Search Results (10)

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

An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is utilized to model the time-varying boundary layer flow of a non-Newtonian fluid over both stationary and oscillating surfaces, taking into account the influence of heat generation that depends on both space and temperature. The continuity equation of the considered incompressible fluid is discretized by first-order backward difference formulas, whereas the dimensionless Navier–Stokes equation, energy, and equation for nanoparticle volume fraction are discretized by the proposed scheme in fractal time. The effect of different parameters involved in the velocity, temperature, and nanoparticle volume fraction are displayed graphically. The velocity profile rises as the parameter I grows. We primarily apply this computational approach to analyze a non-Newtonian fluid’s fractal time-dependent boundary layer flow over flat and oscillatory sheets. Considering spatial and temperature-dependent heat generation is a crucial factor that introduces additional complexity to the analysis. The continuity equation for the incompressible fluid is discretized using first-order backward difference formulas. On the other hand, the dimensionless Navier–Stokes equation, energy equation, and the equation governing nanoparticle volume fraction are discretized using the proposed fractal time-dependent scheme. Full article

The present paper explores the two-dimensional (2D) incompressible mixed-convection flow of magneto-hydrodynamic Eyring–Powell nanofluid through a nonlinear stretching surface in the occurrence of a chemical reaction, entropy generation, and Bejan number effects. The main focus is on the quantity of energy that is lost during any irreversible process of entropy generation. The system of entropy generation was examined with energy efficiency. The set of higher-order non-linear partial differential equations are transformed by utilizing non-dimensional parameters into a set of dimensionless ordinary differential equations. The set of ordinary differential equations are solved numerically with the help of the finite element method (FEM). The illustrative set of computational results of Eyring–Powell (E–P) flow on entropy generation, Bejan number, velocity, temperature, and concentration distributions, as well as physical quantities are influenced by several dimensionless physical parameters that are also presented graphically and in table-form and discussed in detail. It is shown that the Schemit number increases alongside an increase in temperature, but the opposite trend occurs in the Prandtl number. Bejan number and entropy generation decline with the effect of the concentration diffusion parameter, and the results are shown in graphs. Full article

The current article presents the entropy formation and heat transfer of the steady Prandtl-Eyring nanofluids (P-ENF). Heat transfer and flow of P-ENF are analyzed when nanofluid is passed to the hot and slippery surface. The study also investigates the effects of radiative heat flux, variable thermal conductivity, the material’s porosity, and the morphologies of nano-solid particles. Flow equations are defined utilizing partial differential equations (PDEs). Necessary transformations are employed to convert the formulae into ordinary differential equations. The implicit finite difference method (I-FDM) is used to find approximate solutions to ordinary differential equations. Two types of nano-solid particles, aluminium oxide (Al₂O₃) and copper (Cu), are examined using engine oil (EO) as working fluid. Graphical plots are used to depict the crucial outcomes regarding drag force, entropy measurement, temperature, Nusselt number, and flow. According to the study, there is a solid and aggressive increase in the heat transfer rate of P-ENF Cu-EO than Al₂O₃-EO. An increment in the size of nanoparticles resulted in enhancing the entropy of the model. The Prandtl-Eyring parameter and modified radiative flow show the same impact on the radiative field. Full article

In this research, we studied the impact of temperature dependent viscosity and thermal radiation on Eyring Powell fluid with porous channels. The dimensionless equations were solved using the perturbation technique using the Weissenberg number (ε ≪ 1) to obtain clear formulas for the velocity field. All of the solutions for the physical parameters of the Reynolds number (Re), magnetic parameter (M), Darcy parameter (Da) and Prandtl number (Pr) were discussed through their different values. As shown in the plots the two-dimensional and three-dimensional graphical results of the velocity profile against various pertinent parameters have been illustrated with physical reasons. The results revealed that the temperature distribution increases for higher Prandtl and thermal radiation values. Such findings are beneficial in the field of engineering sciences. Full article

Several mechanisms in industrial use have significant applications in thermal transportation. The inclusion of hybrid nanoparticles in different mixtures has been studied extensively by researchers due to their wide applications. This report discusses the flow of Powell–Eyring fluid mixed with hybrid nanoparticles over a melting parabolic stretched surface. Flow rheology expressions have been derived under boundary layer theory. Afterwards, similarity transformation has been applied to convert PDEs into associated ODEs. These transformed ODEs have been solved the using finite element procedure (FEP) in the symbolic computational package MAPLE 18.0. The applicability and effectiveness of FEM are presented by addressing grid independent analysis. The reliability of FEM is presented by computing the surface drag force and heat transportation coefficient. The used methodology is highly effective and it can be easily implemented in MAPLE 18.0 for other highly nonlinear problems. It is observed that the thermal profile varies directly with the magnetic parameter, and the opposite trend is recorded for the Prandtl number. Full article

The aim of this paper is to present experimental data and the constitutive model for the inelastic behavior of polyoxymethylene in wide strain rate and temperature ranges. To capture the non-linearity of the stress responses for both loading and unloading regimes, the composite model of inelastic deformation is utilized and further developed. The equivalent inelastic strain rate is described by the Prandtl–Eyring law, while the temperature dependence is characterized by the modified Arrhenius-type law. Generalized equivalent stress and the flow rule are formulated to capture pressure sensitivity, transverse strain and volumetric strain responses. The results obtained by the constitutive law are compared with experimental data for stress vs. axial strain from standard tension tests as well as with axial and transverse strains measured by digital image correlation. The developed composite model is able to capture the non-linearity of stress–strain curves for complex loading paths within the small strain regime. For higher strains, apart from geometrically non-linear theory, evolution laws for the volume fraction of the constituents should be modified and calibrated. For the small strain regime, the inelastic dilatation is negligible. For higher axial strain values, a decrease in Poisson’s ratio under tension and increase in it under compression are observed. The Drucker–Prager-type equivalent stress and the developed flow rule provide a better description of both the transverse and volumetric strains than that of the classical von Mises–Odqvist flow rules. Full article

Non-Newtonian fluid flow in a single fracture is a 3-D nonlinear phenomenon that is often averaged across the fracture aperture and described as 2-D. To capture the key interactions between fluid rheology and spatial heterogeneity, we adopt a simplified geometric model to describe the aperture variability, consisting of adjacent one-dimensional channels with constant aperture, each drawn from an assigned aperture distribution. The flow rate is then derived under the lubrication approximation for the two limiting cases of an external pressure gradient that is parallel/perpendicular to the channels; these two arrangements provide upper and lower bounds to the fracture conductance. The fluid rheology is described by the Prandtl–Eyring shear-thinning model. Novel closed-form results for the flow rate and hydraulic aperture are derived and discussed; different combinations of the parameters that describe the fluid rheology and the variability of the aperture field are considered. The flow rate values are very sensitive to the applied pressure gradient and to the shape of the distribution; in particular, more skewed distribution entails larger values of a dimensionless flow rate. Results for practical applications are compared with those valid for a power-law fluid and show the effects on the fracture flow rate of a shear stress plateau. Full article

Non-Newtonian fluid flow in a single fracture is a 3D nonlinear phenomenon that is often averaged across the fracture aperture and described as 2D. To capture key interactions between fluid rheology and spatial heterogeneity, we adopted a simplified geometric model to describe aperture variability, consisting of adjacent one-dimensional channels with constant aperture, each drawn from assigned aperture distribution. The flow rate was then derived under the lubrication approximation for the two limiting cases of an external pressure gradient that was parallel/perpendicular to the channels; these two arrangements provided an upper/lower bound to fracture conductance. Fluid rheology was described via the Prandtl–Eyring shear-thinning model. Novel closed-form results for flow rate and hydraulic aperture were derived and are discussed; different combinations of parameters describing the fluid rheology and variability of the aperture field were considered. In general, flow rate depends, in a nonlinear fashion, on the dimensionless pressure gradient and distribution parameters. Full article

In this article, entropy generation of an Eyring–Powell nanofluid through a permeable stretching surface has been investigated. The impact of magnetohydrodynamics (MHD) and nonlinear thermal radiation are also taken into account. The governing flow problem is modeled with the help of similarity transformation variables. The resulting nonlinear ordinary differential equations are solved numerically with the combination of the Successive linearization method and Chebyshev spectral collocation method. The impact of all the emerging parameters such as Hartmann number, Prandtl number, radiation parameter, Lewis number, thermophoresis parameter, Brownian motion parameter, Reynolds number, fluid parameter, and Brinkmann number are discussed with the help of graphs and tables. It is observed that the influence of the magnetic field opposes the flow. Moreover, entropy generation profile behaves as an increasing function of all the physical parameters. Full article