Search Results (38)

The electroosmotic flow (EOF) of non-Newtonian fluids plays a significant role in microfluidic systems. The EOF of Powell–Eyring fluid within a parallel-plate microchannel, under the influence of both electric field and pressure gradient, is investigated. Navier’s boundary condition is adopted. The velocity distribution’s approximate solution is derived via the homotopy perturbation technique (HPM). Optimized initial guesses enable accurate second-order approximations, dramatically lowering computational complexity. The numerical solution is acquired via the modified spectral local linearization method (SLLM), exhibiting both high accuracy and computational efficiency. Visualizations reveal how the pressure gradient/electric field, the electric double layer (EDL) width, and slip length affect velocity. The ratio of pressure gradient to electric field exhibits a nonlinear modulating effect on the velocity. The EDL is a nanoscale charge layer at solid–liquid interfaces. A thinner EDL thickness diminishes the slip flow phenomenon. The shear-thinning characteristics of the Powell–Eyring fluid are particularly pronounced in the central region under high pressure gradients and in the boundary layer region when wall slip is present. These findings establish a theoretical base for the development of microfluidic devices and the improvement of pharmaceutical carrier strategies. Full article

This work aims to explore the magnetohydrodynamic mixed convection boundary layer flow (MHD-MCBLF) on a slanted extending cylinder using Eyring–Powell fluid in combination with Levenberg–Marquardt algorithm–artificial neural networks (LMA-ANNs). The thermal properties include thermal stratification, which has a higher temperature surface on the cylinder than on the surrounding fluid. The mathematical model incorporates essential factors involving mixed conventions, thermal layers, heat absorption/generation, geometry curvature, fluid properties, magnetic field intensity, and Prandtl number. Partial differential equations govern the process and are transformed into coupled nonlinear ordinary differential equations with proper changes of variables. Datasets are generated for two cases: a flat plate (zero curving) and a cylinder (non-zero curving). The applicability of the LMA-ANN solver is presented by solving the MHD-MCBLF problem using regression analysis, mean squared error evaluation, histograms, and gradient analysis. It presents an affordable computational tool for predicting multicomponent reactive and non-reactive thermofluid phase interactions. This study introduces an application of Levenberg–Marquardt algorithm-based artificial neural networks (LMA-ANNs) to solve complex magnetohydrodynamic mixed convection boundary layer flows of Eyring–Powell fluids over inclined stretching cylinders. This approach efficiently approximates solutions to the transformed nonlinear differential equations, demonstrating high accuracy and reduced computational effort. Such advancements are particularly beneficial in industries like polymer processing, biomedical engineering, and thermal management systems, where modeling non-Newtonian fluid behaviors is crucial. Full article

Highlighting the importance of artificial intelligence and machine learning approaches in engineering and fluid mechanics problems, especially in heat transfer applications is main goal of the presented article. With the advancement in Artificial Intelligence (AI) and Machine Learning (ML) techniques, the computational efficiency and accuracy of numerical results are enhanced. The theme of the study is to use machine learning techniques to examine the thermal analysis of MHD boundary layer flow of Eyring-Powell Hybrid Nanofluid (EPHNFs) passing a horizontal cylinder embedded in a porous medium with heat source/sink and viscous dissipation effects. The considered base fluid is water ($H_{2}O$) and hybrid nanoparticles titanium oxide (${TiO}_2$) and Copper oxide ($CuO$). The governing flow equations are nonlinear PDEs. Non-similar system of PDEs are obtained with efficient conversion variables. The dimensionless PDEs are truncated using a local non-similarity approach up to third level and numerical solution is evaluated using MATLAB built-in-function bvp4c. Artificial Neural Networks (ANNs) simulation approach is used to trained the networks to predict the solution behavior. Thermal boundary layer improves with the enhancement in the value of $Rd$. The accuracy and reliability of ANNs predicted solution is addressed with computation of correlation index and residual analysis. The RMSE is evaluated [0.04892, 0.0007597, 0.0007596, 0.01546, 0.008871, 0.01686] for various scenarios. It is observed that when concentration of hybrid nanoparticles increases then thermal characteristics of the Eyring-Powell Hybrid Nanofluid (EPHNFs) passing a horizontal cylinder. Full article

The roll coating method is of considerable significance in several industries, as it is applied practically in the production of paint, the manufacturing of PVC-coated cloth, and the plastic industry. The current study theoretically and computationally analyses the Powell–Eyring fluids with variable viscosity during the non-isothermal roll-over web phenomenon. Based on the lubrication approximation theory (LAT), the problem was formulated. The system of partial differential equations (PDEs) obtained from the mathematical modeling was further simplified to a set of ordinary differential equations (ODEs) using suitable transformations. A regular perturbation method was implemented to obtain the solution in terms of velocity, pressure gradient, pressure, and flow rate per unit width. This study also captures important engineering characteristics such as coating thickness, Nusselt number, shear stress, roll/sheet separating force, and roll-transmitted power to the fluid. Along with a comparison between the present work and published work, both graphical and tabular representations wer made to study the effects of various factors. It was observed that the velocity profile is the decreasing function of non-Newtonian and Reynold viscosity parameters. In addition, the response surface methodology (RSM) was employed to investigate the sensitivity of the shear stress and the Nusselt number. Full article

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 ($Rd$). 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 $f^{\prime }\left(\eta \right)$, $\theta \left(\eta \right),$ and $\varphi \left(\eta \right)$ satisfy the boundary conditions asymptotically for Scenarios 1–7 with LMS-BPNN. The dual solutions for flow performance outcomes (${Cf}_x$, ${Nu}_x$, 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., ${\lambda }_c=-1.06329,-1.097,-1.17694$. 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. Full article

In the field of heat and mass transfer applications, non-Newtonian fluids are potentially considered to play a very important role. This study examines the magnetohydrodynamic (MHD) bioconvective Eyring–Powell fluid flow on a permeable cone and plate, considering the viscous dissipation (0.3 ≤ E_c ≤0.7), the uniform heat source/sink (−0.1 ≤ Q₀ ≤ 0.1), and the activation energy (−1 ≤ E₁ ≤ 1). The primary focus of this study is to examine how MHD and porosity impact heat and mass transfer in a fluid with microorganisms. A similarity transformation (ST) changes the nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs). The Keller Box (KB) finite difference method solves these equations. Our findings demonstrate that adding MHD (0.5 ≤ M ≤ 0.9) and porosity (0.3 ≤ Γ ≤ 0.7) effects improves microbial diffusion, boosting the rates of mass and heat transfer. Our comparison of our findings to prior studies shows that they are reliable. Full article

Nanomaterials have been the focus of intense study and growth in the modern era across the globe because of their outstanding qualities, which are brought about by their nanoscale size; for instance, increased adsorption and catalysis capabilities plus significant reactivity. Multiple investigations have verified the fact that nanoparticles may successfully remove a variety of pollutants from water, and, as a result, they have been utilized in the treatment of both water and wastewater. Therefore, the current research intent is to examine the nonlinear heat source/sink influence on the 3D flow of water-based silver nanoparticles incorporated in an Eyring–Powell fluid across a deformable sheet with concentration pollutants. Silver particles have been used intensively to filter water, due to their potent antibacterial properties. The leading equations involving partial differential equations are renewed into the form of ordinary ordinary differential equations through utilizing the appropriate similarity technique. Then, these converted equations are solved by utilizing an efficient solver bvp4c. Visual displays and extensive exploration of the different impacts of the non-dimensional parameters on the concentration, temperature, and velocity profiles are provided. Also, the important engineering variables including skin friction, the rate of heat, and mass transfer are examined. The findings suggest that the mass transfer rate declines due to pollutant parameters. Also, the results suggest that the friction factor is uplifted by about 15% and that the heat transfer rate, as well as the mass transfer rate, declines by about 21%, due to the presence of the nanoparticle volume fraction. We believe that these results may improve the flow rate of nanofluid systems, improve heat transfer, and reduce pollutant dispersal. Full article

Problem statement: The study offers theoretical formulations for high-viscosity particulate flows in inclined reservoirs, taking into account the presence of homogeneous spheroidal particles of various types to produce discrete two-phase suspensions. Purpose: The primary objective of this analytical and comparative study is to identify the most dependable nanoparticles among hafnium and crystal metals that are suspended in an Eyring–Powell fluid through an inclined channel while being subjected to external magnetic and gravitational forces. Solution methodology: The flow dynamics of multiphase flows are formulated utilizing the stress tensor of the base fluid. The regular perturbation method (RPM) is employed to attain a more closed-form solution. The perturbation method is frequently employed in engineering problems to obtain an approximated solution, even when demonstrating the convergence of the solution is challenging. The rough solution is also validated through a thorough parametric analysis that shows the role of relevant parameters that contribute to the multiphase flow. Results: A concise parametric study is carried out against some of the most pertinent parameters and reveals that additional particles have promising effects on the momentum of each multiphase flow, whereas Eyring–Powell multiphase suspensions lessen in momentum due to strong internal viscous forces. The velocity of fluid and particle phases diminish with Hartmann number M and Froude number Fr. The second-order material constant B and concentration of nanoparticles C boost the motion of the fluid. The velocities of the particulate phase are quicker than the fluid phase. The hafnium particle is more reliable than crystal particles. Solution benchmark: Numerical and graphical findings have also been compared with the existing literature for the limiting case and found to be fully in agreement. Applications: This study’s findings provide a wider understanding of subterranean flows, specifically within the petroleum sector, with a focus on multiphase flows. Originality: The current study represents the authors’ original work and has not been previously submitted or published elsewhere. Full article

This article explores the influence of polymers on the boundary layer flow, heat transfer, and mass transfer control of non-Newtonian-based nanofluids flowing past a stretching surface. The mathematical model incorporates the Oldroyd-B model to analyze the effects of polymers, while the Powell–Eyring and Reiner–Philippoff viscosity models are employed to study the behavior of non-Newtonian fluids. The dispersion model is adopted to account for nanofluid characteristics. Appropriate transformations yield governing equations with similar forms, which are solved numerically to investigate the impact of polymer inclusion on skin friction, Nusselt number, and Sherwood number. The study’s findings reveal that the addition of polymers to the non-Newtonian-based nanofluids leads to a reduction in heat and mass transport while enhancing skin drag. Detailed analysis of these effects sheds light on the underlying physical mechanisms. Full article

The physiological system loses thermal energy to nearby cells via the bloodstream. Such energy loss can result in sudden death, severe hypothermia, anemia, high or low blood pressure, and heart surgery. Gold and iron oxide nanoparticles are significant in cancer treatment. Thus, there is a growing interest among biomedical engineers and clinicians in the study of entropy production as a means of quantifying energy dissipation in biological systems. The present study provides a novel implementation of an intelligent numerical computing solver based on an MLP feed-forward backpropagation ANN with the Levenberg–Marquard algorithm to interpret the Cattaneo–Christov heat flux model and demonstrate the effect of entropy production and melting heat transfer on the ferrohydrodynamic flow of the Fe₃O₄-Au/blood Powell–Eyring hybrid nanofluid. Similarity transformation studies symmetry and simplifies PDEs to ODEs. The MATLAB program bvp4c is used to solve the nonlinear coupled ordinary differential equations. Graphs illustrate the impact of a wide range of physical factors on variables, including velocity, temperature, entropy generation, local skin friction coefficient, and heat transfer rate. The artificial neural network model engages in a process of data selection, network construction, training, and evaluation through the use of mean square error. The ferromagnetic parameter, porosity parameter, distance from origin to magnetic dipole, inertia coefficient, dimensionless Curie temperature ratio, fluid parameters, Eckert number, thermal radiation, heat source, thermal relaxation parameter, and latent heat of the fluid parameter are taken as input data, and the skin friction coefficient and heat transfer rate are taken as output data. A total of sixty data collections were used for the purpose of testing, certifying, and training the ANN model. From the results, it is found that the fluid temperature declines when the thermal relaxation parameter is improved. The latent heat of the fluid parameter impacts the entropy generation and Bejan number. There is a less significant impact on the heat transfer rate of the hybrid nanofluid over the sheet on the melting heat transfer parameter. Full article

In this study, we investigate what happens to entropy in the presence of electrokinetic phenomena. It is speculated that the microchannel has an asymmetrical and slanted configuration. The presence of fluid friction, mixed convection, Joule heating, presence and absence of homogeneity, and a magnetic field are modelled mathematically. It is also emphasized that the diffusion factors of the autocatalyst and the reactants are equal. The governing flow equations are linearized using the Debye–Huckel and lubrication assumptions. The resulting nonlinear couple differential equations are solved using the program’s integrated numerical solver, Mathematica. We take a graphical look at the results of homogeneous and heterogeneous reactions and talk about what we see. It has been demonstrated that homogeneous and heterogeneous reaction parameters affect concentration distribution $f$ in different ways. The Eyring–Powell fluid parameters $B_1$ and $B_2$ display an opposite relation with the velocity, temperature, entropy generation number, and Bejan number. The mass Grashof number, the Joule heating parameter, and the viscous dissipation parameter all contribute to the overall increase in fluid temperature and entropy. Full article

The present study explores the characteristics of 2D MHD melting with reference to mass and heat transportation upon stagnation point Powell–Eyring nanofluid flow on an extensible surface. Melting is an important phenomenon that is involved in many procedures such as permafrost melting, solidification of slag, defrosting frozen ground etc., all of which are examples of soil freezing and melting that involve heat trafficking through a coil in a grounded pump. A mathematical model is developed for the boundary layer flow. The differential equations are solved through a numerical algorithm which makes use of the boundary value problem solver bvp4c, applying MATLAB software. The numerical variations of embedded parameters on velocity lineation, temperature figuration, and concentration delineation are represented graphically, as are the width of the boundary layer value and the delineation rate for the increasing velocity parameter. The velocity function shows a decremental response for M while the opposite behavior is seen against the concentration field. Full article

The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring–Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions $L\times H$. Starting from the initial velocity profiles $(u_1^0,u_2^0)$ in $xy$-planes, the fluid flows along the z-axis subjected to a constant magnetic field and Dirichlet boundary conditions. The global existence is shown in different cases. First, the initial conditions are considered to be squared-integrable; this is the Lebesgue space $(u_1^0,u_2^0)\in L^2\left(\mathsf{\Omega }\right)$, $\mathsf{\Omega }=[0,L]\times [0,H]\times (0,\infty )$. Afterward, the results are extended for $(u_1^0,u_2^0)\in L^p\left(\mathsf{\Omega }\right),$$p>2$. Lastly, the existence criteria are obtained when $(u_1^0,u_2^0)\in H^1\left(\mathsf{\Omega }\right)$. A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring–Powell fluids. Full article

The intention of this study is to carry out a numerical investigation of time-dependent magneto-hydro-dynamics (MHD) Eyring–Powell liquid by taking a moving/static wedge with Darcy-Forchheimer relation. Thermal radiation was taken into account for upcoming solar radiation, and the idea of bioconvection is also considered for regulating the unsystematic exertion of floating nanoparticles. The novel idea of this work was to stabilized nanoparticles through the bioconvection phenomena. Brownian motion and thermophoresis effects are combined in the most current revision of the nanofluid model. Fluid viscosity and thermal conductivity that depend on temperature are predominant. The extremely nonlinear system of equations comprising partial differential equations (PDEs) with the boundary conditions are converted into ordinary differential equations (ODEs) through an appropriate suitable approach. The reformed equations are then operated numerically with the use of the well-known Lobatto IIIa formula. The variations of different variables on velocity, concentration, temperature and motile microorganism graphs are discussed as well as force friction, the Nusselt, Sherwood, and the motile density organism numbers. It is observed that Forchheimer number $Fr$ decline the velocity field in the case of static and moving wedge. Furthermore, the motile density profiles are deprecated by higher values of the bio convective Lewis number and Peclet number. Current results have been related to the literature indicated aforementioned and are found to be great achievement. Full article