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The study is accomplished to explore the pioneering of a two-dimensional ferromagnetic fluid flow over a flat elastic sheet with the magnetic dipole effect. The recent flow design was selected as it is mostly applicable in bioengineering as well as engineering fields that includes magnetic drug targeting systems. In this paper, the impacts of thermal radiation and magnetic dipole in flow of ferromagnetic Sutterby fluid for a stretching surface are examined. Some suitable similarity transformations are exploited to achieve the system of nonlinear ODEs from set of PDEs, then acquired ODEs are resolved by numerical scheme known as bvp4c technique. Impacts of ferromagnetic interaction parameter, viscous dissipation and curie temperature are perceived for velocity as well as temperature fields. Furthermore, velocity as well as thermal gradients are deliberated and scrutinized pictorially. [ABSTRACT FROM AUTHOR]

Process of transportation of heat in ferrofluids has innumerable applications in the fields of electronics and automobile industry. By tracing the materials, the ferrofluid got popularity among researchers and engineers, also most ferrofluids are non-Newtonian in nature so here the non-Newtonian fluid is under consideration. In this study, the influences of viscous dissipation and magnetic parameter in the flow of ferromagnetic Carraeu fluid for a stretching surface are examined. Suitable similarity transformations in the system that consists of nonlinear form of Partial Differential Equations (PDEs) are transformed into a system of nonlinear form of ODEs, then the resulting Ordinary Differential Equations (ODEs) are resolved by use of a mathematical technique known as bvp4c. Effects of ferromagnetic interaction factor, Curie temperature, viscous dissipation and material parameter are examined for temperature profile as well as velocity fields. Moreover, the variations in velocity and thermal gradients are analyzed and described with the help of graphs. An upsurge in the values of magnetic interaction parameter and Weissenberg number causes a decline in the velocity field while the thermal gradient shows opposite behavior. It is detected that the temperature of Carreau fluid intensifies for larger and  λ. [ABSTRACT FROM AUTHOR]

The main idea of this investigation is to introduce an integrated intelligence approach that investigates the chemically reacting flow of non-Newtonian fluid with a backpropagation neural network (LMS-BPNN). The AI-based LMS-BPNN approach is utilized to obtain the optimal solution of an MHD flow of Eyring–Powell over a porous shrinking wedge with a heat source and nonlinear thermal radiation ( R d ). The partial differential equations (PDEs) that define flow problems are transformed into a system of ordinary differential equations (ODEs) through efficient similarity variables. The reference solution is obtained with the bvp4c function by changing parameters as displayed in Scenarios 1–7. The label data are divided into three portions, i.e., 80% for training, 10% for testing, and 10% for validation. The label data are used to obtain the approximate solution using the activation function in LMS-BPNN within the MATLAB built-in command 'nftool'. The consistency and uniformity of LMS-BPNN are supported by fitness curves based on the MSE, correlation index ( R ), regression analysis, and function fit. The best validation performance of LMS-BPNN is obtained at 462, 369, 642, 542, 215, 209, and 286 epochs with MSE values of 8.67 × 10−10, 1.64 × 10−9, 1.03 × 10−9, 302 9.35 × 10−10, 8.56 × 10−10, 1.08 × 10−9, and 6.97 × 10−10, respectively. It is noted that f ′ (η) , θ (η) , and ϕ (η) satisfy the boundary conditions asymptotically for Scenarios 1–7 with LMS-BPNN. The dual solutions for flow performance outcomes ( C f x , N u x , and S h x ) are investigated with LMS-BPNN. It is concluded that when the magnetohydrodynamics increase ( M = 0.01 ,   0.05 ,   0.1 ), then the solution bifurcates at different critical values, i.e., λ c = − 1.06329 , − 1.097 , − 1.17694 . The stability analysis is conducted using an LMS-BPNN approximation, involving the computation of eigenvalues for the flow problem. The deduction drawn is that the upper (first) branch solution remains stable, while the lower branch solution causes a disturbance in the flow and leads to instability. It is observed that the boundary layer thickness for the lower branch (second) solution is greater than the first solution. A comparison of numerical results and predicted solutions with LMS-BPNN is provided and they are found to be in good agreement. [ABSTRACT FROM AUTHOR]

In this computational study, we investigate the gravity and pressure-driven electroosmotic multiphase flow of third-grade fluid through steep microchannel by using the semi-analytical technique. A two-dimensional mathematical model is proposed here for the supercritical bi-phase flow with the suspension of the nanometallic particles. A special type of non-Newtonian fluid (third-grade) is selected as a base fluid. The governing equations for the current flow problem are obtained through Poisson–Boltzmann equations, continuity equations, and Cauchy's momentum equations. The Poisson–Boltzmann equation is simplified by using the Debye–Hückel approximation. The symbolic software MATHEMATICATM is used to obtain the closed-form expression of electric potential, fluid and particle velocities, pressure gradient, and volumetric flow rate, respectively. The computational results are discussed qualitatively under the impact of the physical parameters embedded in the study. The graphical plots of fluid and particle-phase velocities are generated against the different parameters used in this study by adopting the same software as discussed earlier. The electrokinetic forces are responsible for electroosmotic flow which is modeled through the Laplace and Poisson–Boltzmann equations. The externally applied potential and electrical double-layer potential is governed by the Laplace and Poisson–Boltzmann equations, respectively. [ABSTRACT FROM AUTHOR]

Due to the numerous practices of non-Newtonian fluids in technological and industrial fields, the attention towards such fluids increases incredibly. The highly nonlinear equations emerge in the modeling of the non-Newtonian fluids. The differential transform method is one of the analytical methods which is used to acquire the solution to these complicated nonlinear equations in the series form. The current analysis comprises the squeeze flow of non-Newtonian fluid in two dimensions. Two infinite parallel plates are considered in which the time-dependent fluid is squeezed. The heat transfer mechanism is deliberated with the significance of heat absorption/generation. The nonlinear setup of ordinary differential equations is acquired by practicing the appropriate similarity variables on the governing equations of the concerned flow mechanism. The nonlinear setup is analytically resolved with the help of an analytical differential transform method. For the authenticity of the differential transform method, the analytical outcomes are compared with the numerical results. Graphical illustrations of fluid temperature and velocity profiles relative to the pertinent parameters are briefly explicated numerically and analytically. The fluid velocity demonstrates the descending behavior and the temperature field exhibits the expanding nature relative to the squeezing parameter. [ABSTRACT FROM AUTHOR]

We have generalized, in the current study, the results of research presented earlier with the aim of obtaining an approximate solution for the creeping, plane-parallel flow of viscoplastic non-Newtonian fluid where the focus is on the study of rivulet fluid flows on an inclined surface. Namely, profiles of velocity of flow have been considered to be given in the same form as previously (i.e., Gaussian-like, non-stationary solutions) but with a novel type of pressure field p. The latter has been chosen for solutions correlated explicitly with the critical maximal non-zero level of stress τs in the shared plane layer of rivulet flow, when it begins to move as viscous flow (therefore, we have considered here the purely non-Newtonian case of viscoplastic flow). Correlating phenomena such as the above stem from the equations of motion of viscoplastic non-Newtonian fluid considered along with the continuity equation. We have obtained a governing sub-system of two partial differential equations of the first order for two functions, p and τs. As a result, a set of new semi-analytical solutions are presented and graphically plotted. [ABSTRACT FROM AUTHOR]

The study focuses on the flow characteristics with geometrical considerations utilizing electrical-conduct Non-Newtonian Fluid. The tubular concentric annulus is the geometry selected for the investigation. The electric-conductive Non-Newtonian Fluid is a character-wise two-constant Bingham model used in this study. The study also utilized geometry, the magnetohydrodynamic (MHD) effect, and the hall current. The employed system had the inner tube spinning and the outer tube stationary. Prandtl's assumptions of boundary layer principles are applied to solve the governing equations using the finite difference method for various fluid flow parameters, the Gauss-Elimination method to compute the results, and the MHD field and geometrical factors with hall current. This paper discusses fluid flow properties such as axial, radial, tangential velocities, and pressure distribution. Further, the mentioned above flow properties impact the heat transfer effect. This research details how flow parameters in the concentric tube flow process affect the development of heat transfer effects in the MHD field and hall current. [Display omitted] • The development of MHD flow and heat transport have been studied computationally. • The impact of Hall current and Magnetic effect on the flow field has been considered. • This work refers to the non-Newtonian fluid as a two-constant yield stress fluid model. • The heat transfer impact has been calculated using the fluid flow properties. • This work has been done using a variety of fluid and geometric factors. [ABSTRACT FROM AUTHOR]

In this paper, we study the flow of a non-Newtonian fluid through a thin three-dimensional domain with an oscillating boundary. Starting from a nonlinear coupled system describing a non-isothermal regime of the flow, we rigorously derive three different effective models, depending on the period of the boundary roughness. We employ a homogenization technique based on the adaption of the unfolding method and deduce the roughness-induced effects on the fluid flow. [ABSTRACT FROM AUTHOR]

We present a Graphic Processing Units (GPU) implementation of non-Newtonian Hele-Shaw flow that models the displacement of Herschel-Bulkley fluids along narrow eccentric annuli. This flow is characteristic of many long-thin flows that require extensive calculation due to an inherent nonlinearity in the constitutive law. A common method of dealing with such flows is via an augmented Lagrangian algorithm, which is often painfully slow. Here we show that such algorithms, although involving slow iterations, can often be accelerated via parallel implementation on GPUs. Indeed, such algorithms explicitly solve the nonlinear aspects only locally on each mesh cell (or node), which makes them ideal candidates for GPUs. Combined with other advances, the optimized GPU implementation takes ≈ 2.5 % of the time of the original algorithm. [ABSTRACT FROM AUTHOR]

The control mechanism of the pressure drop and bubble size has a guiding significance for selecting the micropump, the pressure resistance design, and the precise control of the microfluidics. In this study, single-phase flows and gas-non-Newtonian fluid two-phase flows are studied in a microchannel containing curved structures. Sodium carboxymethyl cellulose solutions are used as the non-Newtonian fluids; water and nitrogen are used as Newtonian fluid and gas phases, respectively. The pressure drop and the bubble length are measured. The influences of operating conditions are discussed. The non-Newtonian properties of the solutions are found to affect the parameters measured significantly. The experimental results are compared with the existing models, and the fanning friction factor is used to evaluate the pressure drop. The two-phase flow pressure drop can be predicted by the Lockhart-Martinelli method with a newly developed C-coefficient as a function of the fluid characteristic parameters and microchannel structure parameters. The new correlation for two-phase pressure drop prediction has an error within 18%, smaller than existing models. A new prediction method for the dimensionless bubble length containing the two-phase friction multiplier is also given with an error of 16%. [Display omitted] • A novel microchannel containing curved structures was studied experimentally. • Empirical models for predicting pressure drop and bubble length were developed and compared with existing models. • The prediction accuracy of the pressure drop was improved by considering structural and non-Newtonian fluid parameters. • The prediction accuracy of the bubble length was improved by considering the influence of pressure drop. [ABSTRACT FROM AUTHOR]

The electroosmotic and pressure-driven mixed flow was widely used in various biochemical microfluidic fields, where the elastic instability of the viscoelastic fluid cannot be ignored. A viscoelastic fluid was used to numerically simulate electroosmotic and pressure-driven mixed flow in a 10:1:10 microchannel converging-diverging tube. The effects of different pressures and different polymer concentrations on the fluid flow were studied, and the superposition principle for the velocity distributions of Newtonian fluids and viscoelastic fluids in converging-diverging tubes was analyzed. The results show that, the reverse pressure brings the viscoelastic fluid into higher instability, which makes the inlet vortex larger by 25 μm for every 1 Pa pressure increase. The positive pressure makes the eddy current smaller. For a relatively small reverse pressure, the inlet vortex increases with the polymer concentration and tends to be stable gradually. For a relatively large reverse pressure, the vortex size first increases and then decreases with the polymer concentration. [ABSTRACT FROM AUTHOR]

The flow of Casson fluid streaming through a porous zone in a permeable channel with homogeneously distributed dust particles is studied. The flow is oscillatory and exposed to thermal radiation. With non-uniform temperature and velocity slip at the wall, the channel is put under transverse magnetic flux control. The variable separation approach is used to obtain the exact analytic solution for the flow fields of fluid and dust particles. Physical insights of collective effects of suction/injection, magnetic field, thermal radiation, and buoyance force on the fluid velocity, temperature, rate of heat transport and friction at the wall surface are examined and analysed graphically. Results reveal that surface friction increases on both channel plates as an injection on the hot plate rises. [ABSTRACT FROM AUTHOR]

In this paper, a two-dimensional, steady, laminar boundary layer analysis is presented to analyze numerically the internal heat generation and Soret–Dufour effects on mixed convection flows of power-law fluids adjacent to a vertical flat plate maintained at variable heat flux and variable mass flux conditions in a Darcy porous medium. The Ostwald–de Waele power-law model is utilized here. The transformed governing equations are solved by the Keller box method. After performing comparisons with previously published results, good agreement is obtained. [ABSTRACT FROM AUTHOR]

We have examined the magnetized stagnation point flow of non-Newtonian fluid towards an inclined cylindrical surface. The mixed convection, thermal radiation, viscous dissipation, heat generation, first-order chemical reaction, and temperature-dependent thermal conductivity are the physical effects being carried for better novelty. Mathematical equations are constructed for four different flow regimes. The shooting method is used to evaluate the heat transfer coefficient at the cylindrical surface with and without heat generation/thermal radiation effects. For better examination, we have constructed artificial neural networking models with the aid of the Levenberg–Marquardt training technique and Purelin and Tan-Sig transfer functions. The Nusselt number strength is greater for fluctuations in the Casson fluid parameter, Prandtl number, heat generation, curvature, and Eckert number when thermal radiations are present. [ABSTRACT FROM AUTHOR]

In the study of polymer flooding, researchers usually ignore the genetic stress properties of viscoelastic fluids. In this paper, we investigate the process of viscoelastic fluid flooding the remaining oil in the dead end. This work uses the fractional-order Maxwell in the traditional momentum equation. Furthermore, a semi-analytic solution of the flow control equation for fractional-order viscoelastic fluids is derived, and the oil-repelling process of viscoelastic fluids is simulated by a secondary development of OpenFOAM. The results show that velocity fractional-order derivative α significantly affects polymer solution characteristics, and increasing the elasticity of the fluid can significantly improve the oil repelling efficiency. Compared to the Newtonian fluid flow model, the fractional order derivative a and relaxation time b in the two-parameter instanton equation can accurately characterize the degree of elasticity of the fluid. The smaller the a, the more elastic the fluid is and the higher the oil-repelling efficiency. The larger the b, the less elastic the fluid is and the lower the cancellation efficiency. Moreover, the disturbance of the polymer solution to the dead end is divided into two elastic perturbation areas. The stronger the elasticity of the polymer solution, the higher the peak value of the area in the dead end and the higher the final oil displacement efficiency. [ABSTRACT FROM AUTHOR]

In this article, the exact solution for a couple stress fluid flow past a fluid sphere filled with a couple stress fluid is considered using interfacial slip on the boundary. The velocity is expressed with regard to the stream function. The external velocity and internal velocity are alongside the drag coefficient. It was noticed that with the increases in slip parameter, the drag coefficient is decreasing and the inflow pattern has more circulations with more area appearing near the poles and internal flow disappears gradually. The special cases of viscous fluid, no-slip condition, and solid sphere are evaluated. A good understanding of the current and literature outcomes have been obtained, including the special case of a viscous fluid past a couple stress fluid sphere. [ABSTRACT FROM AUTHOR]

Non-isothermal non-Newtonian fluid flow implemented during filling a coaxial channel in the gravity field is investigated with regard to the dissipative heating, the temperature dependence of the effective viscosity, and the presence of the free surface. The rheological behavior of the medium is described by the Сross-WLF model. The problem is solved numerically using the original computational technology based on the control volume approach and the method of invariants for satisfying the boundary conditions on the free boundary. The flow characteristics in the process of filling are demonstrated for various values of the constitutive parameters. [ABSTRACT FROM AUTHOR]

A mathematical model was created to study the influences of Hall current and Joule heating with wall slip conditions on peristaltic motion of Rabinowitsch fluid model through a tapered symmetric channel with Permeable Walls. The governing equations are simplified under low Reynolds number and the long-wavelength approximations. The perturbation method is used to solve the momentum equation. The physiological phenomena are studied for a certain set of pertinent parameters. The effects offered here show that the presence of the hall parameter, coefficient of pseudo-plasticity, and Hartman number impact the flow of the fluid model. Additional, study reveals that a height in the Hall parameter and the velocity slip parameter increases the trapping bolus's apparition. Furthermore, the magnitude of the trapped bolus can be reduced by enhancing the magnetic field. [ABSTRACT FROM AUTHOR]

The effect of elasticity on the peristaltic flow of a micropolar fluid containing nanoparticles in a cylindrical tube is investigated using a mathematical model. The expressions for velocity and flux flow rate are determined by using Homotopy Perturbation method, under long wave length and low Reynold's number approximations. The variation of flux is calculated by Rubinow and Keller, Muzumdar methods. Different parameters' effects on velocity and flow have been discussed. For various settings, the trapping phenomenon is demonstrated. The flux increases as the elasticity parameters, micropolar parameter, thermophoresis parameter, and coupling number increase. The flux similarly reduces as the Brownian motion parameter is increased. The obtained results are same when we apply Rubinow and Keller, Muzumdar methods. [ABSTRACT FROM AUTHOR]

In this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal) fluid is depicted as a continuum in a noninteger dimensional space. Involving vector calculus for the instance of a noninteger dimensional space, we determine an analytical solution of the Cauchy equation for the instance of a non-Newtonian self-similar fluid flow in a cylindrical pipe. The plot of the velocity profile obtained shows that the rheological behavior of a non-Newtonian power-law fluid is essentially impacted by its self-similar structure. A self-similar shear thinning fluid and a self-similar Newtonian fluid take on a shear-thickening way of behaving, and a self-similar shear-thickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology. [ABSTRACT FROM AUTHOR]

This study is a study of three‐dimensional couple stress Casson fluid flow with nonlinear thermal radiation and heat source effects. The convective heat and mass transfer analysis is applied to a porous stretching sheet. In fluid flow direction, a uniform magnetic field can be applied. Using the similarity transformations, nondimensional expressions are achieved. The obtained equations are found numerically via the shooting technique as well as Runge‐Kutta‐Fehlberg method in MATLAB software. The contribution of different physical parameters is explored and discussed. Such parameters are porous parameter, couple stress parameter, heat source parameter, nonlinear thermal radiation, temperature parameter, and Lewis number. We found, the decreasing rate of heat transfer in the case of couple stress fluid motion when comparing Casson fluid flow with various values of Γ1 ${\Gamma }_{1}$ and Pr $\text{Pr}$. [ABSTRACT FROM AUTHOR]

We study a feedback optimal control problem for a three-dimensional model of a stationary flow of a non-Newtonian fluid (with variable viscosity) in a pipeline network with complex geometry. The control parameter is the dynamic pressure on connection surfaces of pipes to nodes. The flow model is a mixed boundary-value problem for a system of strongly nonlinear partial differential equations in a netlike domain with Kirchhoff-type transmission conditions at interior nodes of the network. The solvability of the optimization problem in the weak formulation is proved; namely, we establish sufficient conditions for the existence of a weak solution which minimizes a lower semicontinuous cost functional. [ABSTRACT FROM AUTHOR]

The processes of hydrodynamics and heat transfer during the flow of a non-Newtonian polymeric medium in a plane channel have been investigated with boundary conditions of the first kind. Consideration was given to a steady-state nonisothermal process with low values of the Reynolds number and high values of the Péclet number, which made it possible to neglect gravity and inertial forces, and also longitudinal thermal conductivity. The Ellis model with a viscosity dependent on temperature, pressure, and the degree of chemical transformation was used as the rheological model. A high-viscosity medium was investigated. Therefore, it is the dissipative term that was taken account of in the energy equation. With the above rheological model, an expression in explicit form was obtained from the equation of motion of such a medium for the velocity profile of its flow. It has been established that the dependence of the viscosity of a medium on its temperature, pressure, and the degree of transformation has an appreciable effect on the distribution of the temperature of the medium and the velocity of its flow along the channel's length. Taking account of the temperature dependence of the viscosity of the medium leads to a decline in the role of dissipation in the process of its warmup. The dependence of the medium's viscosity on pressure, conversely, considerably enhances the dissipative effect, which appreciably accelerates the course of a chemical reaction. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to compare a semi-analytical method and numerical method namely the homotopy perturbation method (HPM) and finite difference method (FDM) respectively. These methods were employed for solving the nonlinear problem of the magnetohydrodynamic (MHD) couette flow of third-grade fluid between the two parallel plates. The comparison was made between a solution of HPM and FDM against a solution obtained from regular perturbation and the results are tabulated. From a computational viewpoint, it is revealed that the HPM is more reliable and efficient than FDM. Also, the results show that the FDM requires slightly more computational effort than the HPM, although the HPM yields more accurate results than the FDM. [ABSTRACT FROM AUTHOR]

In the modern day science and medics, scholars are focusing on the behavioral study of non-Newtonian fluid and its relevance with ciliated motion in human body. This would offer advanced avenues of research to mitigate the risks of new and contagious diseases relating to various systems in human body. This manuscript focuses on the behaviour of metachronal wave in Prandtl fluid generated by ciliated movement through a horizontal tapering channel once magnetic field is applied to the fluid. The theoretical approach raises mathematical calculations and results obtained presented highly nonlinear system of PDEs. Latterly, ODEs are developed which accrue the accurate results by using scaling group of transformations. Second, approximation of long wavelength and low Reynold's number used to analyze the flow motion caused by metachronal waves. The emerging equations achieved are further solved numerically using the bvp4c method. Results are engendered through graphical attempt of velocity, temperature, pressure gradient, pressure rise and wall shear stress graphs in relation to various factors. It can be inferred that theoretical impact of velocity profile for magnetic parameter decreases near the walls of the ciliated channel while increases in the middle of channel. It concludes that magnetic field opposes the strength of the flow close to the walls. Another observation is the flow of temperature across the subject domain is accelerated by the Brinkman number. Thus, the flow of heat transfer may be increased by the fast metachronal wave and fixed initial temperature. While streamlines are also fabricated to exhibit the flow phenomenon of ciliary motion. [ABSTRACT FROM AUTHOR]

• Various industrial configurations were simulated and evaluated for optimal heat transfer efficiency. • Nano metal particles were employed in the simulation to enhance heat transfer efficiency. • The results show that the square geometry with a certain amount of nano metals performs better than other common industrial geometries. • The simulation results align well with other researchers' laboratory results in this field. Spiral tube heat exchangers represent a conventional type of exchanger that finds use in industries such as food, chemical reactors, ventilation, and heat recovery systems. The compact structure, high mass, and heat transfer coefficient of spiral tubes have made them popular in many industries as heat exchangers. This article delves into the investigation of the flow of non-Newtonian Nano fluid CuO-CMC within pipes that possess different cross-sections. In order to analyze the heat transfer of the non-Newtonian Nano fluid flow in the spiral channel, both the single-phase model and the ANSYS Fluent commercial software were employed for simulation. In the realm of numerical simulation, investigation has been conducted on the flow of non-Newtonian water-copper oxide Nano fluid through spiral tubes having three distinct cross-sections, namely circular, square, and oval. The study aimed to delve into the effects of varying volume fractions of nanoparticles, inlet velocities, and cross-sectional areas on several parameters, including but not limited to average Nusselt number, local Nusselt number, vorticity, bulk temperature, transferred heat, average friction coefficient, and local friction coefficient. Elevating Re has a greater impact on Nu than adding nanoparticles. Even with 4% nanoparticles, Nu is lower than pure water with Re of 5000. Incorporating nanoparticles enhances fluid's thermal characteristics but disrupts flow. [ABSTRACT FROM AUTHOR]

This paper deals with the MHD peristaltic flow of Williamson fluids through a porous medium between two joint cylinders. The fluid flow was considered to be that of a non-Newtonian fluid, i.e., a Williamson fluid. The inner tube was uniform, while the flexible outer tube had a Sine wave moving down its wall. The analytical solutions for velocity and temperature were obtained as functions (Bessell functions of the first and second types). The solution for velocity profile, temperature, and concentration distribution were obtained as functions of the physical parameters of the problem (Darcy number, magnetic parameter, Grasoff thermal number, Reynolds number, Prantl number, and Schmidt number) along with other physical parameters. The effect of the physical parameters was discussed graphically. A comparison with previously published graphical results was also carried out. The ambition of the present paper is to contribute to practical applications in geographical and physiological fluid dynamics, such as on sandstone, in the human lungs, on beach sand, on limestone, and in the bile duct. This study is based on theoretical research and can be helpful in the fields of fluid mechanics and mathematics. [ABSTRACT FROM AUTHOR]

Porous materials are used in thermal devices such as heat exchangers to improvement the heat transfer. The heat transfer of a non-Newtonian fluid flow in an annular pipe with porous discs is numerically investigated in this paper. The flow regime in both porous medium and clear region are considered to be turbulent. The effects of power-law index of the non-Newtonian fluid and porous discs pitch variationson the heat transfer rate, friction coefficient are studied and compared to each other for two porous layer thicknesses. Finally, the thermal performance is defined which determines the optimum porous media and non-Newtonian fluid characteristics in the annular pipe. [ABSTRACT FROM AUTHOR]

The study of electromagnetohydrodynamics (EMHD) of non‐Newtonian fluid plays a significant role for optical design, thermal management of electronic components, and various operations of microfluidic devices. The use of parallel geometry is seen in the circulatory system, extrusion process, and respiratory system. By considering various practical applications, in the current study, the Poiseuille flow of an incompressible Casson liquid between the plates is investigated. The effects of MHD, Joule heating, thermal radiation, modified Darcy's law, and chemical reaction have been taken into account. The dimensional governing equations have been converted into dimensionless equations with pertinent nondimensional quantities. The resulting system of nondimensional system of equations has been analytically solved with nondimensional slip boundary conditions. The graphical results have been displayed with various fluid flow parameters. From the current study, it is concluded that the influence of Darcy number and Casson fluid parameter enhances the velocity profile, but the concentration declines with the enhancement of Casson fluid parameter. The radiation parameter and Prandtl number suppress the temperature profile. [ABSTRACT FROM AUTHOR]

Non‐Newtonian fluids flowing in a concentric annulus have been widely observed in industrial chemical processes. In this study, the hydrodynamic characteristics of a non‐Newtonian fluid (polymer solution) in concentric annulus are investigated using computational fluid dynamics (CFD) modeling and numerical simulation methods. First, a simple grid independence analysis is carried out to select appropriate grid parameters. Then the rationality of the proposed CFD model is confirmed by the near‐wall velocity profiles. Based on the validated model, the effects of the fluid properties and radius ratio on the flow structure characteristics are studied at various inlet velocities. According to the simulated flow fields (i.e., velocity, pressure, strain rate, and wall shear stress), the flow pattern, flow resistance, and residence time distribution characteristics are analyzed in the laminar and turbulent regimes. The presented results show that non‐Newtonian fluids have unique flow behaviors in concentric annulus when compared with Newtonian fluids. [ABSTRACT FROM AUTHOR]

Analytical and numerical solutions are investigated to study solution of the Magneto hydrodynamics (MHD) natural convection flow of grade three of a non- Newtonian fluid flow between two vertical flat plates through embedded in a porous medium and considering the effect heat source using Multi−step differential transform method and finite difference method. The system of coupled nonlinear ordinary differential equations are solved analytically using Multi−step differential transform method (MDTM) and numerically using finite difference method (FDM). The results of (MDTM), (FDM), and another analytical method are all in good agreement, demonstrating that these methods are capable of solving similar problems. Graphs and tables show the effect of various parameters on velocity and temperature. The current studies, as well as comparisons to previous findings, are presented in figures and tables. The study results showed that the analytical solution using Multi−step differential transform method and numerical solution using finite difference method agrees well with recent analytical and numerical solutions. [ABSTRACT FROM AUTHOR]

The present exploration is based on the contributions of heat and mass transport on the non‐Newtonian viscoelastic liquid motion under the impact of magnetism, Soret and Dufour numbers. The model equations that describe the flow mechanism of heat and mass transport are partial differential equations (PDEs). The PDEs were simplified using suitable similarity functions to obtain coupled nonlinear total ordinary differential equations. The simplified equations are numerically solved utilizing the spectral homotopy analysis method. Findings show that the process of heat transport is because of thermal radiation. The velocity, as well as temperature distributions, enhances due to a higher viscoelastic term. The present analysis is examined closely with past works and was discovered to concord. [ABSTRACT FROM AUTHOR]

In this paper, the analytical investigation of non‐Newtonian fluid flow through a turbine disc with a heat generation effect is considered. The flow mechanics through the turbine disc is modeled using a coupled system of higher‐order partial equations, which are transformed into ordinary order utilizing proper similarity transforms. Governing models are analyzed using the variation iteration and homotopy perturbation analytical methods. As observed from the results, the study shows enhancement of heat generation for non‐Newtonian fluid flow through turbine disc, reveals abating thermal distribution. More so, the graphical expression shows that heat generation improves up till mid‐disc. Thereafter, an increasing trend toward the fluid injection surface is observed. Validation of analytical solutions with numerical analysis boosts confidence in this study, which may be used to provide further insights into the engineering science of non‐Newtonian flow of hydraulic/lube oil in practical applications, such as hydraulic couplings. [ABSTRACT FROM AUTHOR]

• An experimental methodology to measure a non-Newtonian fluid flow with free surface. • Photometric and ultrasonic systems providing similar amplitude of roll wave. • An absorbance photometric technique to measure the steep front of the roll wave with high precision. This work aims to measure forced steady roll waves evolving non-Newtonian fluid flow by using absorbance photometric technique. Instabilities on the free surface of the uniform flow were induced by controlled air pulses, generating roll waves under specific conditions of Froude number and disturbance frequency. A systematic procedure was presented to clarify a compromise between the aqueous concentrations of Carbopol (with adequate viscosity) and methylene blue dye (avoiding optical opacity), providing both sensitivity and resolution for absorbance measurements. Roll waves amplitudes were also measured using an ultrasonic sensor in order to compare the results with the absorbance photometric technique. Given a channel inclination, six scenarios defined by different flow rates were tested, which allowed us to observe the generation of roll waves as a succession of shocks. The measured profiles showed a better precision (maximum error of 0.11 mm against 1.37 mm, for pump rotation equal to 475 RPM) using the absorbance photometric technique compared to the ultrasonic system, respectively. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation of power-law fluid flow past and through elliptical porous cylinder, considering heat transfer effects. The study covers a wide range of parameters, including Reynolds number, power-law index, cylinder aspect ratio and Darcy number. The wake pattern, streamline distribution, drag coefficient, pressure distribution, and Nusselt number are analyzed comprehensively for various cases. Within the investigated parameter range, four distinct vortices are observed: an external vortex separated from the cylinder, an external vortex attached to the cylinder, a boundary vortex partially inside and outside the cylinder, and an internal vortex entirely inside the cylinder. The occurrence of the external and separated vortex is limited to AR = 0.2 and = 10 − 3 , while the internal and boundary vortices are exclusively observed at AR = 2.0. Additionally, increasing the aspect ratio of the elliptical cylinder results in shorter vortices at a given Reynolds and Darcy number. For example, at Re = 40 and D a = 10 − 4 , vortex lengths decrease from 5 to 0.6 with increasing aspect ratio from 0.2 to 2. Furthermore, by decreasing aspect ratio, the drag coefficient generally increases and the Nusselt number decreases from 0.2 to 1, but this trend reverses as the aspect ratio rises from 1 to 2. • Four distinct vortices (external separated, external attached, boundary, and internal) are observed. • External separated vortex is limited to AR = 0.2 and D a = 10 − 3 . • Internal and boundary vortices are exclusively observed at AR = 2.0. • Drag coefficient is considerably affected by vortex type. • At high values of Da number (Da = 10−1, 10−2), as the power index increases, the Nusselt number increases. [ABSTRACT FROM AUTHOR]

• A first numerical study on gas-focused non-Newtonian micro-jets, described by power-law rheology. • New findings on stability, shape, and velocities of such jets. • A detailed analysis of fluid flow patterns in the nozzle and in the jet as a function of the power-law index. The present numerical study assesses the jet length, diameter and velocity of various non-Newtonian power-law fluids of a gas dynamic virtual nozzle. A related two-phase flow problem is formulated within the mixture framework and solved with the finite volume method and volume of fluid interface treatment in axisymmetry. The process parametric range allows the incompressible laminar flow assumption. A comprehensive jet characteristics analysis is carried out in a typical micro-nozzle configuration for a range of shear-thinning to shear-thickening fluids with power law indices 0.5 ≤ n < 1.5, gas mass flow rate of 10 mg/min and liquid volumetric flow rate of 43 µl/min, resulting in a gas Reynolds number of 130 with Reynolds and Weber numbers for a reference water jet being 90 and 10, respectively. It is observed that jets from shear-thinning fluids (0.5 ≤ n < 1.0) tend to be thicker, longer, and slower when compared with the shear-thickening fluids (1.0 < n ≤ 1.5). A dripping-jetting phase diagram of the nozzle is constructed by varying the power law index, gas and liquid flow rates in the range 0.9–1.1, 5–15 mg/min and 5–50 µl/min, respectively. It is observed that the area of stable jetting decreases with the increase of the power law index. The obtained novel information on the behaviour of non-Newtonian gas-focused micro-jets provides a possible new dimension for tailoring the serial crystallography sample delivery systems where the micro-jets carry dispersed crystals into an X-ray beam. [Display omitted] [ABSTRACT FROM AUTHOR]

Recently, the increasingly strict safety and emission regulations in the automotive industry drove the interest towards automatic length compensating devices, e.g., hydraulic lash adjusters (lower emission) and slack adjuster in brake systems (faster brake response). These devices have two crucial requirements: (a) be stiff during high load, while (b) be flexible in the released state to compensate for environmental effects such as wear and temperature difference. This study aims to use the advantageous properties of shear thickening fluids to develop a less complicated, cost-efficient design. The proposed design is modeled by a system of ordinary differential equations in which the effect of the non-Newtonian fluid flow is taken into account with a novel, simplified, semi-analytical flow rate-pressure drop relationship suitable for handling arbitrary rheology. The adjuster's dimensions are determined with a multi-objective genetic algorithm based on the coupled solid-fluid mechanical model for six different shear thickening rheologies. The accuracy of the simplified flow model is verified by means of steady-state and transient CFD simulations for the optimal candidates. We have found that the dominating parameters of such devices are (a) the shear thickening region of the fluid rheology and (b) the gap sizes, while the piston diameters and the zero viscosity or the critical shear rate of the fluid have less effect. Based on the results, we give guidelines to design similar-length compensating devices. [ABSTRACT FROM AUTHOR]

Many studies have been performed on non-Newtonian fluid flow through the nonuniform stretching sheet. In most cases, the problem is assumed to be two-dimensional fluid flow and a similarity solution is exploited. In this paper, we consider the effect of viscous dissipation on the MHD non-Newtonian fluid flow and heat mass transfer due to slendering stretching sheet with thermal radiation. Both Williamson and Casson models are opted here while the mathematical modeling is used for the principle flow equations. By dimensionless transformation, the governing equations are transformed to identically coupled three equations along with three common boundary conditions imposed. They are then solved numerically by using Chebyshev spectral method for different values of the physical parameters involved. These governing parameters are graphically shown to have a considerable influence on the fluid flow and heat mass transfer characteristics of this model. Local heat transfer rate is found to depend on both magnetic parameter and Casson parameter in addition to the Eckert number dependence. Likewise, due to increase of Casson parameter, the sheet temperature and the thermal boundary layer thickness enhances and also the same behavior is observed for increasing the radiation parameter. [ABSTRACT FROM AUTHOR]

[Display omitted] • The unique flow patterns of non-Newtonian fluid were observed and analyzed; • The influences of gas and liquid flow rate and flow pattern on the two-phase pressure drop were investigated; • A new two-phase friction multiplier correlation was developed to calculate the two-phase pressure drop. An experiment of gas-non-Newtonian fluid flow was performed in a horizontal square microchannel to investigate the two-phase pressure drop and flow pattern. The pressure drops were measured and the images of the flow pattern were captured. In the non-Newtonian fluid, the flow pattern and flow regime map were different from those in water. The non-Newtonian behavior of the liquid phase also significantly affected the two-phase pressure drop. The relationship between the two-phase pressure drop and the gas and fluid flow rates relied on the flow pattern. A new two-phase friction multiplier correlation considering the gas-liquid flow rate ratio and the rheological properties of the liquid phase was developed to calculate the two-phase pressure drop. The new correlation can predict the experimental pressure drop data within the root mean square percentage errors of 12% for the gas-non-Newtonian fluid two-phase flow and 17% for the gas-water two-phase flow. [ABSTRACT FROM AUTHOR]

In this study, a numerical investigation on mixed convection inside a trapezoidal cavity with a pair of rotating cylinders has been conducted. Three different power-law fluid indexes (n = 1.4, 1.0, and 0.6) have been considered to model different sets of non-Newtonian fluids. Four separate cases are considered based on the rotational orientation of the cylinders within the cavity. In the first two cases, the cylinders rotate in the same direction, i.e., both counterclockwise (CCW), and both clockwise (CW), whereas, in the other two cases, cylinders rotate in opposite directions (CW-CCW and CCW-CW). Simulations have been carried out over a broad range of Reynolds number (from 0.5 to 500) and angular speeds (a dimensionless value from 0 to 10). The average Nusselt number values at the isothermal hot inclined cavity surface are determined to evaluate heat transfer performance in various circumstances. Streamlines and isotherm contours are also plotted for a better understanding of the effects of different cases for various parameters on thermal and fluid flow fields. It is found that the Nusselt number varies nonlinearly with different angular speeds of the cylinders. The combined effect of the mixing induced by cylinder rotation and viscosity characteristics of the fluid dictates the heat transfer in the system. Predictions from the numerical investigation provide insights into the sets of key parametric configurations that have a dominant influence on the thermal performance of the lid-driven cavity with double rotating cylinders. [ABSTRACT FROM AUTHOR]

This paper simulated the free convective heat transfer (CHT) and generation of entropy (GOE) of a non-Newtonian fluid (NNF) in a square chamber using the FDLBM approach. The NNF is modeled by the power-law method. A magnetic field (MF) is able to take different angles which has affected the chamber. A hot square barrier exists in the middle of the chamber. The side edges of the chamber have sinusoidal temperature profiles, and the top and bottom sides are insulated. The effective studied parameters include the Hartmann number (Ha), angle of MF, exponential function index, and the aspect ratio (AR) of the hot barrier. The results of simulation disclosed that shear-thinning NNF has the highest CHT and shear-thickening NNF has the lowest GOE. Increasing the AR of the hot barrier led to an increase in the Nusselt number (Nu) and GOE and a decrease in the Bejan number (Be). Increasing the angle of the MF at small ARs with Newtonian fluid increases the Nu. Increasing the Ha from 0 to 40 in shear-thinning NNF, shear-thickening NNF, and Newtonian fluid reduced CHT by 43%, 15%, and 43%, respectively. Increasing the Ha also reduces the GOE by 27% for Newtonian fluid and 763% and 4% shear-thinning NNF and shear-thickening NNF, respectively. Eventually, a relation is proposed for the mean Nu, GOE, and Be. [ABSTRACT FROM AUTHOR]

We consider the equations of a rotating incompressible non-Newtonian fluid flow of grade two in a three dimensional torus. We prove two different results of global existence of strong solutions. In the first case, we consider that the elasticity coefficient α is arbitrary and we suppose that the third components of the vertical average of the initial data and of the forcing term are small compared to the horizontal components. In the second case, we consider a forcing term and initial data of arbitrary size but we restrict the size of α. In both cases, we show that the limit system is composed of a linear system and a second grade fluid system with two variables and three components. [ABSTRACT FROM AUTHOR]

In this work, analytical solution of hybrid Maxwell nanofluid of the vertical channel due to pressure gradient is discussed. By introducing dimensionless variables the governing equations with all levied initial and boundary conditions is converted into dimensionless form. Fractional model for Maxwell fluid is developed by Caputo time fractional differential operator by using the constitutive relation. The dimensionless expression for temperature and velocity are found using Laplace transform. Draw graphs of temperature and velocity by Mathcad software and discuss the behavior of flow parameters and the effect of fractional parameters. As a result, we have found by increasing the volumetric fraction of copper and alumina temperature increases and velocity decreases. Also, fluid flow properties showed dual behavior for small and large time, respectively, by increasing fractional parameters values. [ABSTRACT FROM AUTHOR]

• Wall-Modeled large-Eddy simulation (WMLES) of Non-Newtonian (NN) fluids is studied. • The conventional WMLESs are shown to be incapable of predicting correct statistics. • Novel wall-stress models (WSMs) are proposed for WMLES of power-law NN fluid flows. • Assessment against wall-resolved LES proves the fine performance of the new models. For high-fidelity predictions of turbulent flows in complex practical engineering problems, the Wall-Modeled (WM) Large-Eddy Simulation (LES) has aroused great interest. In the present study, we prove that the conventional Wall-Stress Models (WSMs) developed for WMLES of Newtonian fluids fail to predict the shear-thinning-induced drag reduction in power-law fluids. Therefore, we propose novel algebraic, integrated, and Ordinary-Differential-Equation (ODE) WSMs, for the first time, for WMLES of power-law Non-Newtonian (NN) fluids and assess their performance against reference Wall-Resolved (WR) LES solutions. In addition, the effects of the key model parameters, including the WSM type, sampling height, sampling cell, and axial grid resolution are explored, and it is revealed that turbulent NN flow predictions have a much higher sensitivity to the choice of WSM, compared to their Newtonian counterparts. It is manifested that, in contrast to WRLES, accurate modeling of the mean apparent and subgrid-scale NN viscosities in the Non-Newtonian ODE (NNODE) model can improve the predictions considerably. Therefore, closures with lower uncertainties on coarse WMLES grids are sought for these terms. Finally, the best performance for the present test cases is obtained via the integrated NN WSM, sampling at the lower edge of the log layer within the third off-the-wall grid cell. Nevertheless, the new NNODE WSM can have an advantage in the presence of non-equilibrium effects in more complex problems. [ABSTRACT FROM AUTHOR]

• A VMS finite element formulation is used to solve 3D non-linear problems. • Hemodynamics in carotid artery bifurcations under three different conditions are studied. • Blood is modeled using three non-Newtonian models: Cross, Carreau-Yasuda, and power-law equations. • Flow rates through each part of the carotid artery are measured. • Wall shear stresses regions are classified according to their magnitude. In this work, a variational multiscale finite element formulation is used to study bifurcation flows of non-Newtonian fluids, using a representative simplified Carotid Artery geometry. In particular, the flow pattern and wall shear stress (WSS) computed using power-law, Cross, and Carreau–Yasuda models, are assessed. First, the formulation is validated by contrasting simulations of a benchmark test for bifurcation flows reported in the literature. After that, a study of blood flow through the carotid artery is presented. Hemodynamics conditions aimed to describe the flow behavior from diastole to systole of the cardiac cycle for healthy arteries and two specific conditions (60% carotid stenosis due to atherosclerosis and 20% increased bifurcation angle due to aging), are specifically analyzed. For each condition, the hemodynamics present different velocity fields that lead to distinctive distribution of WSS enable us to classified three regions, depending on their magnitude: low-WSS, medium-WSS and high-WSS. Results show that power-law flows predict lower wall shear stresses, especially in sections where geometry concentrates stresses, compared to those predicted using Cross and Carreau–Yasuda models. Overall, low-WSS are usually present in zones where stenosis develops even in healthy arteries, however, both geometries lead to a decrease of WSS magnitude in low-WSS regions, increasing the risk factor associated with plaque building. [ABSTRACT FROM AUTHOR]

The current endeavor examines the convective heat transfer characteristics on magnetohydrodynamic stagnation point flow of micropolar fluid past an exponential curved surface. The flow is supposed to be laminar and time-independent. The influence of radiation, irregular heat source/sink, Joule heating, and variable thermal conductivity are supposed. Suitable similarity renovations are considered to transform the original partial differential equations as ordinary ones and then resolved by shooting and fourth-order Runge-Kutta methods. Graphs are drawn to inspect the impacts of sundry nondimensional parameters on the distributions of velocity, microrotation, and temperature. We detect that there is an escalation in temperature with Eckert number and variable heat source/sink parameters. Also, it is motivating to comment that Biot number is an increasing function of local Nusselt number. [ABSTRACT FROM AUTHOR]

The performance of fluid devices, such as channels, valves, nozzles, and pumps, may be improved by designing them through the topology optimization method. There are various fluid flow problems that can be elaborated in order to design fluid devices and among them there is a specific type which comprises axisymmetric flow with a rotation (swirl flow) around an axis. This specific type of problem allows the simplification of the computationally more expensive 3D fluid flow model to a computationally less expensive 2D swirl flow model. The topology optimization method applied to a Newtonian fluid in 2D swirl flow has already been analyzed before, however not all fluids feature Newtonian (linear) properties, and can exhibit non-Newtonian (nonlinear) effects, such as shear-thinning, which means that the fluid should feature a higher viscosity when under lower shear stresses. Some fluids that exhibit such behavior are, for example, blood, activated sludge, and ketchup. In this work, the effect of a non-Newtonian fluid flow is considered for the design of 2D swirl flow devices by using the topology optimization method. The non-Newtonian fluid is modeled by the Carreau-Yasuda model, which is known to be able to accurately predict velocity distributions for blood flow. The design comprises the minimization of the relative energy dissipation considering the viscous, porous, and inertial effects, and is solved by using the finite element method. The traditional pseudo-density material model for topology optimization is adopted with a nodal design variable. A penalization scheme is introduced for 2D swirl flow in order to enforce the low shear stress behavior of the non-Newtonian viscosity inside the modeled solid material. The optimization is performed with IPOPT (Interior Point Optimization algorithm). Numerical examples are presented for some 2D swirl flow problems, comparing the non-Newtonian with the Newtonian fluid designs. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluid flows through packed beds are common in many industries. Our understanding of this flow system is very limited, and the correlations for describing the fluid-particle interaction are not fully established. To overcome these problems, this paper presents a comprehensive study of this system on a sub-particle scale, with a special reference to the interaction between fluid rheology and bed properties. This is done by conducting about five hundred Lattice Boltzmann simulations under different conditions. The fluid rheology is represented by the power-law model to consider the shear-thinning, shear thickening and Newtonian behaviors of fluids. The simulation condition covers a wide range of bed porosity, particle size distribution and Reynolds number (Re). The results show that the effect of fluid rheology on the fluid behavior is strong. This effect varies significantly with bed porosity which is a function of particle size distribution. The interplay between fluid rheology and bed properties is however not strong in determining the distributions of particle-fluid interaction force. Based on the simulation data, a new drag correlation is established and validated against the experimental data in the literature. This correlation is more accurate and consistent than those reported in the past. It can estimate the mean drag forces on individual particles of different sizes, and is recommended to be used generally in the modeling of particle-fluid flows either for Newtonian fluids or for non-Newtonian fluids obeying the power-law model. Unlabelled Image • Lattice Boltzmann simulation has been conducted to study the non-Newtonian fluid flow in packed beds. • The interplay between fluid rheology and bed properties is examined under different conditions. • Particle-fluid interaction forces are quantified in terms of spatial and statistical distributions. • A new correlation is formulated to estimate generally the mean drag force. [ABSTRACT FROM AUTHOR]

In this paper, laminar flow of non-Newtonian (Bingham) fluid is studied numerically in a two-dimensional lid-driven skewed cavity that incorporates Papanastasiou exponential regularization approach of Bingham constitutive model [Papanastasiou, Flows of materials with yield, J. Rheol. 31 (1987), pp. 385–404]. Numerical simulation has been done using the finite-volume method with collocated grid arrangement. The governing equations including continuity and momentum are initially non-dimensionalized using appropriate transformation. To simulate irregular shape cavity flow problem, body-fitted non-orthogonal grids are used, and governing equations have been transformed to generalized curvilinear co-ordinates. In this study, two dimensionless parameters namely, Reynolds number and Bingham number are considered. A wide range of skew angles are considered which comprises both acute and obtuse angles. The obtained results are presented in terms of velocity and streamlines with yielded/unyielded region for different values of Bingham number and Reynolds number having different angles of the skewed cavity. The present results may be serve as benchmark results for comparison purpose in the case of non-Newtonian (Bingham) fluid flow. [ABSTRACT FROM AUTHOR]

Shear thickening fluid polishing (STFP) is one type of the non-Newtonian fluids which is used to polish the complex shapes. This method is applied to machine the spherical hardened steel in this study. The principle and performance of STFP was introduced. There are many parameters that significantly influence the STFP process; however, the inclination angle of the workpieces is one of the parameters that greatly affect the pressure distribution and deviation of surface roughness at different area on the workpiece surfaces. The effect of inclination angle, fluid viscosity, and polishing speed to the machining process is carried out by simulating. The inclination angle parameters of the workpieces such as 0°, 3°, 5°, 7°, 10°, 12°, and 15° are used during the simulation and experimental process. The distributed pressure area and polishing fluid flow characteristics will be presented and analyzed. Simulation results show that the inclination angle of 5° and fluid viscosity of 3 Pa.s are the best combination. The pressure area is distributed throughout all the surface of the spherical steel and maximum pressure value is achieved about 9.29 Pa in the case of 5° inclination angle. In addition, experimental results illustrated that the surface roughness achieved is the smallest when inclination angle of 5°, the fluid viscosity of 3 Pa.s, and polishing speed of 100 rpm. The best surface roughness can be reach 12 nm after 15 min polishing. The deviation of surface roughness is about 14 nm in this case. This result agrees well with simulation results. The simulation and experimental results show that STFP was a promising and feasible processing method in the polishing of workpieces with complex shape. [ABSTRACT FROM AUTHOR]