Flow Of Power-law Fluid Research Articles

Exploring slip flow and heat transfer of power-law fluid past an induced magnetic stretching regime subject to Cattaneo-Christov flux theory

This work investigates the heat transmission and boundary layer (BL) slip flow of a power-law fluid induced by stretching surfaces. The power-law fluid, induced magnetic field, and finite thermal relaxation have significant applications in a variety of industrial settings, including thin-layer growth, cooling systems, the extrusion process, and coating and shaping operations in a heat transfer mechanism. With these significant industrial applications, the current study explores BL flow and heat transfer in the context of the of the Cattaneo-Christov theory against the backdrop of an induced magnetic field over a stretching surface. The shear-thinning and thickening features are captured by the power-law fluid model, while the Cattaneo-Christov theory solves the deficiencies of Fourier's law. The BVP4c technique is used to construct and solve BL equations numerically. The surface drag and heat transmission rates at the wall are studied using statistical multi-regression analysis. The findings clarify that the magnetic and power law indices have a favorable effect on the Nusselt number, while their influence on skin friction is conflicting. A lower heat transmission is predicted with thermal relaxation as compared to Fourier's law in the energy equation. The accumulated thermal relaxation parameter produces a non-equilibrium state, delaying the internal thermal processes.

Power-law fluid flow in the entrance region between two parallel plates

Flow of non-Newtonian fluids between parallel plates has many uses including heat transfer applications. Many non-Newtonian fluids can be categorized as pseudoplastic fluids. A broader category, power-law fluids, covers in addition dilatant and Newtonian fluids. Models for developing power-law fluid flow between parallel plates include computational and integral boundary layer methods. Most published studies include partial results and apply to one of the three categories. The present work addresses the three cases and exclusively shows the transition from developing to fully developed flow. In the inlet region, viscous effects are restricted to the boundary layer. The present approach is based on the inlet-filled region concept, and includes an additional zone, called filled region in which viscous effects are present in the whole region, with the flow asymptotically reaching the fully developed solution. The integral boundary layer method is used in both regions to solve for the flow. The results are found to be in good agreement with published Newtonian, pseudoplastic and dilatant fluid results for boundary layer thickness, centerline velocity, local friction factor, pressure drop profiles, and entrance region size. The present model is fundamentally analytical with minor computational work required.

Soret and dufour impacts on radiative power-law fluid flow via continuously stretchable surface with varying viscosity and thermal conductivity

The intricate dynamics of mixed convective thermic and species transport in a power-law flowing fluid through a continuously stretched surface are investigated. The uniqueness of this study lies in the consideration of fluid variable thermic conductivity and viscosity, which introduces a higher degree of realism into the analysis. The transformation of similarity is used to transform the fundamental governing equations, and after that, the set of equations is processed numerically utilizing a non-similarity local approach. Furthermore, the effects of Soret and Dufour represent the cross-diffusion phenomena, accounting for the energy exchange with the surroundings. These factors collectively influence the stretching surface’s gradient velocity, affecting the thermal and species concentration rates. The findings offer a comprehensive understanding of these complex interactions, paving the way for optimizing thermic and species transport processes in various industrial applications. This study, therefore, holds significant potential for enhancing efficiency and performance in relevant industrial sectors. The main terms are the combinations of Dufour and Soret numbers that significantly impact the flow rate profile and mass transfer field. The coupled study of the nonlinear velocity, energy distribution and chemical mixture variance made the study more impactful in practicality. Skin friction variation shows limited impact with variations in the Soret number. The enhanced thermal gradient results in improved non-similarity parameters, yet it demonstrates a decrease with an increase in variable thermal diffusivity. There is a decrease in the temperature gradient as the buoyancy term reduces, while an increase is observed with changes in the Prandtl number. Similarly, the Nusselt number experiences a comparable impact due to changes in the Soret number.

Superimposed squeeze and rotational flows of Newtonian and power-law fluids a)Dedicated to Nicolás M. Páez-Flor, Ph.D. In memoriam (1983–2023).

This study theoretically predicted the response of superimposed squeeze and rotational flows (SSRF) of fluids with different viscous behaviors (i.e., Newtonian, shear-thinning, and shear-thickening fluids). The theoretical predictions were verified using the plate-plate geometry for the SSRF measurements with the Newtonian and power-law fluids. In all the cases, the squeeze force increased as the gap decreased, but the response was very different for each rheological behavior. The variation in the squeeze force with the gap was not affected by the superimposed rotational shear stress value, owing to the nondependency of the viscosity on the shear for Newtonian fluids. However, for the power-law fluids, the squeeze force variation with the gap value was based on the value of the superimposed shear stress value. The decrease and increase in the viscosity with the shear stress for the shear-thinning and shear-thickening fluids, respectively, resulted in opposite trends of the squeeze force with the gap value variation. For the shear-thinning fluids, the squeeze force for each gap value decreased with increasing superimposed rotational shear stress. The opposite trend was observed for the shear-thickening fluid. In the absence of wall slip, the theoretical predictions well agreed with the experimental results.

Study on the motion characteristics of Janus based on the squirmer model in the flow

The motion characteristics of Janus in the flow are studied numerically using the lattice Boltzmann method based on the squirmer model. The effects of velocity ratio J on the right and left hemisphere surface of Janus, particle Reynolds number Rep, flow Reynolds number Rec, initial orientation angle φ0 on Janus trajectory, and lateral equilibrium position yeq/H are analyzed. The results showed that, for the motion of Janus in stationary power-law fluids in a channel, Janus moves randomly in a small space in shear-thickening fluids when Rep is low and exhibits three motion modes at Rep = 5. The larger the J value, the easier it is for Janus to reach yeq/H. The higher the Rep, the closer the yeq/H is to the lower wall. In shear-thinning fluids, the motion of Janus exhibits significant randomness at Rep = 0.5 and 1, reaches the same yeq/H at Rep = 2 and 3, and tends toward yeq/H near the centerline and along the upper wall, respectively, at Rep = 4 and 5. For the motion of Janus particles in a channel flow of power-law fluids, in shear-thinning fluids, no matter what value J is, Janus reaches yeq/H on the centerline. The lower the Rep, the closer the yeq/H is to the wall. Two particles move toward yeq/H when Rep ≥ 1. The higher the Rep, the closer the yeq/H is to the centerline. The two particles will exhibit the upstream mode at Rep = 2. Two particles eventually reach yeq/H at different Rec. When φ0 > 0°, the two particles first eventually tend toward yeq/H = 0.2 and 0.8. When the value of φ0 is negative, the larger the absolute value of φ0 and higher the Rep, the more likely particles are to exhibit upstream mode.

Computational analysis of radiative flow of power law fluid with heat generation effects: Galerkin finite element simulations

This research aims to presents the free convective flow power law fluid due to vertical cone. The investigation for observing the heat transfer phenomenon is accounted to heat generation and radiative effects. The assumption of variable viscosity is taken into account. A vertical cone induced the flow. The dimensionless variables are followed to attains the simplified form. The numerical computations are performed with help of famous finite element method (FEM). The FEM algorithm is supported with applications of quadratic Lagrange polynomials. The results are confirmed with peak accuracy. The physical aspect of problem is presented in view of shear thickening, shear thinning and viscous material case. A comparative thermal reflection in absence and presence of heat generation have been endorsed. Moreover, the insight of various parameters on Nusselt number is also presented.

On the stability and accuracy of TRT Lattice-Boltzmann method for non-Newtonian Ostwald-de Waele fluid flows

This paper brings a numerical analysis of the TRT modeling for the Lattice-Boltzmann method when solving flow for dilatant and pseudoplastic power-law fluids. Firstly, the method was reviewed to describe the required simulation parameters and the numerical methodology. Secondly, a mathematical procedure was performed to identify the characteristic relaxation frequency as a function of both flow and fluid properties and to work as a guide parameter for LBM operation. Then, a simple shearing Poiseuille flow was employed so its characteristic shear rate could be calculated as a function of fluid properties, given the flow was characterized by the Reynolds and Mach numbers. For this test case, convergence was then explored for a broad range of parameters, and its non-monotonic dependency on the Mach number for a given convergence criterion was shown. Then, stability maps were constructed based on the characteristic relaxation frequency, which showed a strong dependency between consistency and flow index so the simulation could converge. This was explored against the results from the converged tests, which pointed out the usefulness of the characteristic relaxation frequency in predicting stable solutions. Finally, quantitatively, it was shown that for this power-law fluid flow, the ||L2|| relative error depends on the Mach number to the power of 2(2−n) being now a function of the flow index, extending the previously reported dependency of the Mach number to the power of 2 for plane-Poiseuille flow.

Transient Friction Analysis of Pressure Waves Propagating in Power-Law Non-Newtonian Fluids

Modulated pressure waves propagating in the drilling fluids inside the drill string are a reliable real-time communication technology that transmit data from downhole to the surface during oil and gas drilling. In the analysis of pressure waves’ propagation characteristics, the modeling of transient friction in non-Newtonian fluids remains a great challenge. This paper establishes a numerical model for transient pipe flow of power-law non-Newtonian fluids by using the weighted residual collocation method. Then, the Newton–Raphson method is applied to solve the nonlinear equations. The numerical method is validated by using the theoretical solution of Newtonian fluids and is proven to converge reliably with larger time steps. Finally, the influencing factors of the wall shear stress are analyzed using this numerical method. For shear-thinning fluids, the friction loss of periodic flow decreases with the increase in flow rate, which is opposite to the variation law of friction with the flow rate for stable pipe flow. Keeping the amplitude of pressure pulsation unchanged, an increase in frequency leads to a decrease in velocity fluctuations; therefore, the friction loss decreases with the increase in frequency.

Scaling laws for optimal power-law fluid flow within converging–diverging dendritic networks of tubes and rectangular channels

Flows in dendritic–fractal networks have garnered extensive research attention, but most studies assume a constant tube or channel cross section. In many applications, the cross section of the tube or channel changes as the flow progresses through it, such as the blood flow through the arterial system, which is a prime example of a deformable or non-uniform tree-like network. Heating, ventilation, and air conditioning ductwork also exemplify a tree-like network with varying cross sections. This research investigates power-law fluid flows in the converging–diverging tubes and rectangular channels, prevalent in engineered microfluidic devices, many industrial processes, and heat transfer applications. Power-law fluid flows through linear, parabolic, hyperbolic, hyperbolic cosine, and sinusoidal converging–diverging dendritic networks of tubes and rectangular channels are studied. The flow is assumed to be steady, incompressible, two-dimensional planar, and axisymmetric laminar flow without considering network losses. A theoretical model has been derived to evaluate the flow conductance under network volume and surface-area constraints. The flow conductance is highly sensitive to network geometry. The effective conductance of all networks increases with increasing daughter-to-parent radius ratio before eventually declining. The maximum conductance occurs when a specific radius or channel-height daughter–parent ratio β* is achieved. This value depends on the constraint and vessel geometry, such as tubes or rectangular channels. The optimal flow conditions for maximum conductance in a constrained tube volume network, βmax*=βmin*=N−1/3, while for a constrained tube's surface-area network, βmax*=βmin*=N−(n+1)/(3n+2). This scaling applies to all converging–diverging tube network profiles. Here, βmax*, βmin* are the radius ratios of the daughter–parent pair at the maximum divergent or minimum convergent part of the vessel. N represents the number of branches splitting at each junction, and n is the power-law index of the fluid. Furthermore, the optimal flow scaling for the height ratio in the rectangular channel, βmax*=βmin*=N−1/2α−1/2 for constrained channel volume and βmax*=βmin*=N−1/2α−n/(2n+2) for constrained surface area for all converging–diverging channel networks, respectively, where α is the channel-width ratio between parent and daughter branches. Additionally, at optimal conditions in both the channels and tube network, pressure drops are equally partitioned across each branching level. The results in this work are validated with experiments and existing theories for limiting conditions. This research expands existing design principles for efficient flow systems, previously in the literature developed for uniform vessels, to encompass non-uniform converging–diverging vessels. Additionally, it provides a valuable framework for studying non-Newtonian flows within complex, non-uniform tree-like networks.

Numerical study on thermocapillary flows of power-law fluids with the lattice Boltzmann method

Numerical study on thermocapillary flows of power-law fluids with the lattice Boltzmann method

Scaling laws for optimized power-law fluid flow in self-similar tree-like branching networks

The power-law fluid flow in tree-like self-similar branching networks is prevalent throughout the natural world and also finds numerous applications in technology such as oil recovery and microfluidic devices. We investigate analysis of optimal power-law fluid flow conditions and the optimal structures within tree-like branching networks, focusing on maximizing flow conductance under the constraint of the network tube’s volume and the surface area. The study considered fully developed laminar power-law fluid flow regimes without considering any losses in the network system. A key observation was the sensitivity of the dimensionless effective flow conductance to the network’s geometrical parameters. We found that the maximum flow conductance occurs when a dimensionless radius ratio β∗ satisfies the equation β∗=N−1/3 and β∗=N−(n+1)/(3n+2) under constrained tube-volume and surface-area, respectively. Here, N represents the bifurcation number of branches splitting at each junction, and n is the fluid power-law index. We further find that this optimal condition occurs when pressure drops are equipartition across each branching level. We validated our results with various experimental results and theories under limiting conditions. Further, Hess–Murray’s law is justified and extended for the shear-thinning and shear-thickening fluid flows for an arbitrary number of branches N. Further, in this study, we also derive the relationships between the geometrical and flow characteristics of the parent and daughter tubes as well as the generalized scaling laws at the optimal conditions for the other essential parameters such as tube-wall stresses, length ratios, mean velocities, tube-volume, and surface-area of the tube distributing within the networks. We find that the fluid power-law index n does not influence the constrained tube-volume scaling at the optimal conditions; however, the scaling laws vary with n under the constrained tube’s surface area. These findings offer valuable design principles for developing efficient transport and flow systems.

Predicting the gravity-driven flow of power law fluids in a syringe: a rheological map for the IDDSI classification

Predicting the gravity-driven flow of power law fluids in a syringe: a rheological map for the IDDSI classification

More accurate solution of mixed convection radiative power law fluid flow over a stretching porous surface with presence of Forchheimer and chemical reaction

In hydraulic analysis, one of the most popular viscosity models for non-Newtonian fluids is the Power Law model. In shear-thinning and shear-thickening, the governing system of partial differential equations is transformed into a system of coupled highly non-linear ordinary differential equations. The effects of emerging parameters on velocities, temperature, and concentration as well as the engineering quantities (friction factor, Nusselt number, and Sherwood number) are presented in tables, graphs, and discussed. Most previous studies do not care about studying the effect of different parameters on stream velocity, and this is one of the advantages of our current study, which can be used by researchers in the future to make comparisons and verify the validity of the solutions. The higher accuracy of fifth-order FDM is tested by comparing it (in the Newtonian case) with previously published works and the results are in excellent agreement with these analytical and numerical works.

Hall and ion-slip current efficacy on thermal performance of magnetic power-law hybrid nanofluid using modified Fourier’s law

Magnetohydrodynamic free convection liquid considering Hall along with ion-slip current has many engineering usages. In addition, boundary layer flow of power-law fluids due to a stretching plane possesses sundry applications in biological sciences, geophysics, and petroleum industries. Further, hybrid nanofluids are important due to their high heat transfer capability. In view of such relevance, the goal of this investigation is to analyze Hall along with ion-slip effects on thermo-fluidic flow of magnetic power-law hybrid nanofluid so as to accomplish effective cooling in the desired thermal systems. Present investigation’s novelty is adding hybrid nanostructure to power-law fluid flow influenced by Hall and ion-slip mechanism and implementation of modified Fourier’s law featured with velocity and temperature gradients. The key results are that fluid velocity amplifies with rise in ion-slip and Hall parameters. Modified Prandtl numbers and Hall parameter ameliorate heat transfer rate while ion-slip parameter diminishes it.

A New Solution of Drag for Newtonian Fluid Droplets in a Power-Law Fluid

Understanding flow behaviors of multiple droplets in complex non-Newtonian fluids is crucial in many science and engineering applications. In this study, a new and improved analytical solution is developed based on the free surface cell model for the flow drag of swamp of Newtonian fluid drops through a power-law fluid. The developed solution is accurate and compares well to the numerical solutions. The improvement involves a new quantification of shear stress boundary condition at the interface and a more consistent approximation in linearizing the power-law fluid flow governing equation. The Newtonian fluid solutions can be reasonably used to linearize the flow governing equation. The approximation of the boundary conditions at the interface, however, has a major impact on the model prediction. The main improvement in the new solution is observed under the condition of comparable viscosities of the Newtonian drops and the outside power-law fluid when the results are sensitive to the interface boundary condition. Under the two extreme conditions of high viscosity ratio (approaching particles) and low ratio (approaching bubbles), the present and existing solutions converge.

Lattice boltzmann simulation of power-law fluids flow around a forced-oscillation circular cylinder

Direct numerical simulations of power-law non-Newtonian fluids flow around a circular cylinder are performed by lattice Boltzmann method coupled with immersed moving boundary scheme. Obvious differences in macroscopic hydrodynamics and wake vortex dynamics between shear-thinning and shear-thickening fluids are resolved. Results show that shear-thickening effect increased drag coefficient but decreased lift coefficient, and delayed separation of boundary layer leading to lower vortex shedding frequency. The position with lowest viscosity on surface of cylinder in shear-thinning fluid is closer to leading edge stagnation point than the position in shear-thickening fluid. Wake vortex appears from surface of cylinder in shear-thinning fluid, however appears after some distance away from rear end of cylinder in Newtonian and shear-thickening fluid through dynamic mode decomposition. Vortex shedding modes in shear-thinning and shear-thickening fluids are very different at high oscillation amplitudes and transited from Chaos to 2S mode (two single vortexes with opposite directions but same energy shed) or P + S mode (a pair of vortexes with opposite rotation direction shed on one side of the cylinder and a single vortex shed on the other side) when increasing power-law index.

Impact of magnetic induction on the flow of self-rewetting power-law fluid over a disk surface: Onset of Marangoni convection

In the present investigation, the onset of Marangoni convection in the flow of self-rewetting fluid over a stretching disk has been discussed. The self-rewetting fluid is considered to be electrically conducting and the flow problem is discussed under the influence of an induced magnetic field. The fluid flow is mainly induced due to two different mechanisms: (i) onset of Marangoni convection due to presence of temperature gradient along the liquid-gas interface and (ii) induction of magnetic field due to presence of an external magnetic field, which modifies the original field. The governing partial differential equations are written, following Navier-stokes equations and Prandtl boundary layer equation. With the use of similarity transformations, the governing equations are turned into a system of ordinary differential equations. Nonlinear systems of ordinary differential equations are solved by the bvp4c technique. The reciprocal of the magnetic Prandtl number diminishes the induced magnetic profile.

Influence of Permeability and Shear-Thinning Behavior on the Hydrodynamics Flow Features Around Porous Square Cylinders

Abstract This article investigates the laminar flow of power-law fluids through two porous square cylinders in a side-by-side configuration. The effects of power-law index (n), Darcy number (Da), and gap ratio (g/W) are examined within ranges of g/W = 0.5–5, n = 0.4–0.8, and Da = 10−6–10−2, respectively. Two flow conditions are considered: first, for a creeping flow (unseparated flow) at Re = 1 where Darcy's law is applicable; second, for a viscous dominant flow at Re = 100, where Darcy–Forchheimer-extended model is exercised. Flow patterns behind the porous cylinders are analyzed using streamlines, velocity profiles, pressure distribution curves, and vorticity structural parameters (Г). In low permeability levels, the flow exhibits an irregular nonperiodic vortex shedding characterized by a single large vortex street far off the downstream for g/W = 0.5. However, synchronized wake patterns were observed in either antiphase or in-phase modes for higher gap ratios. Leading-edge separation with two-side recirculation induces quasi-periodicity in the flow for all g/W. It was found that increasing the permeability can prevent the leading edge separation. Additionally, a transition from antiphase to in-phase mode occurs when the permeability is altered while maintaining constant flow-time. The presence of a jet-like flow between cylinders significantly impacts unsteady wake patterns. The impact of g/W, power-law index, and permeability on drag is also examined. A jump in some flow parameters was observed at higher Re for the midrange Darcy number, but no such increase was noted for the high shear-thinning behavior. These findings provide a potential approach for improving the design of fluidic systems involving porous cylinders.

Effect of topographical pattern on vortex shedding and heat transfer phenomena in power-law fluid flow around a rotating cylinder

The present numerical investigation studies the momentum and heat transfer phenomena from a heated rotating patterned cylinder in the vortex shedding regime. In particular, the effect of surface patterns ( ω , δ ), fluid behavior ( 0.4 ≤ n ≤ 1.6 ), cylinder rotation speed ( 0.5 ≤ α ≤ 2 ), and Prandtl number ( 1 ≤ Pr ≤ 100 ) at Reynolds number 100 on the force coefficients and Nusselt number are studied. Vorticity and isotherm profiles demonstrate the flow dynamics and heat transfer characteristics. According to the findings of this study, the formation of the vortex (including its size, shape, and number of vortices) and the time period during which the vortex shedding pattern repeats itself demonstrates a dependency on the shape of the cylinder, fluid behavior, and rotating speed. It has been noted that a significant decrease in the frequency of vortex shedding occurs on adding topographical patterns. Additionally, it has been noticed that on increasing rotational speed, vortex shedding can be suppressed for all fluid behaviors. Numerical simulation results reveal that the average drag coefficient ( C ¯ D ) for a rotating patterned cylinder decreases with increasing rotational speed ( α ), and it further reduces on increase in pattern frequency ( ω ) and amplitude ( δ ) compared to a smooth circular cylinder. The shear-thinning fluid behavior helps to dissipate the heat from the cylinder to the surrounding fluid. Conversely, shear-thickening fluid behavior exhibits the opposite trend.

Pulsating non-Newtonian heat and fluid flow in a concentric annular duct: An analysis using perturbation series method

In the current study, an analytical analysis is conducted to examine laminar pulsating flow and heat transfer of power-law fluid in a concentric annular channel that is uniformly heated. The momentum and energy balance equations are solved analytically using the perturbation series method under the assumption that fully developed hydrodynamic and thermal conditions exist. Nondimensional frequency and amplitude effects on periodic and period-averaged friction factor and Nusselt number are obtained for various power-law index values, representing pseudoplastic, Newtonian, and dilatant fluids. The results from the present study are compared to those from the literature for some specific cases, and an excellent agreement is observed.