooting technique is utilized here with Maple 2017 software. In the exploration of the consequences of requisite parameters on thermal, concentration, and flow features, numerous schematics are involved. The nature of physical quantities like Nusselt numbers, friction coefficients, and Sherwood numbers is stated in a tabular manner. It is perceived from the outcomes that the fluid velocity towards the x-direction is reduced for the variable viscosity parameter, whereas the unsteadiness parameter promotes it. The enhancement of inconstant thermal conductivity brings a positive influence on the thermal profile of fluid. Nusselt number drops against the thermal radiation & variable viscosity with a rates 4.50% and 25.88% correspondingly.

Exploring the enigmatic interplay between polymers and nanoparticles in a non-Newtonian viscoelastic fluid

Non-Newtonian fluids have variable viscosity in response to shear rate, and the presence of polymers and nanoparticles further modifies their flow characteristics. In this paper, the effects of polymers and nanoparticles on mass and heat transfer control, drag reduction, boundary layer flow development in a polymeric finitely extensible nonlinear elastic-Peterlin (FENE-P) fluid, and the significance of nanoscience in modern day life are discussed. We examine the behavior of polymer additives by utilizing a dispersion model in conjunction with the polymeric FENE-P model. Our work includes a comparison with Cortell’s [1] earlier work, which only looked at the behaviour of polymers inclusion into the base fluid. This research investigates numerically how the inclusion of polymers and nanoparticles into the base fluid reduces drag while increasing heat and mass transfer. The observed variations in skin friction, reduced Nusselt, and Sherwood numbers indicate an intriguing correlation between the rates of heat and mass transport and surface drag. More precisely, as the heat and mass transfer efficiency improve, the surface encounters less resistance, which is commonly referred to as drag. In summary, the research highlights the capability of polymers and nanoparticles to effectively modify fluid dynamics, minimize drag, and enhance mass and heat transfer inside the flow region.

Lie similarity analysis of MHD Casson fluid flow with heat source and variable viscosity over a porous stretching sheet

The current study presents a novel examination of heat transfer properties in a magnetohydrodynamic (MHD) flow of Casson fluid across a porous stretching sheet, uniquely incorporating the effects of heat source and variable viscosity. Unlike previous studies, this research employs the Lie similarity transformation to convert the governing equations into a dimensionless form. These transformed equations are then solved using advanced numerical techniques, specifically the fourth-order Runge-Kutta (RK) along with shooting method. The findings reveal that the velocity decreases with the adjustment of significant parameters such as the Casson fluid properties, variable viscosity, heat source, magnetic field, and porosity, leading to an inverse increase in temperature within the convection system. As the Prandtl number increases, the temperature gradient and thermal boundary layer thickness decrease, resulting in reduced heat transfer rates within the convection system. Likewise, an increase in the Schmidt number decreases the concentration gradient and mass transfer rate within the fluid. This novel approach provides new insights into the behavior of Casson fluids, with significant applications in industrial processes, energy systems, environmental engineering, material science, and aerospace and automotive industries, where understanding heat transfer mechanisms in complex systems can enhance efficiency, performance, and safety.

Bioconvective variable viscosity flow of Carreau nanofluid with external heat source and nonlinear radiation: Analysis with convective heat and mass constraints

In this study, an unsteady model for Carreau nanofluid with microorganism decomposition is developed. The viscosity and thermal conductivity of the Carreau nanofluid are considered variable. Magnetic and porosity effects are included using a magneto-porosity parameter. An additional heat source is introduced to improve heat transfer. Nonlinear analysis is applied for radiative applications. The flow is modeled using an oscillatory stretching surface. Convective mass and heat constraints are used to analyze the problem. Analytical computations are performed on the developed model. The significance of various parameters for the thermal problem is discussed. The results may enhance the performance of transport problems, heat transmission, energy systems, and thermal devices.