Slip Parameter Research Articles

Numerical study of hybrid nanofluid and thermal transport in sun-powered energy ship within the application of parabolic trough solar collectors

PurposeRecent advancements in technology have led to the exploration of solar-based thermal radiation and nanotechnology in the field of fluid dynamics. Solar energy is captured through sunlight absorption, acting as the primary source of heat. Various solar technologies, such as solar water heating and photovoltaic cells, rely on solar energy for heat generation. This study focuses on investigating heat transfer mechanisms by utilizing a hybrid nanofluid within a parabolic trough solar collector (PTSC) to advance research in solar ship technology. The model incorporates multiple effects that are detailed in the formulation.Design/methodology/approachThe mathematical model is transformed using suitable similarity transformations into a system of higher-order nonlinear differential equations. The model was solved by implementing a numerical procedure based on the Wavelets and Chebyshev wavelet method for simulating the outcome.FindingsThe velocity profile is reduced by Deborah's number and velocity slip parameter. The Ag-EG nanoparticles mixture demonstrates less smooth fluid flow compared to the significantly smoother fluid flow of the Ag-Fe3O4/EG hybrid nanofluids (HNFs). Additionally, the Ag-Ethylene Glycol nanofluids (NFs) exhibit higher radiative performance compared to the Ag-Fe3O4/Ethylene Glycol hybrid nanofluids (HNFs).Practical implicationsAdditionally, the Oldroyd-B hybrid nanofluid demonstrates improved thermal conductivity compared to traditional fluids, making it suitable for use in cooling systems and energy applications in the maritime industry.Originality/valueThe originality of the study lies in the exploration of the thermal transport enhancement in sun-powered energy ships through the incorporation of silver-magnetite hybrid nanoparticles within the heat transfer fluid circulating in parabolic trough solar collectors. This particular aspect has not been thoroughly researched previously. The findings have been validated and provide a highly positive comparison with the research papers.

Numerical study of fluid flow and entropy optimization subject to second order slip condition across a permeable curved surface

The entropy generation analysis has great significance in the industrial sectors with heat transmission and fluid flows, for evaluating the irreversibility aspect of a system in heat transfer operations. The numerical simulation of entropy generation and the nanofluid flow across a permeable curved surface subject to cross-diffusion and irregular heat source/sink is reported in the current investigation. The thermodynamics 2nd law is used to simulate the entropy optimization. The flow phenomena are mathematically described by partial differential equations (PDEs), which are derived in a curvilinear coordinate system. The system of ODEs (ordinary differential equations) is derived by using the similarity conversion, which is further numerically calculated through the parametric continuation method (PCM) using MATLAB software. The results reveal that the velocity slip and curvature parameters improve the velocity profile whereas the inverse effect is observed against the surface permeability parameter. It can also be noticed that the entropy optimization enhances with the variation in Brinkman number and temperature ratio parameter. The impact of Schmidt number and chemical reaction decline the mass transmission ratio.

MHD Stefan Flow of Casson Nanofluid Complete a Porous Medium in The Presence of Chemical Reaction with The Effect of Thompson as Well as Troian Slip Over a Plate in the Company of Radiation

In this work, we report the effects of Thompson, Troian slip, and Stefan blowing on the magnetohydrodynamic (MHD) Cassonnanofluid behavior via a porous media while a chemical reaction is taking place. We also examine the effects of radiation parameters, Joel heat, and velocity distribution using a two-phase model for nanofluids. Similarity transformations may be used to convert the primary Partial Differential Equations (PDEs) into Ordinary Differential Equations (ODEs). MATLAB Shooting and Runge-Kutta algorithms may be used to solve nonlinear equations. The variations in non-dimensional parameters show the effects on mass transfer, heat, and fluid flow properties. It is shown that the skin friction coefficient falls as the Stefan blowing parameter S increases. As the values of the Thompson and Troian slip parameters increase, the fluid concentration decreases. With an increase in Nt, Nb, and k, the fluid's heat rises but its concentration falls. The results of this analysis provide several enticing aspects that are going to give merits for further study of the problems.

The effect of slip parameter in an axisymmetric oscillatory Stokes flow

A general solution of Stokes equations for the problem of an axisymmetric oscillatory flow of an incompressible, viscous fluid past a sphere satisfying general boundary conditions is obtained. The behavior of the magnitude of drag is observed with the variation of the slip parameter. Some more interesting behaviors are detailed, and several existing results pertaining to steady flows and flows with rigid and shear free boundary conditions are recovered as special cases. The corresponding results are discussed for four different axisymmetric oscillatory Stokes flows, namely, uniform flow, flows generated due to a dipole, a source, and a Stokeslet. A few interesting streamline patterns like formation, elongation, and disappearance of viscous eddies in the vicinity of the sphere with a periodic reversal of the flow are observed at different frequencies for different values of the slip parameter.

Significances of melting heat transfer and bioconvection phenomena in nanofluid flow over a three different geometries

This study addresses the numerical investigation of the steady and two-dimensional flow of magnetohydrodynamic nanofluid containing motile microorganisms over three distinct configurations: a wedge, a plate, and the stagnation point of a flat plate. The impacts of activation energy, melting phenomena, thermophoresis, and Brownian motion are taken into account. The dimensionless form of the governing coupled nonlinear partial differential equations is obtained by using similarity transformations. The system of ordinary differential equations is numerically solved using the “bvp4c” solver in MATLAB, and obtained results are also validated with an analytical approach Optimal Auxiliary Function Method (OAFM). Skin friction, heat, mass and motile microorganisms transfer rates are discussed through graphs and tables. Findings indicate that profile for Nusselt number enhances for higher inputs of melting parameter while Sherwood number lowers with increasing inputs of activation energy parameter. An improving pattern of velocity profiles is magnificent for stagnation point flow [f(η = 1) = 0.943711] compared to wedge [f(η = 1) = 0.915698]and horizontal plate [f(η = 1) = 0.868617]with respect to wedge angle parameter keeping velocity ratio parameter A < 1. For the wedge surface, the temperature profiles decrease [θ(η = 1.5) = 0.933075, 0.895245, 0.858931] for increasing inputs of radiation parameter (2.5 ≤ Nr ≤ 4.5) while motile microorganism profiles enhance [χ(η = 1.3) = 0.532505, 0.621569, 0.690635] with bioconvection Schmidtt number (0.3 ≤ Sb ≤ 0.7) respectively. Furthermore, it was found that, as velocity slip parameter increases then velocity of fluid also improves over a plate, wedge, and stagnation point of a flat plate considering velocity ratio parameter A < 1 .

Stagnation point flow of hybrid nanofluid driven towards a sinusoidal-radius permeable circular cylinder

ABSTRACT Recent advancements in nanofluid technology have emphasized the potential of ternary hybrid nanofluids (THNFs) to significantly enhance thermal and hydrodynamic properties. The implementation of a wavy sinusoidal cylinder is proposed as a novel approach to optimize heat transfer in a variety of engineering applications. This study focuses on analysing the flow and thermal behaviour of TiO2-Al2O3-MoS2/Kerosene oil a THNF around a circular cylinder with a sinusoidal radius, demonstrating enhanced heat conduction capabilities compared to conventional hybrid nanofluids. The governing equations, formulated as partial differential equations, are solved using the bvp4c solver. The study reveals that the shape of nanoparticles plays a crucial role in heat transfer efficiency. Specifically, when the solid volume fraction increases from 1% to 3%, brick-shaped particles exhibit the lowest heat transfer enhancement of 25.80%, while blade-shaped particles achieve the highest enhancement of 68.24%. Additionally, the heat transfer coefficient improves from 1.5% to 1.8% across different nanoparticle shapes under varying dissipation parameters. Similar trends are observed in the reduction of drag force with changes in the velocity slip parameter. These findings underscore the significant impact of nanoparticle shape and volume fraction on the thermal performance of THNFs, offering valuable insights for optimizing heat transfer systems in engineering applications.

Influence of radiation and thermal slip on electrically conductive dusty Walter’s B fluid moving peristaltically through an asymmetric channel

MotivationThe motivation of this recent article is to study dusty Walter’s B fluid flow due to its wide range of applications in biology and polymer industry. The fluid is traveling peristaltically through an asymmetric channel with wall slip. A discussion is also presented to examine heat transfer effects with thermal radiation and slip. MethodologyThe regular perturbation technique is employed to evaluate the mathematical model of the problem, which is first simplified by using stream functions. Mathematical results are simulated to illustrate flow characteristics of fluid and solid particles in salient quantities. Also, graphs of temperature distribution of fluid and dust particles have been discussed to study the impacts of various parameters. OutcomesWalter’s B fluid parameter reduces speed of both fluid and dust particles. By increasing thermal slip parameter, temperature transference becomes slower through the fluid, while Brinkman number significantly raises the temperature profile of both fluid and particles. This article presents a theoretical analysis of the problem. Moreover, the characteristics of liquids involved in the plastic industry and medical science can also be understood using the current analysis. Originality/ValueWalter’s B fluid with dust particle suspension has not been investigated for slip and thermal radiation effects.

A numerical study of heat and mass transfer characteristic of three-dimensional thermally radiated bi-directional slip flow over a permeable stretching surface

Within fluid mechanics, the flow of hybrid nanofluids over a stretching surface has been extensively researched due to their influence on the flow and heat transfer properties. Expanding on this concept by introducing porous media, the current study explore the flow and heat and mass transport characteristics of hybrid nanofluid. This investigation includes the effect of magnetohydrodynamic (MHD) with chemical reaction, thermal radiation, and slip effects. The nanoparticles, copper, and alumina are combined with water for the formation of a hybrid nanofluid. Using the self-similar method for the reduction of Partial differential equations (PDEs) to the system of Ordinary differential equations (ODEs). These nonlinear equation systems are solved numerically using the bvp4c (boundary value solver) technique. The effect of the different physical non-dimensional flow parameters on different flow profiles such as velocity, temperature, concentration, skin friction, Nusselt and mass transfer rate are depicted through graphs and tables. The velocity profiles diminish with the effect of magnetic and slip parameters. The temperature and concentration slip parameters reduce the temperature and concentration profile respectively. The higher values of magnetic factor lessened the skin friction coefficient for both slip and no-slip conditions. An elevation in the thermal slip parameter reduced the boundary layer thickness and the heat transfer from the surface to the fluid. The Nusselt number amplified with the climbing values of the radiation parameter. The mass transfer rate depressed with the solutal slip parameter. Comparison is made with the published work in the literature and there is excellent agreement between them.

Impact of the Brownian motion and thermophoretic diffusion during the radiative MHD hybrid nanofluid flow past a stretching sheet

The article aims to analyze the effects of thermophoretic and Brownian motion on steady three-dimensional magnetohydrodynamics with fully developed natural convective hybrid nanofluid flow past a bidirectionally extending sheet. We assumed the water-based copper and aluminum nanoparticles suspension under the influence of the rotational effect, nonlinear chemical reaction, thermal radiations, viscous dissipation, and heat source. The flow field is modeled with the help of the basic equations. Furthermore, the problem is reduced to ordinary differential equations (ODEs) with the similarity variables. The reduced system of ODEs is solved with the semianalytical method (homotopy analysis method). The results for the state variables are displayed through graphs tables for various pertinent parameters. The thermal profile falls with the higher values of the Brownian and thermophoresis parameters, while the concentration profile shows an opposite trend with the increasing values of the Brownian parameter. Also, the slip parameter decreases both the thermal and concentration profiles as well as the surface drag. The velocity profiles along both directions fall with the higher magnetic strength and porosity parameters. The heat source and radiations parameter enhances the thermal profile with increasing values. The study also recommends the opposite trends for the axial and transverse velocities with increasing value of the stretching ratio factor. The proposed method convergence is present through [Formula: see text] curves for the regions [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] The skin friction and Nusselt number are displayed through tables numerically for various values of volume fraction and other important parameters.

Diffusion-thermo and thermo-diffusion impacts on MHD natural convection flow of maxwell nanofluids over a stretching sheet

The present study carried out significant importance in its magnetic field and crosswise diffusion influenced the Maxwell nanofluid flow past a nonlinear stretching sheet. This investigation aimed to shed light on the behavior of critical parameters, particularly in the presence of thermophoresis and Brownian motion. The primary aim is to investigate the impact of thermal diffusion, diffusion-thermo, and various influencing factors on a Maxwell nanofluid near a stretching sheet in the magnetic field, and the impact of three distinct slip conditions (velocity, thermal, and solutal). The partial differential equations by the nonlinear coefficients are utilized in obtaining the most important equations. These equations are distorting to beneficial nonlinear ordinary differential equations making use of the appropriate transformations variables and transformation coefficients. To investigating the computational solutions for the reducing sets of the nonlinear ordinary differential equations, these were developing and utilized the Keller box methodology. The simulations are carried out the nanofluids velocity, temperature, concentration, skin friction coefficients, the rate of temperature transport, in addition to the rate of mass transportation, amongst previous variables. The validations of this methodology are displayed via the comparison of the present outputs through the preceding judgments into the literatures. The major conclusions drawn from this study are the concentration profiles exhibited opposing behaviours as concentration slip parameter increased. However, the temperature profile increases for Brownian motion parameter and thermophoresis parameter parameters. Secondly, concentration displayed an increasing behavior as the Soret number increased.

Novel treatments for the radiative-magnetive Ellis hybrid nanofluids flow inside stenotic shrinking artery with imposed convective slip boundary conditions and entropy generation: An application in cardiovascular disease

This research delves into the theoretical and computational analysis of blood flow dynamics within a constricted, porous artery using a novel hybrid nanofluid model known as the Ellis model, which incorporates gold and silver nanoparticles. The investigation encompasses a spectrum of physical phenomena, including magnetic effects, Darcy-Forchheimer porous medium flow, viscous dissipation, and non-linear thermal radiation. Additionally, a convective slip boundary condition is applied at the arterial surface. By transforming the governing nonlinear partial differential equations into nonlinear ordinary differential equations, the study facilitates a comprehensive analysis. Subsequently, employing the bvp4c algorithm in MATLAB enables the numerical solution of these equations, yielding dual solutions for the system. Graphical representations are then utilized to elucidate various profiles, including velocity, temperature, skin friction coefficient, Nusselt number, and entropy. The findings highlight intriguing trends, such as the contrasting behaviors of skin friction and Nusselt number between the Au/Blood nanofluid and the Au − Ag/Blood hybrid nanofluid. Dual solutions can not be found beyond the critical values of suction (Sc) and curvature (γc) parameters. The critical values Sc are 2.3554 and 2.3170; γc are 0.2248 and 0.2654 for Au/Blood and Au − Ag/Blood, respectively. Moreover, insights are gained into the influence of magnetic field, Darcy-Forchheimer parameters on velocity reduction and the effect of the Ellis fluid, velocity slip parameters on temperature reduction profile. The heat transference rate increases in the situation of augmentation in shrinking parameyer and thermal radiation effect, which helps remove the toxic plaque from the blood flowing at the surface of the artery. Notably, the study underscores the significance of nanoparticle presence, porous and magnetic field parameters in enhancing entropy near the artery, with implications for cancer treatment and stroke prevention strategies.

Artificial boundary method for the fractional second-grade fluid flow on a semi-infinite plate with the effects of magnetic field and a power-law viscosity

As a typical representative of viscoelastic fluids, second-grade fluids have many applications, such as paints, food products, and cosmetics. In this paper, the equation for describing the fractional second-grade fluid with the power-law viscosity on a semi-infinite plate under the influence of a magnetic field is studied. The numerical solution is obtained using the finite difference method. To handle the semi-unbounded region, the (inverse) z-transform is applied to establish the absorbing boundary condition (ABC) for the solution at the cut-off point. In addition, the numerical example analyzes the superiority of the ABC over the directly truncated boundary condition and the effects of different parameters on the velocity distribution. The conclusion is that the slip parameter, power-law exponent parameter, and power-law index parameter promote the fluid flow, while the magnetic field and fractional parameter hinder the fluid flow.

A numerical approach to radiative ternary nanofluid flow on curved geometry with porous media and multiple slip constraints

AbstractEnergy scarcity is among the biggest global challenges which is aggravating with each passing day due to ever increasing energy demands of contemporary livings as well as industrial requirements verses finite and rapidly depleting fossil reserves of our planet. Improving energy efficiency is one of the effective ways to cope with this challenge. Ternary nanofluids (TNF) are a dynamic novel class of fluids possessing unique thermophysical and other functional characteristics making them the most efficient heat transporting fluids of 21st century. These fluids have promising applications in major manufacturing and processing industries, emerging nanotechnologies and bio‐medical domains. The novel theme of this pragmatic study is analysis of bio‐convective TNF flow by stretchable porous curved surface considering effects of thermal radiation, chemical reaction, magnetic field, and various slip constraints. The modeled partial differential equations (PDEs) governing fluid flow under presumptions are converted to ordinary differential equations (ODEs) by suitable transformation relations. Numerical solutions are presented in graphical sketches and tabular forms using MATLAB bvp4c package for physical interpretations of sundry controlling variables impacts. To gauge veracity of computed results, comparisons with already published results have been presented. Moreover, the statistical concept of Pearson correlation coefficient has been employed to prove strong relationship between slip parameters and physical quantities. Research concludes that thermal efficiency of TNF improves by rising velocity slip, magnetic force, curvature factor, thermal radiation, and thermophoresis effects. Velocity slip and thermal slip improve concentration boundary layer. Gyrotactic microorganisms’ density improves for higher velocity slip, temperature slip while depreciates for larger values of nanoparticle concentration slip and motile organism density slip.

Multiple slip nonlinear radiative bioconvective flow of nanofluid with variable thermal conductivity

Owing to the improved thermal applications of nanomaterials, various applications have been suggested in various era of engineering including heat transfer devices, chemical processes, thermal management devices, electronic cooling etc. The aim of current investigation is to presents the bioconvective flow of nanofluid with applications of multiple slip effects. The motivations for considering the slip effects for heat and mass transfer analysis are associated to its significance in the petroleum sciences, extrusion processes, oil recovery and plasma physics. The nonlinear thermal radiation effects and chemical reaction consequences have been attributed. In contrast to traditional investigations, the thermal conductivity of nanofluid have been assumed to be temperature dependent. Following the assumptions of dimensionless variables, a system of nonlinear differential equations is obtained. The shooting technique is employed for computing the numerical simulations. The accuracy of solution is ensured. The physical assessment of problem is incorporated in view of involved parameter. It has been claimed that interaction of slip effects enhances the heat and mass transfer effects. Change in microbes density slip parameter leads to improvement in the microorganisms profile. Moreover, local Nusselt number and Sherwood number reduces for slip parameters. Current results present significance in heat transfer systems, thermal engineering, chemical engineering, fertilizers, biofuels etc.

Impacts of unsteady MHD hybrid nanofluid over a non-linear stretchable porous sheet with thermal radiation and gyrotatic microorganisms

This study offers a numerical assessment of unsteady laminar flow, heat and mass transfer of conventional hybrid nanofluid considering activation energy which is noticed in chemical processes. Further, non linear radiation and bioconvection flow with first order slip is also accounted. Nanoparticles as Cu and Al2O3 in the base fluid H2O are included in this analysis. Similarity transformation is applied to the governing model equations to reduce dimensionless form and "bvp4c" a MATLAB solver, is applied to get numerical outputs of flow problem. Validation of numerical outcomes is done by an analytical approach optimal auxiliary function method (OAFM). This analysis reports better thermal characteristics when volume fractions 0.0 ≤ φ1 ≤ 0.5 and 0.0 ≤ φ2 ≤ 0.5 of both nanoparticles Cu and Al2O3 are enhanced. Results for present analysis are interpreted numerically and graphically for distinct enhanced values of dimensionless parameters and physical quantities. The high resistance offered by velocity slip (0 ≤ Sv1 ≤ 1.0) and Forchheimer parameter (0 ≤ Fr ≤ 10) cause a drop in velocity profiles. It is noticed that bioconvection Peclet number (0 ≤ Pe ≤ 0.7) leading to a drop (χ(η) = 0.139972 to χ(η) = 0.0817063, at η = 1) in density distribution of motile microorganisms.

Computation of SWCNT/MWCNT-doped thermo-magnetic nano-blood boundary layer flow with non-Darcy, chemical reaction, viscous heating and Joule dissipation effects

CNTs have been shown to exhibit exceptional electrical and thermal conductivities, chemical and mechanical stability and physiochemical reliability in wide-ranging applications covering biomedicine, energy and aerospace. Motivated by emerging applications in nano-drug delivery in medicine and radiative ablation therapy, a steady-state mathematical model is established for magnetohydrodynamic boundary-layer transport of chemically reactive carbon nanotubes (CNTs)-doped electrically conducting blood along a porous stretching wall of a blood vessel. Multiple and single walls CNTs are considered using the model developed by Xue (2005). Heat generation, radiative flux, wall mass (concentration) slip, viscous heating and Joule magnetic dissipation are incorporated. Chemical reaction effects are addressed utilizing homogenous first-order model. The Darcy-Forchheimer drag force model is utilized for bulk matrix and inertial drag effects in the porous medium. Radiative heat-transport is studied considering Rosseland's diffusion model. The governing partial differential conservation equations for mass, momentum, energy and species are formulated in a two-dimensional Cartesian coordinate system with allied wall and free-stream boundary conditions. Via scaling transformations, a nonlinear boundary value problem is derived. Numerical computations are achieved through bvp4c scheme. The impact of selected parameters on dimensionless quantities (velocity, temperature, concentration, skin friction, local Nusselt and Sherwood numbers) are computed and elaborated through tables and graphs. A good correlation of the numerical solutions with earlier simpler models from the literature is included. The simulations show that with augmentation in Hartmann magnetic number and Forchheimer inertial drag number, significant damping in the nano-doped blood flow is produced for both SWCNTs and MWCNTs. Temperature is elevated with increment in dissipation effect i. e. Eckert number. Higher values of mass (solutal) slip parameter induce a depletion in the concentration. Nusselt number i. e. heat transfer rate to the blood vessel wall is improved with greater values of solid volume fraction for both CNTs. The present model is relevant to radiative ablation therapy combined with nano-medical treatments in blood vessels wherein constant mechanical loading via blood pressure and flow can elevate internal stresses (circumferential wall stress and endothelial shear stress) and induce morphological alterations in blood vessel wall (stretching) and endothelium in conjunction with biochemical reactions.

Enhanced Thermal Study in Hybrid Nanofluid Flow through a Channel Motivated by Water/Cu+Al2o3 and Entropy Generation

This study examines the analysis of entropy generation in the magnetohydrodynamic oscillatory convective flow of hybrid nanofluid through a porous horizontal channel with velocity slip. The analysis incorporates suction at the cold wall and injection at the hot wall. Variable viscosity, thermal radiation, and viscous dissipation are also considered. Utilizing similarity transformations, the governing nonlinear partial differential equations are converted into ordinary differential equations, and exact solutions are obtained using Mathematica. Graphs are used to illustrate the impact that a variety of physical factors have on velocity, temperature, entropy generation, the Bejan number, skin friction, and the Nusselt number. The graphic results demonstrate that the fluid velocity is positively correlated with the cold wall slip parameter and negatively correlated with the hot wall slip parameter. There is an opposite relationship between fluid temperature and thermal radiation and an ascending relationship between fluid temperature and the Brinkman number. Findings from this study have important implications for better thermal management, device performance, and reliability as well as for optimizing microelectronic cooling systems.

Significance of Thompson and Troian slip effects on Fe3O4-CoFe2O4 ethylene glycol-water hybrid nanofluid flow over a permeable plate

This study aims to analyze the electromagnetic, hydro-thermal characteristics of hybrid nanofluid (Fe3O4-CoFe2O4/EG-water) flow over a permeable plate considering the Thompson and Troian slip, and suction/injection effects. By employing suitable similarity transformations, the governing partial differential equations (PDEs) describing the flow are converted into a set of highly nonlinear ordinary differential equations (ODEs). These transformed equations are computationally solved using the “bvp4c technique” in MATLAB. The detailed graphs illustrate the impact of various factors for instance, the Hartmann number, electric parameter, velocity slip parameter, critical shear rate, permeability parameter, heat generation/absorption parameter and suction/blowing parameter on velocity and temperature distributions. Also, the tabular data facilitates a detailed quantitative examination of these influences. The velocity and temperature profiles exhibit opposite nature influenced by factors such as the Hartmann number, velocity slip, critical shear rate, permeability parameter, and suction/blowing effects. Furthermore, as the critical shear rate, velocity slip, permeability and suction/blowing parameters increase, so do the absolute values of the Nusselt number. Conversely, higher heat generation/absorption parameter and Eckert number cause a decrease in these absolute values.

Amplitude‐dependent modal viscous damping for distributed stick–slip systems

AbstractAn accurate damping model serves as the foundation for reliable structural analysis. One of the primary sources of structural damping is the stick–slip mechanism caused by interfacial friction. Structural damping is usually represented by the modal damping ratio, and the modal equivalent viscous damping ratio (EVDR) of a stick–slip system is crucial in structural dynamic modeling. To date, an accurate yet simple prediction method for modal amplitude‐dependent EVDR that considers the distribution characteristics of the stick–slip mechanism remains unavailable. In the present study, the modal EVDRs of a distributed stick–slip system (DSSS) extended from a single degree‐of‐freedom stick–slip system were calculated using the modal energy equivalence method. The correlation between the stick–slip parameters and the modal damping behavior was investigated at various amplitude levels on the basis of the assumption of equal stick–slip parameters. A two‐parameter damping model represented by a single stick–slip damping model was developed to capture the amplitude dependence of the frictional EVDR. Furthermore, a practical prediction method based on the stick–slip parameters was proposed for the modal EVDR of the fundamental and higher‐order modes. The seismic analysis of two illustrative structures with nonuniform and uniform interstory stiffness demonstrated the effectiveness and applicability of the proposed method in predicting the modal EVDR of the DSSS. The proposed equivalent linear viscous damping system is suitable for the quick prediction of structural dynamic responses.

The analytical study of double diffusive convection in a rectangular enclosure bounded by porous lining with thermal radiation

The current analytical study is dedicated to the boundary layer regime where heat and mass transfer rates are ruled by natural convection. A rectangular enclosure filled with a combination of an arbitrary buoyancy ratio has an Oseen-linear solution, and the position of Beavers and Joseph's condition is employed at the porous fluid interface. Thermal radiation's interaction with a porous lining influences overall heat transfer in a system. Porous linings and radiation are employed in many applications, such as furnaces, insulation, heat exchangers, solar energy collecting and storage, and heat control in electronics. The effect of slip and radiation is to increase the flow rate because of the reduction in friction at the surface. It indicates the fact that temperature and concentration are rapidly lowering. As the slip parameter and radiation parameter increase, the heat and mass transport increase due to the rise in velocity. The Nusselt and Sherwood numbers reach their maximum when the radiation parameter, Rayleigh number, and slip parameter are increased. The findings of the Nusslet number and Sherwood numbers are related to the finite situations of the slip parameter tending to infinity, the radiation parameter going to zero and the angle 90°.