Dimensionless Form Research Articles

Darcy-Forchheimer magnetohydrodynamic flow of non-Newtonian Reiner-Rivlin hybrid nanofluid bounded by double-revolving disks

The applications of fluid flow and heat transfer between coaxial double-revolving disks are diverse and can be found in various engineering and scientific domains. In general, the utilization of engine oil ( EO) mixed with hybrid nanoparticles serves various purposes in engine cooling, such as maintaining viscosity-temperature properties, preventing corrosion, and achieving other cooling-related objectives. This investigation focuses on the Darcy-Forchheimer flow of a non-Newtonian Reiner-Rivlin hybrid nanofluid confined between double-revolving disks. The hybrid nanoparticles used include cadmium telluride ( CdTe) and titanium dioxide ( TiO2), combined with the base fluid engine oil. The dimensional flow equations are converted into dimensionless forms using suitable similarity transformations. Subsequently, a semi-analytical methodology known as the homotopy analysis method ( HAM) is utilized to tackle this problem. Graphs are used to determine the effects of the various flow parameters of the hybrid nanofluids on the velocities, temperature, skin friction coefficient, and the Nusselt number. After validating the findings against previous research, an attractive agreement was observed. Some major outcomes from this present problem are that axial, radial, and temperature profiles increase with the rise of the cross-viscosity parameter while the tangential velocity decreases. Radial velocity increased, and tangential velocity diminished with an enhanced magnetic field parameter. Radial velocity is increased for higher values of the dimensionless forced parameter. For higher values of the porosity parameter, the temperature profile improved. Also, the exploration of the Nusselt number and skin friction for the disks, incorporating the effects of a magnetic field and porous medium, reveals that skin friction for both disks increase with the rising Reynolds number and volume fraction of the cadmium telluride nanoparticles.

Analysis of visco-inelastic biphasic fluid flow in wire coating process

To ensure the safety of data transmission, wires and fibers undergo a coating process to shield against potential damage. This process is critical in fields such as telecommunications, power transmission, and electronics, where durability and insulation are key factors. The current investigation is focused on the coating process by employing Eyring–Powell fluid in the presence of the magnetic field. The governing equations are developed by employing the biphasic (Buongiorno) model and temperature-dependent thermophysical properties. These equations are subsequently transformed into dimensionless form and tackled numerically. The study extensively explores critical aspects including shear stress rate, flow rate, and heat transfer rate for pertinent parameters. Furthermore, utilizing the response surface methodology, the optimization of shear stress and heat transfer rates in coated wire is pursued. This approach determines optimal levels for the viscosity parameter, Eyring–Powell fluid parameter, and thermophoresis parameter. The analysis concludes that the best outcomes are achieved by minimizing the viscosity parameter while maximizing the Eyring–Powell fluid parameter.

Internal heating and distribution in electromagnetic Powell-Eyring [formula omitted]/glycerin hybridized nanomaterial with radiation and wall slip conditions

The synergistic influences of the hybridization of molybdenum disulfide (MoS2) and graphene oxide (GO) nanoparticles on electromagnetic radiation absorption and augmentation of thermal conductivity coupled with the industrial demand for an enhanced non-Newtonian working fluid spurred this study. Therefore, the study examines the radiative properties and thermal behaviour of hybridized MoS2 and GO nanoparticle systems dispersed in a glycerin Powell-Eyring fluid with wall slip conditions. A theoretical mathematical setup is modelled for the nanoparticle thermophysical characteristics with viscous dissipation and heat generation under the influence of the electromagnetic Riga plate. The model is transformed into an invariant dimensionless form and solved utilizing the pseudo-spectral collocation technique. The effect of fluid rheology, nanoparticle concentration, and fluid-wall slip conditions interface on radiative heat transfer and thermal propagation is investigated. The results reveal momentous augments in radiation absorption and thermal conductivity of about 4.13% to 10.22% due to MoS2 and GO hybridized nanoparticles. Also, it was found that thermal transport is enhanced close to the solid boundary wall slip, leading to an improve heat distribution rate. Hence, this study contributes to the interplay complexity between external stimuli, fluid dynamics, and nanoparticle morphology in thermal systems, offering insights into the advanced materials synthesis, thermal management systems, and optimization and design of nanoparticle fluid enhancement applications.

Optimized physics-informed neural network for analyzing the radiative-convective thermal performance of an inclined wavy porous fin

The significance of radiation and inclination on the temperature dispersion of the wavy porous fin has been addressed in the present study. Also, the influence of convection and internal heat generation on the thermal dissipation of the inclined wavy porous fin (IWPF) is examined. The pertinent temperature expression of the fin is represented using basic laws, and this equation is reduced to a dimensionless form via dimensionless variables. Additionally, a mix-encoding Genetic algorithm and Particle swarm optimization technique is shown to optimize the network hyperparameters. This resolves the issue of arbitrarily identifying the PINN's ideal network and successfully limits local optimization during the training phase. Further, the equation is also resolved numerically using Runge-Kutta Fehlberg's fourth-fifth (RKF-45) scheme, and the solutions are subsequently used to verify the PINN model's applicability. The temperature results estimated by PINN and their associated RKF-45 values correlate excellently, which indicates the accuracy of the applied PINN model. The obtained findings denote that reduced measures of convective-conductive variables stimulate the IWPF's thermal distribution. An inclination angle of the fin has a significant impact on the thermal variation of the IWPF.

The Stellar Bar–Dark Matter Halo Connection in the TNG50 Simulations

Stellar bars in disk galaxies grow as stars in near-circular orbits lose angular momentum to their environments, including their dark matter (DM) halo, and transform into elongated bar orbits. This angular momentum exchange during galaxy evolution hints at a connection between bar properties and the DM halo spin λ, the dimensionless form of DM angular momentum. We investigate the connection between halo spin λ and galaxy properties in the presence/absence of stellar bars, using the cosmological magnetohydrodynamic TNG50 simulations at multiple redshifts (0 < z r < 1). We determine the bar strength (or bar amplitude, A 2/A 0), using Fourier decomposition of the face-on stellar density distribution. We determine the halo spin for barred and unbarred galaxies (0 < A 2/A 0 < 0.7) in the center of the DM halo, close to the galaxy’s stellar disk. At z r = 0, there is an anticorrelation between halo spin and bar strength. Strongly barred galaxies (A 2/A 0 > 0.4) reside in DM halos with low spin and low specific angular momentum at their centers. In contrast, unbarred/weakly barred galaxies (A 2/A 0 < 0.2) exist in halos with higher central spin and higher specific angular momentum. The anticorrelation is due to the barred galaxies’ higher DM mass and lower angular momentum than the unbarred galaxies at z r = 0, as a result of galaxy evolution. At high redshifts (z r = 1), all galaxies have higher halo spin compared to those at lower redshifts (z r = 0), with a weak anticorrelation for galaxies having A 2/A 0 > 0.2. The formation of DM bars in strongly barred systems highlights how angular momentum transfer to the halo can influence its central spin.

Physics-informed neural network solution for thermo-elastic cavity expansion problem

ABSTRACT This paper proposes a physics-informed neural network (PINN) to solve the thermo-elastic coupled cavity expansion problem under plane strain conditions. The solid is modelled as a linear thermo-elastic material, and cavity expansion is driven by a constant temperature and a radial displacement subjected to the inner cavity wall. Governing partial differential equations (PDEs) for the problem is firstly presented, and an analytical solution is available to help benchmark the PINN approach. Then, the PDEs are normalised into dimensionless forms and neural network details for solving the coupled PDEs are demonstrated. Finally, the performance of the PINN approach is shown by comparison with the analytical benchmark solution and it is found that the PINN can predict thermo-elastic cavity expansion behaviour with high accuracy. The PINN approach and the analytical solution can also serve as a benchmark for solving thermo-elastic coupled problems in geotechnical engineering by more advanced PINN.

Blood Based Magnetohydrodynamic Casson Hybrid Nanofluid Flow on Convectively Heated Bi-Directional Porous Stretching Sheet with Variable Porosity and Slip Constraints

Abstract Fluid flow through porous spaces with variable porosity has wide-range applications, notably in biomedical and thermal engineering, where it plays a vital role in comprehending blood flow dynamics within cardiovascular systems, heat transfer and thermal management systems improve efficiency using porous materials with variable porosity. Keeping these important applications in view, in current study blood based hybrid nanofluid flow has considered on a convectively heated sheet. The sheet exhibits the properties of a porous medium with variable porosity and extends in both the x and y directions. Blood has used as base fluid in which the nanoparticles of Cu and CuO have been mixed. Thermal radiation, space-dependent, and thermal-dependent heat sources have been incorporated into the energy equation, while magnetic effects have been integrated into the momentum equations. Dimensionless variables have employed to transform the modeled equations into dimensionless form and facilitating their solution using bvp4c approach. It has concluded in this study that, both the primary and secondary velocities augmented with upsurge in variable porous factor and declined with escalation in stretching ratio, Casson, magnetic and slip factors along x- and y-axes. Thermal distribution has grown up with upsurge in Casson factor, magnetic factor, thermal Biot number and thermal/space dependent heat sources while has retarded with growth in variable porous and stretching ratio factors. The findings of this investigation have been compared with the existing literature, revealing a strong agreement among present and established results that ensured the validation of the model and method used in this work.

Numerical study of magneto convective ag (silver) graphene oxide (GO) hybrid nanofluid in a square enclosure with hot and cold slits and internal heat generation/absorption

Energy transmission is widely used in various engineering industries. In recent times, the utilization of hybrid nanofluids has become one of the most popular choices in various industrial fields to increase thermal performance and enhance power generation, entropy reduction, solar collectors, and solar systems. Motivated by this wide range of applications, the present article explores the mixed convection flow and heat transfer of magnetohydrodynamic \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:Ag$$\\end{document} (Silver) and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:GO$$\\end{document} (Graphene) nanofluids hybrid nanofluids in a square enclosure with heat generation/absorption by using the MAC method. The vertical walls of the enclosure are assumed to be adiabatic. The horizontal walls are also assumed adiabatic except for the center portion of the top and bottom walls of the cavity. The center portion of the horizontal upper wall is maintained as a cold is \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{(T}_{c})$$\\end{document}and the lower wall is maintained as hot \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:\\left({T}_{h}\\right)$$\\end{document}. The dimension equations are transformed into dimensionless form and then discretized and solved with the finite difference Marker and cell (MAC) method. Numerical modelling is implemented, by changing Richardson number \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:\\left(Ri\\right)$$\\end{document}, The results are located graphically using MATLAB software. The Nusselt number graph was displayed for the Reynolds number (Re), Richardson number\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:\\:\\left(Ri\\right)$$\\end{document}, and Hartmann number \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:\\left(Ha\\right)$$\\end{document}. The findings show that enhancing the values of the Richardson number and Reynolds number enhances the Nusselt number values except for the Hartmann number. The findings indicate that the combination of the new model is very good at predicting thermal conductivity and correlates experimental results well. The augmenting strength of magnetic force diminishes fluid flow. Developing the coefficients for the heat source and sink improves energy transmission and heat transfer enhancement. Hybrid nanofluids like \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:Ag-GO$$\\end{document} enhance heat transfer and efficiency. They improve cooling in heat exchangers, radiators, and electronics, boost solar energy systems, aid in cancer treatment and drug delivery, enhance geothermal and wind turbine efficiency, and improve manufacturing processes. Overall, they optimize thermal management in various applications.

Three-dimensional Darcy-forchheimer modelling of MHD hybrid nanofluid over rotating stretching/shrinking surface with Hamilton-Crosser and Yamada-Ota conductivity models

Instead of single nanoparticles, the combined effects of more than one solid nanoparticle have presented wide range of real-word application in several engineering as well as biomedical areas. The present analysis brings out a combined effect of Hamilton-Crosser and Yamada-Ota thermal conductivity models for the magnetohydrodynamic flow of hybridised fluid vi a rotating stretching/shrinking surface. The hybridised fluid comprised of silver and molybdenum tetrasulphide nanoparticle in association with the effect of Joule heating enriches the flow properties. Additionally, the Darcy-Forchheimer inertial drag with the impose of thermal radiation affecting the flow as well as heat transfer properties. The proposed mathematical model equipped with physical assumptions is transmuted into dimensionless form by utilizing similarity functions. Further, the traditional numerical technique is taken care of for the solution of the transmuted model equipped with diversified factors. The important characteristic of several factors are deployed graphically affecting various flow profiles. Finally, the outstanding features explored in the proposed investigation are stated as below; the comparative analysis reveals that, the heat transport properties became advanced in case of Hamilton-Crosser model rather than the Yamada-Ota conductivity model. However, the heat transportation rate is controlled by the increasing Eckert number but thermal radiation enhances it significantly.

Comparative analysis of buoyancy-driven hydromagnetic flow and heat transfer in a partially heated square enclosure using Cu-Fe3O4 and MoS2-Fe3O4 nanofluids

Purpose This study aims to investigate entropy generation through natural convection and examine heat transfer properties within a partially heated and cooled enclosure influenced by an angled magnetic field. The enclosure, subjected to consistent heat production or absorption, contains a porous medium saturated with a hybrid nanofluid blend of Cu-Fe3O4 and MoS2-Fe3O4. Design/methodology/approach The temperature and velocity equations are converted to a dimensionless form using suitable non-dimensional quantities, adhering to the imposed constraints. To solve these transformed dimensionless equations, the finite-difference method, based on the MAC (Marker and Cell) technique, is used. Comprehensive numerical simulations address various control parameters, including nanoparticle volume fraction, Rayleigh number, heat source or sink, Darcy number, Hartmann number and slit position. The results are illustrated through streamlines, isotherms, average Nusselt numbers and entropy generation plots, offering a clear visualization of the impact of these parameters across different scenarios. Findings Results obtained show that the Cu-Fe3O4 hybrid nanofluid exhibits higher entropy generation than the MoS2-Fe3O4 hybrid nanofluid when comparing them at a Rayleigh number of 106 and a Darcy number of 10–1. The MoS2 hybrid nanofluid demonstrates a low permeability, as evidenced by an average Darcy number of 10–3, in comparison to the Cu hybrid nanofluid. The isothermal contours for a Rayleigh number of 104are positioned parallel to the vertical walls. Additionally, the quantity of each isotherm contour adjacent to the hot wall is being monitored. The Cu and MoS2 nanoparticles exhibit the highest average entropy generation at a Rayleigh number of 105 and a Darcy number of 10–1, respectively. When a uniform heat sink is present, the temperature gradient in the central part of the cavity decreases. In contrast, the absence of a heat source or sink leads to a more intense temperature distribution within the cavity. This differs significantly from the scenario where a uniform heat sink regulates the temperature. Originality/value The originality of this study is to examine the generation of entropy in natural convection within a partially heated and cooled enclosure that contains hybrid nanofluids. Partially heated corners are essential for optimizing heat transfer in a wide range of industrial applications. This enhancement is achieved by increasing the surface area, which improves convective heat transfer. These diverse applications encompass fields such as chemical engineering, mechanical engineering, surface research, energy production and heat recovery processes. Researchers have been working on improving the precision of heated and cold corners using various methods, such as numerical, experimental and analytical approaches. These efforts aim to enhance the broad utility of these corners further.

Significance of gyrotactic microorganism's analysis for magnetized convectively heat 3D Sisko fluid flow with bioconvection phenomenon

In this research article, the bioconvection of oxytactic microorganisms with magneto-hydrodynamic (MHD) 3D steady flow of Sisko nanomaterial over a stretching sheet through convective conditions is deliberated and analyzed. Possessions of thermophoresis, Brownian motion as well as mixed convection in the Sisko fluid are also deliberated. Sisko fluid is supposed to be electrically conducted over and done with a constant pragmatic magnetic field. The flow problem is communicated using governing relations and problem is transmuted into dimensionless form among non-similar procedure. To obtain convergent solutions we must solve nonlinear differential systems. The consequences of several physical parameters have been deliberate and discussed. Our results displayed that the higher microorganism difference parameter condensed the microorganism profile, while an opposite influence is established for magnetic parameter. Concentration proises of the Sisko fluid flow are improved by growing Biot number whereas contracted beside the Lewis number. In recent years, the scientists have shown great attention in the field of bioconvection owing to its countless applications such as amassing the cells, bioreactors, gas-bearing sedimentary, modeling oil, exclusion of living, and nonliving cells, and lots of additional.

Mathematical thermo‐mechanical analysis on flame‐solid interaction: Steady laminar stagnation flow flame stabilized at a plane wall coupled with thermo‐elasticity model

AbstractA laminar stagnation flow flame stabilized at a plane wall is theoretically analyzed, coupled with a thermo‐elasticity model in the wall. Mathematical models for both the flame and the wall will be proposed, and corresponding analytical solutions based on their dimensionless forms will be obtained. The mathematical analysis of this flame‐solid interaction primarily focuses on the effect of the flame on combustion‐induced thermo‐mechanical stresses and the influence of wall material on flame properties such as flame temperature and stability against extinction. A sensitivity analysis is further performed to examine how thermo‐mechanical stress inside the wall is affected by changes in other combustion conditions (e.g., mixture composition, flame stretch rate). This study offers valuable insights into understanding the interaction between flames and solids, a relationship crucial in engineering applications such as the interaction between combustion processes and blades within gas turbine machinery.

Computational analysis of heat transport dynamics in viscous dissipative blood flow within a cylindrical shape artery through influence of autocatalysis and magnetic field orentation

Nanofluids consisting of tetra nanoparticles are crucial in bio medical sciences due to their improved thermal transport characteristics. The advanced tailored properties of tera nanoparticles make them useful in several medical interventions, such as hyperthermia treatment, where the targeted tissue can be heated more efficiently, leading to better treatment outcomes. The current study investigates the heat transfer enhancement in a hemodynamic system using tetra nanoparticles. The physical configuration of the blood flow is assumed with in a permeable cylindrical shape stenosed artery. The model incorporates the Carreau model with inclusion of diverse factors such as, exponential space-based heat source, viscous dissipation, infinite shear rate and permeability of surface. Additionally, impact of chemical reaction (autocatalysis) and magnetohydrodynamic (MHD) consequences is also integrated into the system. The framed partial differential equations (PDEs) generated by physical problem are converted into new dimensionless form of an ordinary differential system (ODEs). Bvp4c MATLAB procedure is fetched for numerical investigation. It is observed that, velocity profile of the fluid is reduced due to intensification in inclined magnetic effect, whereas autocatalysis effect promotes the concentration of nanoparticles in blood flow mixture, which increases the temperature field of fluid. Furthermore, augmentation in the values of Wassenberg number increased the elasticity in blood which enables it to deform and stretch more readily in reaction to alterations in flow conditions and hence reduction is seen in overall blood flow rate. The results revealed the significance of these integrated factors for accurate modelling of blood flow passing through a stenosed artery, which is crucial in medical interventions.

Heat and mass transfer in MHD flow of SWCNT and graphene nanoparticles suspension in Casson fluid

AbstractThe exceptional mechanical properties of carbon nanotubes (CNTs) and graphene nanoparticles, particularly their high aspect ratio and flexibility, position them as highly promising materials for the next generation of armor technology. Their incorporation into protective wear, such as bullet‐proof vests, offers the potential for significant improvements in both performance and cost efficiency. By replacing traditional materials with CNTs and graphene, the durability and maintenance of these protective devices could be substantially enhanced, leading to more effective and sustainable solutions for personal safety. This study focuses on the complex phenomena of heat and mass transport within a suspension of CNTs and graphene nanoparticles dispersed in a Casson fluid, particularly under the influence of an applied magnetic field. The analysis begins by reformulating the governing equations using similarity variables to transform them into a dimensionless form to simplify the problem. The resulting dimensionless equations are then solved using the three‐stage Lobatto IIIa finite difference method, a robust numerical technique well‐suited for solving boundary value problems in fluid dynamics. The results of this investigation highlight a significant 78.41% reduction in skin friction when compared with traditional CNT‐water nanofluid systems. This considerable decrease in skin friction not only reveals the superior performance of the CNT‐graphene nanofluid suspension but also opens up new possibilities for the design and development of advanced protective materials. These findings contribute to the growing body of knowledge on nanofluid applications and offer valuable insights for future research in the field of advanced armor technology.

Flow dynamics over cylinder in two‐dimensional benchmark problem: A finite element approximation

This research investigates 2D benchmark flow around a circular cylinder, utilizing the incompressible Navier–Stokes equations alongside the continuity and energy equations. The numerical solution is achieved through finite element discretization for space variable, combined with a second‐order Crank–Nicolson scheme for time integration. The computational results are derived using the FEATFLOW finite element based library package. Our study focuses on the dimensionless form of the flow equations and examines three key dimensionless parameters: drag, lift, and pressure drop. Upon applying finite element method (FEM) discretization, the system is converted into a set of linear or nonlinear ordinary differential equations or algebraic equations for steady‐state scenarios. We then apply the Newton–Raphson method as the outer nonlinear solver, and the multigrid method for efficiently resolving the linear subproblems. To ensure numerical accuracy, we evaluated the and errors, confirming that the experimental order of convergence matches the theoretical predictions. Flow profiles were both graphically represented and tabulated, offering a detailed understanding of the simulation results.

Effects of new nonlinear curvature models and non-local elasticity on buckling investigation of FG tapered nano-beams locating on elastic foundations

New nonlinear curvature models are proposed to show their effects on the compressive critical buckling load on functionally graded (FG) tapered nano-beams locating on elastic foundations in the presence of non-local elasticity. Fourth and fifth orders finite difference methods (bvp4c and bvp5c) are applied on the governing differential equation which is a highly non-linear, due to curvature and has variable coefficients, due to properties. Dimensional analyses have been applied on the governing system together with the problem conditions to produce their dimensionless forms. For different considered parameters, the critical buckling load is computed using the eigenvalue theorem. The effects of nonlinear curvature, variable Young modulus, variable moment inertia and foundation parameters are studied and displayed in tables and figures. The stability and convergence of the present solution are tested using more than one strategy as: comparison with available results, comparison between bvp4c and bvp5c with different mesh intervals and tolerances of truncation errors. These comparisons show that, the new curvature model affects the critical buckling with different ratios depending on variability of properties and foundation parameters. The new results show that the nonlinear curvature model reduces the critical buckling load in comparison with the classical linear model, which, leads to decreasing in factor of safety in design of structures. The new results show that the design of structures will be influenced with the new reduction of the compressive critical buckling load, since it may affect the factor of safety in design of structures. The new results can lead, generally, to more reduction of critical buckling load for large or small input parameters and it will affect other critical values such that frequencies. The introduced Tables and Figures of the present problem with comparisons of previously exact, analytical and numerical works establish the higher accuracy and stability of current findings using bvp4c or bvp5c with preferable of the later. This study is related to some practical applications such as aeronautical and structural engineering.

Unsteady thermal efficiency and temperature isotherms of an inclined radiative porous concave parabolic tapered fin: An application of design of tapered fin featuring

The present article investigates the unsteady energy efficiency and isotherms for the inclined radiative concave parabolic fin. Fourier Law is employed by incorporating the radiation and convection phenomena. Darcy model has been employed to study the porous effects on a fin. The novelty of the present problem is transient thermal analysis of a radiative porous concave parabolic fin by consideration of fin tapper ratio and angle of inclination for several pertinent parameters. Calculation of fin efficiency is the added feature of present study. The governing partial differential is transformed into the dimensionless form by employing the non-dimensional variables. With the help of MATHEMATICA a partial differential equation is solved by applying the ND Solve. The isotherms are obtained for the variations in time and space variables. It is unveiled that temperature distribution diminishes for the upsurge in the convective radiative parameters. Temperature distribution elevates as the enhancement in heat generating parameter. It has been concluded that the fin taper ratio and angle of inclination palys a vital role in heat transfer performance. An elevated thermal dispersal is seen for increasng time.

Elastoplastic plate shakes down under repeated impulsive loadings

When subjected to repeated dynamic impacts at identical load level, a metallic monolithic beam/plate may reach a stable state wherein measurable deformation ceases (i.e., shakedown in elastic state) after undergoing a sequence of elastoplastic deformations, which has been termed as “pseudo-shakedown” (P-S) (Jones, 1973, Shen and Jones, 1992). While the response of a single beam/plate under repeated low-velocity impacts has been thoroughly studied, its dynamic behavior under high-velocity impacts, such as explosive or alternating impulsive loads, is difficult to measure experimentally, due mainly to high costs and setup challenges. In the current study, the method of metallic foam projectile impact was employed to produce repeated impulsive loadings on a fully-clamped elastoplastic monolithic plate made of L907A (a Chinese standard shipbuilding steel). Its dynamic responses, including mid-point deflection versus time histories, final deflections, and deformation modes after each impact, were systematically measured. The phenomenon of dynamic shakedown was observed. To further explore this phenomenon, the method of finite elements (FE) was employed to simulate the repeated impulsive impact test, and its prediction accuracy was validated against experimental results. Unlike an elastoplastic (e.g., steel) monolithic plate subjected to repeated low-velocity impacts, which exhibits zero plastic energy dissipation in the P-S (pseudo-shakedown) state, the same plate under repeated high-velocity impacts shows a small level of plastic energy dissipation in the P-S state, mainly due to more extreme loading conditions. The initial impact momentum, yield strength, and tangent modulus of the material the plate is made of significantly affect both the stable deflection in the P-S state and the number of impacts needed to reach it, while the elastic modulus has limited influence. A modified dimensionless impulse loading number, accounting for the strain-hardening effect, is proposed. An approximately linear relationship between stable deflection in the P-S state and impulsive loading is found in dimensionless form.

Heat transfer analysis of Walter’s-B flow over a vertical plate by using fractional operator

The present study deals with the unsteady Walter’s-B fluid with hybrid fractional derivative namely constant proportional Caputo type with singular kernel. In this paper, we find new analytical solutions of a well-known problem of the fluid dynamics known as Stokes’ first problem. Using dimensional variables governing equations convert into dimensionless form. To solve the model analytically, one uses the Laplace transform approach. Analytical and numerical evaluations of the inverse Laplace transform have been conducted. The influence of several embedded flow properties, including the magnetic parameter, Grashof number, dimensionless time, Prandtl number, Schmidt number, and fractional parameter is analyzed graphically. More specifically, compared to the classical model, the fractional model provides a wider range of integral curves and better represents the flow behavior. The temperature and velocity of the fluid decrease with increasing fractional parameters during short intervals of time, but exhibit the reverse pattern over longer durations. Skin friction, the Sherwood number, and the Nusselt number are numerical quantities linked to engineering that are statistically computed and provided in tabular form.

A comparative analysis on the dynamics of solid-liquid interfacial layer and nanoparticle diameter of magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface

In this work, a comparative analysis on magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface is mainly focused. The effects of Brownian motion, Joule heating, thermophoresis, chemical reaction and activation energy are taken into consideration in this work. It is important to mention that this analysis considers a 4 % volume fraction of the alumina nanoparticles. A thermal convective and zero-mass flux conditions are imposed to scrutinize the heat transfer analysis. The leading equations are transformed into dimensionless form by using suitable similarity variables. A numerical solution is obtained using the shooting technique. The acquired outcomes depict that greater magnetic factor enhances the skin friction coefficient. The greater magnetic factor, thermal Biot number, Eckert number, and interfacial layer thickness augment the heat transfer rate, while a greater nanoparticle diameter diminishes the thermal transfer rate. A higher magnetic factor has an increasing impact on thermal distribution and a reducing impact on velocity distribution. A greater curvature factor enhances both the velocity and thermal distributions. The concentration distribution is enhanced by the higher interfacial layer thickness and activation energy factor, while it is reduced by a higher nanoparticle diameter, Brownian motion factor, and chemical reaction factor. From the comparative analysis, it is found that the velocity, thermal, and concentration distributions are higher for the cylindrical-shaped nanoparticles compared to spherical-shaped nanoparticles.