Fluid Model Research Articles

Spherical Penetration Grouting Model for Bingham Fluids Considering Gravity and Time-Varying Slurry Viscosity

Spherical Penetration Grouting Model for Bingham Fluids Considering Gravity and Time-Varying Slurry Viscosity

Influence of plasma-chemical processes on the parameters of an atmospheric pressure Helium microdischarge.

This study investigates the influence of plasma-chemical processes on the parameters of an atmospheric pressure (AP) Helium microdischarge. Using a one-dimensional fluid model with both Maxwellian and non-Maxwellian electron energy distribution function (EEDF), we analyze the spatial profile of plasma parameters in a microdischarge with a 0.2mm gap. There are significant differences in the recorded rate coefficients for dissociative recombination (DR) and three-body recombination (TR), which are essential for determining the densities of excited atoms and molecules in the high-pressure plasma, where the balance of charged particles is determined by volume recombination. A careful examination of the relevant literature reveals these contradictions. In order to adequately represent the main channels of creation and destruction of excited and charged particles, it is necessary to take into account the atomic states of Helium up to the quantum level n=4. The full set of plasma-chemical reactions includes elastic electron collisions, excitation and de-excitation by electrons and atoms, direct and stepwise ionization, associative ionization, molecular excimer creation and destruction, ion conversion, recombination, and radiation. The results reveal that the selected rate coefficients and EEDF form significantly influence the simulation outcomes. This highlights the need to develop improved theoretical models to enhance the control and use of plasma technologies.

Prediction model and real-time diagnostics of hydraulic fracturing pressure for highly deviated wells in deep oil and gas reservoirs

It is a common occurrence in the fracture processes of deep carbonate reservoirs that the fracturing construction pressure during hydraulic fracturing operation exceeds 80 MPa. The maximum pumping pressure is determined by the rated pressure of the pumping pipe equipment and the reservoir characteristics, which confine the fracture to the target area. When the pump pressure exceeds the safety limit, hydraulic fracturing has to reduce the construction displacement to prevent potential accidents caused by overpressure. Therefore, real-time prediction of the fracturing construction pressure and diagnosis of abnormal fluctuations during hydraulic fracturing of highly deviated wells are indispensable. Based on the well trajectory, pumping process, and string structure of highly deviated wells, a movement interface model for the fracturing fluid at different stages within the wellbore has been established, using the method of computational fluid dynamics. This model analyzes the fluid movement behavior with diverse properties at various fracturing times and determines the relationship between the pressure changes at the leading and trailing edges of fluid movement in each section of the wellbore over time by combining different string structures and preset pumping procedures. The frictional pressure within the wellbore fluid, the hydrostatic fluid pressure, and the near-well friction drags have been calculated and predicted. A real-time prediction model for diagnosing pumping fracturing has been constructed to further comprehend “abnormal” fracturing construction pressures in highly deviated wells. This offers a theoretical foundation for the correct diagnosis and decision-making regarding hydraulic fracturing in highly deviated wells while guiding its smooth implementation in real time.

Penetration of ionization wave through dielectric microhole in atmospheric pulsed discharges

Microstructure-enhanced discharges are critical for achieving higher plasma electron density and energy, offering significant potential in advanced plasma applications. A two-dimensional fluid model of pulsed dielectric barrier discharge was developed in atmospheric helium with a dielectric microhole. Two distinct high-electron-density regions, the T-region and L-region, were identified, driven, respectively, by transverse and longitudinal electric fields as the ionization wave traversed the microhole. The axisymmetric T-region is approached and squeezed as the radius decreases, in which the discharge intensity and electron density are enhanced. Based on the electron reaction source item, a virtual electrode is proposed in the dielectric microhole, which segregates the T- and L-regions. The width of the virtual electrode decreases with the microhole radius, and the virtual electrode extinguishes with the discharge ignition in the lower chamber and the formation of ionization wave in the dielectric microhole. These findings offer insights into plasma behavior in microstructures for advanced applications.

Hybrid molecular-scale and continuum modeling of two-dimensional flow between inhomogeneous solid surfaces and its application to the thrust bearing.

The flow equations are derived for describing the two-dimensional hybrid molecular-scale and continuum flows in the very small surface separation with inhomogeneous solid surfaces and they can be applied for designing the specific bearings. The aim of the present study is to solve this specific flow problem in engineering with normal computational cost. The flow factor approach model describes the flow of the molecule layer adjacent to the solid surface and the Newtonian fluid model describes the flow of the intermediate continuum fluid. By using these flow equations, the simulation results show that designing the inhomogeneous stationary surface can very significantly improve the load-carrying capacity of the hydrodynamic thrust bearing with low clearances. The flow of the physically adsorbed layer is treated as non-continuum and it is modeled by the equivalent non-continuum flow model by considering the fluid molecules orientated normal to the solid surface. The fluid between the two adsorbed layers is treated as continuum and Newtonian. The slippage can occur between the adsorbed layer-solid surface interface. It is assumed as absent on the adsorbed layer-continuum fluid interface. The flow equations are derived according to the equilibrium of the momentum transfer in the surface clearance. The film pressures and carried load of the thrust bearing with low clearance and inhomogeneous surfaces are derived by applying the obtained flow equations.

Numerical Analysis of Heat Transfer and Flow Characteristics of Jeffrey Nanofluid Over Stretched Surfaces With MHD and Slip Effects

ABSTRACTThis study employs the Jeffrey fluid model to investigate stress relaxation in non‐Newtonian fluids, offering a more precise representation than conventional viscous models. It explores the influence of multiple slip conditions and magnetohydrodynamics (MHD) on Jeffrey fluid flow and heat transfer across irregular surfaces. Additionally, the impact of thermal radiation and internal heat sources on heat transfer is examined, essential for a comprehensive understanding of the system's thermal dynamics. Using the Buongiorno model, the diffusion and thermophoresis of nanoparticles within the flow are analyzed. Nonlinear coupled governing equations covering flow dynamics, heat transfer, and nanoparticle transport are transformed into ordinary differential equations (ODEs) through similarity transformations and solved numerically using the Runge–Kutta fourth‐order (RK4) method combined with shooting techniques. Results indicate significant effects of physical parameters on temperature, velocity, and mass profiles: a 20% decrease in temperature profiles with an increase in the dimensionless thermal slip coefficient from 0.1 to 0.5 and a 15% reduction in velocity profiles from a 0.1 unit increase in the magnetic parameter . The study also quantifies mass and heat transfer rates to elucidate their impacts. These findings have profound implications for engineering applications involving non‐Newtonian and nanofluids in complex geometrical configurations.

Stabilization of loosely coupled schemes for 0D–3D fluid–structure interaction problems with application to cardiovascular modelling

Abstract In this paper we analyze the numerical oscillations affecting loosely coupled schemes for hybrid-dimensional 0D–3D fluid–structure interaction (FSI) problems, which arise e.g. in the field of cardiovascular modeling, and we propose a novel stabilized scheme that cures this issue. We study several loosely coupled schemes, including the Dirichlet–Neumann (DN) and Neumann–Dirichlet (ND) schemes. In the first one, the 0D fluid model prescribes the pressure to the 3D structural mechanics model and receives the flow. In the second one, on the contrary, the fluid model receives the pressure and prescribes the flow. The terms DN and ND, employed in the FSI literature, are borrowed from domain decomposition methods, although here a single iteration is performed before moving on to the next time step (that is, the coupling is treated explicitly). Should the fluid be enclosed in a cavity, the DN scheme is affected by non-physical oscillations whose origin lies in the balloon dilemma, for which we provide an algebraic interpretation. Moreover, we show that also the ND scheme can be unstable for a range of parameter choices. Surprisingly, increasing either the viscous dissipation or the inertia of the structure favours the onset of oscillations and, for certain parameter choices, the ND is unconditionally unstable. In the presence of inertial terms, by reducing the time step size below a certain threshold, the amplitude of the numerical oscillations is even amplified. We provide an explanation for these facts and establish sharp stability bounds on the time step size. Our analysis extends to Robin–Robin schemes, based on linear combinations of the conditions of pressure continuity and either volume or flux continuity. While appropriate choices of Robin coefficients can achieve numerical stability, tuning these coefficients can be challenging in practice. To address these issues, we propose a numerically consistent stabilization term for the Neumann–Dirichlet scheme, inspired by physical insight on the onset of oscillations. We prove that our proposed stabilized scheme is absolutely stable for any choice of time step size. Notably, the proposed scheme does not require parameter tuning. These results are verified by several numerical tests. Finally, we apply the proposed stabilized scheme to an important problem in cardiac electromechanics, namely the coupling between a 3D cardiac model and a closed-loop lumped-parameter model of blood circulation. In this setting, our proposed scheme successfully removes the non-physical oscillations that would otherwise affect the numerical solution.

Data-Driven Identification of Variational Equations for Vortex-Induced Vibration Systems

Abstract In this study, a data-driven approach using the embedded variational principle is used to identify the variational equations of vortex-induced vibration fluid–structure interaction systems, in particular the coupling term and the aerodynamic damping term. Under the data-driven paradigm, variational equation identification is primarily accomplished through five steps: collecting discrete data, setting variational functions, building the product function, solving linear equations, and evaluating errors. The explicit variational equations of the system are eventually determined automatically from the excitation and response. Gaussian white noise is added to the excitation to evaluate the method's noise robustness. The findings demonstrate that numerical estimation which stays away from higher-order derivatives significantly enhances the variational law identification's noise robustness by taking advantage of the variational law's lower-order time derivatives. Furthermore, the arbitrariness of the variational setting inherent in the variational law significantly improves the effectiveness of data utilization and lowers the necessary data volume. In addition, a system of linear equations is solved by identifying connected nonlinear equations, which significantly increases modeling efficiency. The basis for engineering modeling, optimization, and control of intricate fluid–structure interaction systems are provided by these benefits.

Game-Theoretic Analysis of a Fluid Queue with Markovian Vacations and an N-Policy

Game-Theoretic Analysis of a Fluid Queue with Markovian Vacations and an N-Policy

Optimizing bioconvective heat transfer with MHD Eyring–Powell nanofluids containing motile microorganisms with viscosity variability and porous media in ciliated microchannels

Purpose This paper aims to optimize bioconvective heat transfer for magnetohydrodynamics Eyring–Powell nanofluids containing motile microorganisms with variable viscosity and porous media in ciliated microchannels. Design/methodology/approach The flow problem is first modeled in the two-dimensional frame and then simplified under low Reynolds number and long wavelength approximations. The numerical method is used to examine the impact of thermal radiation, temperature-dependent viscosity, mixed convection, magnetic fields, Ohmic heating and porous media for velocity, temperature, concentration and motile microorganisms. Graphical results are presented to observe the impact of physical parameters on pressure rise, pressure gradient and streamlines. Findings It is observed that the temperature of nanofluid decreases with higher values of the viscosity parameter. It is absolutely in accordance with the physical expectation as the radiation parameter increases, the heat transfer rate at the boundary decreases. Nanoparticle concentration increases by increasing the values of bioconvection Rayleigh number. The density of motile microorganisms decreases when bioconvection Peclet number is increased. The velocity of the nanofluid decreases with higher value of Darcy number. With increase in the value of bioconvection parameter, the flow of nanofluid is increased. Originality/value The bioconvective peristaltic movement of magnetohydrodynamic nanofluid in ciliated media is proposed. The non-Newtonian behavior of the fluid is described by using an Eyring–Powell fluid model.

Supercritical Crossover Lines in the Cell Fluid Model

The cell fluid model with a modified Morse potential is studied. The supercritical states are considered with respect to the possibility of the construction of a separation boundary between liquid-like and gas-like behaviors. We will calculate three different lines that can be used for this purpose: the loci of the isothermal compressibility maxima, the loci of the thermal expansion coefficient maxima, and the line, where the effective chemical potential is zero, M = 0. By the symmetry of the functionals for the partition functions, the condition M = 0 in fluids is analogous to the absence of an external field in the Ising model.

3D fluid simulation of the propagation of a nanosecond discharge in air above a liquid surface: investigation of the pattern formation under various conditions and comparison with experiments

Abstract Plasma-liquid interaction remains one of the fundamental processes influencing the various applications. Understanding the influence of external parameters on discharge properties, particularly the discharge dynamic at the liquid surface, is therefore essential. In previous studies, we investigated the impact of voltage polarity, gap distance, and liquid dielectric permittivity and electrical conductivity on nanosecond discharges initiated in air at atmospheric pressure in a pin-to-liquid configuration. Herein, we present a 3D fluid model, improved with stochastic photoionization, to simulate the discharge dynamics under the previously mentioned conditions. The model outputs are compared with the discharge dynamics measured experimentally. For instance, filamentation and the homogeneous emission over solution’s surface measured in positive and negative discharges, respectively, are well reproduced by the simulation. Furthermore, the simulation allowed us to report other plasma properties not accessible experimentally such as the spatio-temporal distributions of electric field (E-field) and electron density. Notably, we observe that the E-field at the front of the negative surface ionization wave (SIW) is nearly four times lower than that of the positive SIW, which may explain the absence of filaments for negative discharges. Furthermore, we find that increasing solution conductivity or gap distance reduce the radial propagation velocity of the circular SIW front and stopping its expansion before a destabilization can occur. The simulation allowed investigating the influence of photoionization strength, and we find that increasing the number of ionizing photons leads to supress the filamentation while keeping the ionization front circular and propagating at high speed.

Rheology of Bingham viscoplastic flow triggered by a rotating and radially stretching disk

Purpose This study aims to investigate the flow and heat transfer characteristics of a Bingham viscoplastic fluid subjected to the combined effects of axial rotation and radial stretching of a circular disk. Building upon existing models for Bingham fluids on stationary walls, we extend the formulation to incorporate the effects of a linearly stretching disk using von Kármán similarity transformations. Design/methodology/approach The resulting system of nonlinear ordinary differential equations is solved to characterize the flow and thermal fields. Three dimensionless parameters govern the momentum layer: a swirling number capturing the balance between rotation and stretching, a Bingham number characterizing the fluid’s yield stress and a modified Reynolds number incorporating the disk stretching. The Prandtl number controls the thermal response. Findings For purely stretching flows, a two-dimensional flow structure emerges. However, the introduction of rotation induces three-dimensional flow behavior. Unlike previous studies suggesting that moderate Bingham numbers are sufficient for non-Newtonian effects on purely revolving disks, the findings indicate that significantly higher yield stresses are required to observe non-Newtonian characteristics under radial stretching conditions. This difference can be attributed to the enhancing influence of wall movement on the fluid dynamics. At high Bingham numbers, a two-layer flow structure develops, comprising an unyielded plug region above the disk and a yielded shear layer adjacent to the wall. The von Kármán viscous pump mechanism drives the Bingham flow within this regime. Originality/value Physical quantities such as drag force due to wall shear stress, torque resulting from tangential shear stress and Nusselt number are extracted from the quantitative data.

A Pore-Scale Investigation of Oil Contaminant Remediation in Soil: A Comparative Study of Surfactant- and Polymer-Enhanced Flushing Agents

Pore-scale remediation investigation of oil-contaminated soil is important in several environmental and industrial applications, such as quick responses to sudden accidents. This work aims to investigate the oil pollutant removal process and optimize the oil-contaminated soil remediation performance at the pore scale to find the underlying mechanisms for oil removal from soil. The conservative forms of the phase-field model and the non-Newtonian power-law fluid model are employed to track the moving interface between two immiscible phases, and oil pollutant flushing removal process from soil pores is investigated. The effects of viscosity, interfacial tension, wettability, and flushing velocity on pore-scale oil pollutant removal regularity are explored. Then, the oil pollutant removal effects of two flushing agents (surfactant system and surfactant–polymer system) are compared using an oil content prediction curve based on UV-Visible transmittance. The results show that the optimal removal efficiency is obtained for a weak water-wetting system with a contact angle of 60° due to the stronger two-phase fluid interaction, deeper penetration, and more effective entrainment flow. On the basis of the dimensionless analysis, a relatively larger flushing velocity, resulting in a higher capillary number (Ca) in a certain range, can achieve rapid and efficient oil removal. In addition, an appropriately low interfacial tension, rather than ultra-low interfacial intension, contributes to strengthening the oil removal behavior. A reasonably high viscosity ratio (M) with a weak water-wetting state plays synergetic roles in the process of oil removal from the contaminated soil. In addition, the flushing agent combined with a surfactant and polymer can remarkably enhance the oil removal efficiency compared to the sole use of the surfactant, achieving a 2.5-fold increase in oil removal efficiency. This work provides new insights into the often-overlooked roles of the pore scale in fluid dynamics behind the remediation of oil-contaminated soil via flushing agent injection, which is of fundamental importance to the development of effective response strategies for soil contamination.

Viscoelastic wetting transition: beyond lubrication theory

Abstract The dip-coating geometry, where a solid plate is withdrawn from or plunged into a liquid pool, offers a prototypical example of wetting flows involving contact-line motion. Such flows are commonly studied using the lubrication approximation approach which is intrinsically limited to small interface slopes and thus small contact angles. Flows for arbitrary contact angles, however, can be studied using a generalized lubrication theory that builds upon viscous corner flow solutions. Here we derive this generalized lubrication theory for viscoelastic liquids that exhibit normal stress effects and are modelled using the second-order fluid model. We apply our theory to advancing and receding contact lines in the dip-coating geometry, highlighting the influence of viscoelastic normal stresses for contact line motion at arbitrary contact angle.

Impacts of variable magnetic field on ternary Casson nanofluid flow through ciliated arterial walls incorporating interfacial nanolayer

ABSTRACT The current investigation explores tri-hybrid mediated blood flow through a ciliary annular model, designed to emulate an endoscopic environment. The human circulatory system, driven by the metachronal ciliary waves, is examined in this study to understand how ternary nanoparticles influence wave-like flow dynamics in the presence of interfacial nanolayers. We also analyze the effect of an induced magnetic field on Ag–Cu– A l 2 O 3 /blood flow within the annulus, focusing on thermal radiation, heat sources, buoyancy forces and ciliary motion. The Casson fluid model characterizes the non-Newtonian viscous properties of the biofluid. To describe the steady fluid flow mathematically, we use coupled partial differential equations and apply the homotopy perturbation method to derive rapidly convergent series solutions for the non-linear flow equations. The obtained hemodynamic consequences are graphically represented with the variations of emerging parameters. These are significantly influenced by the rheological factors of the nanofluid flow, improving flow velocity with changes in shear viscosity, while a decrease in flow is observed for intensified Lorentz forces. Ciliary motion accelerates the expansion of the induced magnetic field on nanolayers, while a higher Magnetic Reynolds number decreases the current density distribution. Increased radiative heat generation lowers the temperature, indicating that thermal radiation enhances heat transfer and improves cooling efficiency. In contrast, an increased ciliary length along the wall raises the temperature due to wave-like motion, which strengthens the thermal boundary layer in the fluid flow. Additionally, a higher nanoparticle concentration increases wall shear stress due to frictional forces, while enhanced magnetic forces decrease the shear stress along the ciliary wall. Furthermore, a higher Strommer’s number may regulate the formation of blood boluses in the wavy flow. The key findings play an important role in the development of analytical benchmarks to validate computational methods, ensuring accuracy in clinical research tools and supporting reliable medical applications.

Relativistic reconnection with effective resistivity

Context. Relativistic magnetic reconnection is one of the most fundamental mechanisms that is considered responsible for the acceleration of relativistic particles in astrophysical jets and magnetospheres of compact objects. Understanding the properties of the dissipation of magnetic fields and the formation of non-ideal electric fields is of paramount importance to quantify the efficiency of reconnection at energizing charged particles. Aims. Recent results from particle-in-cell (PIC) simulations suggest that the fundamental properties of how magnetic fields dissipate in a current sheet might be captured by an “effective resistivity” formulation, which would locally enhance the amount of magnetic energy dissipated and favor the onset of fast reconnection. Our goal is to assess this ansatz quantitatively by comparing fluid models of magnetic reconnection with a non-constant magnetic diffusivity and fully kinetic models. Methods. We performed 2D resistive relativistic magnetohydrodynamic (ResRMHD) simulations of magnetic reconnection combined to PIC simulations using the same initial conditions (i.e., a Harris current sheet). We explored the impact of crucial parameters such as the plasma magnetization, its mass density, the grid resolution, and the characteristic plasma skin depth. Results. Our ResRMHD models with effective resistivity are able to quantitatively reproduce the dynamics of fully kinetic models of relativistic magnetic reconnection. In particular, they lead to reconnection rates consistent with PIC simulations, whereas for constant-resistivity fluid models, the reconnection dynamics is generally ten times slower. Even at modest resolutions, adopting an effective resistivity can qualitatively capture the properties of kinetic reconnection models and produce reconnection rates compatible with collisionless models (i.e., on the order of ∼10−1).

A flexible parameterization to test early physics solutions to the Hubble tension with future CMB data

One approach to reconciling local measurements of a high expansion rate with observations of acoustic oscillations in the CMB and galaxy clustering (the “Hubble tension”) is to introduce additional contributions to the ΛCDM model that are relevant before recombination. While numerous possibilities exist, none are currently well-motivated or preferred by data. However, future CMB experiments, which will measure acoustic peaks to much smaller scales and resolve polarization signals with higher signal-to-noise ratio over large sky areas, should detect almost any such modification at high significance.We propose a method to capture most relevant possible deviations from ΛCDM due to additional non-interacting components, while remaining sufficiently constraining to enable detection across various scenarios. The phenomenological model uses a fluid model with four parameters governing additional density contributions that peak at different redshifts, and two sound speed parameters. We forecast possible constraints with Simons Observatory, explore parameter degeneracies that arise in ΛCDM, and demonstrate that this method could detect a range of specific models. Which of the new parameters gets excited can give hints about the nature of any new physics, while the generality of the model allows for testing with future data in a way that should not be plagued by a posteriori choices and would reduce publication bias.When testing our model with Planck data, we find good consistency with the ΛCDM model, but the data also allows for a large Hubble parameter, especially if the sound speed of an additional component is not too different from that of radiation. The analysis with Planck data reveals significant volume effects, requiring careful interpretation of results. We demonstrate that Simons Observatory data will mitigate these volume effects, so that any indicated solution to the Hubble tension using our model cannot be mimicked by volume effects alone, given the significance of the tension.

A time-domain finite element formulation of the equivalent fluid model for the acoustic wave equation

Sound-absorptive materials such as foam can be described by the equivalent fluid (EF) model. The homogenized fluid’s acoustic behavior is thereby described by complex-valued, frequency-dependent acoustic material parameters. When transforming the acoustic wave equation for the EF model from the frequency domain to the time domain, convolution integrals arise. The auxiliary differential equation (ADE) method is used to circumvent the direct calculation of these convolution integrals. The wave equation and the coupled set of ordinary ADEs are solved in the time domain using the finite element (FE) method. The approach relies on approximating the complex-valued frequency response functions of the inverse equivalent bulk modulus and density by a sum of rational functions consisting of real and complex poles. The order of the rational function approximation defines the number of additionally introduced auxiliary variables per nodal degree of freedom. The presented FE formulation includes a narrow-band non-reflecting boundary condition (NRBC) for normal incidence. The implementation in openCFS shows optimal temporal and spatial convergence for a semi-infinite duct based on the analytic plane wave solution for harmonic excitation. The simulation of a pressure pulse propagating in an infinite EF domain with a scatterer demonstrates the capability for multidimensional, actual transient problems.

Analysis of thermal transport and wall stresses for MHD peristaltic motion of Reiner‐Philippoff fluid with viscous dissipation and mixed convection effects

AbstractThe present study examines the thermal characteristics and stresses at the boundary for peristaltic motion of Reiner‐Philippoff fluid through a symmetric channel. The Reiner‐Philippoff (R‐P) fluid model is widely recognized for its ability to provide a comprehensive representation of the unique properties exhibited by non‐Newtonian fluids. One notable aspect that initiates this model is the nonlinear relationship between velocity gradient and shear stress. Moreover, this model captures the implicit connection between deformation rate and stress. Additionally, the R‐P fluid model exhibits distinct characteristics, acting as a dilatant fluid for , exhibiting pseudoplastic behavior for , and behaving as a Newtonian fluid when . Governing equations are mathematically modeled under the consideration of mixed convection, viscous dissipation, magnetic field, and Joule heating effects. Long wavelength and small Reynolds number approximations are used to simplify the system. To compute the numerical solution of the simplified nonlinear system, BVP4c technique is employed via MATLAB. The influences of key parameters on Reiner‐Philippoff fluid flow are physically visualized through graphs. A detailed analysis of heat transfer for dilatant, pseudoplastic, and Newtonian fluids is also provided. Additionally, numerical assessments of heat transfer and stresses at the wall are presented via tables. Outcomes reveal that the temperature profile decreases due to R‐P fluid parameter and Bingham number. The findings for the pseudoplastic case indicate that both the enhanced Grashof and Hartmann numbers lead to an increase in the temperature profile. Tabular results indicate that rate of thermal transfer is improved by developing values of Grashof and Brinkman numbers, while stresses at the wall exhibit the opposite behavior. Additionally, the wall stresses decrease with greater values of R‐P fluid parameter and the Bingham number. Furthermore, dilatant fluid is more effective for improving thermal transfer and reducing stresses at the wall compared to Newtonian and pseudoplastic fluids.