Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet

We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.

Impact of a Magnetic Dipole on Heat Transfer in Non-Conducting Magnetic Fluid Flow over a Stretching Cylinder

The thermal behavior of an electrically non-conducting magnetic liquid flowing over a stretching cylinder under the influence of a magnetic dipole is considered.The governing nonlinear differential equations are solved numerically using a finite element approach,which is properly validated through comparison with earlier results available in the literature.The results for the velocity and temperature fields are provided for different values of the Reynolds number,ferromagnetic response number,Prandtl number,and viscous dissipation parameter.The influence of some physical parameters on skin friction and heat transfer on the walls of the cylinder is also investigated.The applicability of this research to heat control in electronic devices is discussed to a certain extent.

Hybrid Nanofluid Flow over a Stretching Curved Surface with Induced Magnetic Field and Homogeneous-Heterogeneous Reactions

This study explores the 2D stretching flow of a hybrid nanofluid over a curved surface influenced by a magnetic field and reactions. A steady laminar flow model is created with curvilinear coordinates, considering thermal radiation, suction, and magnetic boundary conditions. The nanofluid is made of water with copper and MWCNTs as nanoparticles. The equations are transformed into nonlinear ODEs and solved numerically. The model’s accuracy is confirmed by comparing it with published data. Results show that fluid velocity increases, temperature decreases, and concentration increases with the curvature radius parameter. The hybrid nanofluid is more sensitive to magnetic field changes in velocity, while the nanofluid is more sensitive to magnetic boundary coefficient changes. These insights can optimize heat and mass transfer in industrial processes like chemical reactors and wastewater treatment.

Chronic effects of stretching on range of motion with consideration of potential moderating variables:A systematic review with meta-analysis

Background:It is well known that stretch training can induce prolonged increases in joint range of motion(ROM).However,to date more information is needed regarding which training variables might have greater influence on improvements in flexibility.Thus,the purpose of this metaanalysis was to investigate the effects of stretch training on ROM in healthy participants by considering potential moderating variables,such as stretching technique,intensity,duration,frequency,and muscles stretched,as well as sex-specific,age-specific,and/or trained state-specific adaptations to stretch training.Methods:We searched through PubMed,Scopus,Web of Science,and SportDiscus to find eligible studies and,finally,assessed the results from 77 studies and 186 effect sizes by applying a random-effect meta-analysis.Moreover,by applying a mixed-effect model,we performed the respective subgroup analyses.To find potential relationships between stretch duration or age and effect sizes,we performed a meta-regression.Results:We found a significant overall effect,indicating that stretch training can increase ROM with a moderate effect compared to the controls(effect size=-1.002;Z=-12.074;95%confidence interval:-1.165 to-0.840;p<0.001;I^(2)=74.97).Subgroup analysis showed a significant difference between the stretching techniques(p=0.01)indicating that proprioceptive neuromuscular facilitation and static stretching produced greater ROM than did ballistic/dynamic stretching.Moreover,there was a significant effect between the sexes(p=0.04),indicating that females showed higher gains in ROM compared to males.However,further moderating analysis showed no significant relation or difference.Conclusion:When the goal is to maximize ROM in the long term,proprioceptive neuromuscular facilitation or static stretching,rather than ballistic/dynamic stretching,should be applied.Something to consider in future research as well as sports practice is that neither volume,intensity,nor frequency of stretching were found to play a significant role in ROM yields.

A new model of flow over stretching(shrinking)and porous sheet with its numerical solutions

The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a relation.Consequently,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one go.As a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary conditions.The final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and manipulated.Moreover,we have recovered the classical results for special and appropriate values of the parameters(δ_(1),δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special cases.It is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing parameters.Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible solutions.The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable(uniform)thickness with variable(uniform)stretching/shrinking and injection/suction velocities.

Chemically Radiative MHD Flow of a Micropolar Nanofluid over a Stretching/ Shrinking Sheet with a Heat Source or Sink

This study examines the behavior of a micropolar nanofluidflowing over a sheet in the presence of a transverse magneticfield and thermal effects.In addition,chemical(first-order homogeneous)reactions are taken into account.A similarity transformation is used to reduce the system of governing coupled non-linear partial differ-ential equations(PDEs),which account for the transport of mass,momentum,angular momentum,energy and species,to a set of non-linear ordinary differential equations(ODEs).The Runge-Kutta method along with shoot-ing method is used to solve them.The impact of several parameters is evaluated.It is shown that the micro-rota-tional velocity of thefluid rises with the micropolar factor.Moreover,the radiation parameter can have a remarkable influence on theflow and temperature profiles and on the angular momentum distribution.

Mixed convectional and chemical reactive flow of nanofluid with slanted MHD on moving permeable stretching/shrinking sheet through nonlinear radiation,energy omission

Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.

Static Stretching Combined with Conscious Slower Breathing May Increase Parasympathetic Activity and Reduce Stress in Adult Women

Background: Women are thought to be more susceptible to stress than men in a stressful society, and reducing stress is crucial for women to maintain their health. Static stretching (SST) is applied in various fields to not only increase muscle flexibility but also reduce stress. Additionally, conscious slower breathing (CSB) predominates parasympathetic activity, causing a relaxing effect. These results indicate that combining SST and CSB may be more useful in reducing stress. However, to the best of our knowledge, the effect of this combination remains unclear. Objective: This study aimed to elucidate the effects of the combination of SST and CSB on autonomic activity and stress in adult women. Methods: Eleven healthy Japanese adult female participants performed SST with nonconscious natural breathing for 20 min. The same participants performed SST in combination with CSB (2 s inspiratory and 4 s expiratory) for 20 min on another day. Salivary cortisol and chromogranin A levels were measured before and after stretching as stress markers of the hypothalamic-pituitary-adrenal axis and sympathetic nervous system. The coefficient of variation of the R-R interval (CVR-R) and high-frequency component (HF), which reflect parasympathetic nerve activity, and heart rate and low-frequency component (LF)/HF ratio, which reflect sympathetic nerve activity, were measured before, during, and after stretching. Results: SST decreased cortisol levels but with no significant changes in chromogranin A, heart rate, CVR-R, HF, or LF/HF ratio. The combination of SST and CSB increased CVR-R and HF levels in addition to decreasing cortisol levels but with no significant changes in chromogranin A, heart rate, or LF/HF levels. Conclusion: These results indicate that the combination of SST and CSB may increase parasympathetic activity and reduce stress. However, future randomized controlled trials with larger sample sizes should support this conclusion.

MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.

Effect of different stretching strategies on the kinetics of vertical jumping in female volleyball athletes

Purpose： The present study aimed to examine the effect of static stretching （SS） and a sport-specific dynamic stretching （DS） session at two specific post-stretch time intervals in highly trained female athletes （age 19.90 ± 1.60 years; height 1.80 ±0.06 m; mass 76.87 ± 9.95 kg） on kinetic parameters of peak force, time-to-takeoff, and rate of force development. Methods： The data were collected over 3 days （randomized within subject design with control session）. Following each stretch session （SS vs. DS vs. control） of equal duration （7 min total： 30 s per targeted muscle group） participants performed countermovement jumping on a force platform at 1 and 15 rain after stretching. Results： The DS session significantly improved upon kinetic variables of rate of force development, peak force, and time-to-takeoffrelative to SS at 1 min after stretching. No significant effect was found at 15 min. Conclusion： Together these findings suggest that when training and competing to jump quickly and maximally the female athlete should incorporate DS instead of SS as part of their pre-competition warm-up, but conduct performance within 15 min of their warm-up to elicit maximal gains

Diffusion of chemically reactive species in third grade fluid flow over an exponentially stretching sheet considering magnetic field effects

This article addresses the magnetohydrodynamics(MHD) flow of a third grade fluid over an exponentially stretching sheet. Analysis is carried out in the presence of first order chemical reaction. Both cases of constructive and destructive chemical reactions are reported. Convergent solutions of the resulting differential systems are presented in series forms. Characteristics of various sundry parameters on the velocity, concentration, skin friction and local Sherwood number are analyzed and discussed.

Mixed convection stagnation-point flow on vertical stretching sheet with external magnetic field

The problem of steady laminar magnetohydrodynamic （MHD） mixed con- vection stagnation-point flow of an incompressible viscous fluid over a vertical stretch- ing sheet is studied. The effect of an externally magnetic field is taken into account. The transformed boundary layer equations are solved numerically by using an implicit finite-difference scheme. Numerical results are obtained for various values of the mixed convection parameter, Hartmann number, and Prandtl number. The effects of an exter- nally magnetic field on the skin friction coefficient, local Nusselt number, velocity, and temperature profiles for both A 〉 1 and A ~ 1, where A is the velocity ratio parameter, are presented graphically and discussed in detail. Both assisting and opposing flows are considered, and it is found that dual solutions exist for the opposing flow.

Analytic solution for magnetohydrodynamic boundary layer flow of Casson fluid over a stretching/shrinking sheet with wall mass transfer

In this analysis,the magnetohydrodynamic boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet in the presence of wall mass transfer is studied.Using similarity transformations,the governing equations are converted to an ordinary differential equation and then solved analytically.The introduction of a magnetic field changes the behavior of the entire flow dynamics in the shrinking sheet case and also has a major impact in the stretching sheet case.The similarity solution is always unique in the stretching case,and in the shrinking case the solution shows dual nature for certain values of the parameters.For stronger magnetic field,the similarity solution for the shrinking sheet case becomes unique.

Hydromagnetic Nanofluid Film Flow over a Stretching Sheet with Prescribed Heat Flux and Viscous Dissipation

Thermal radiative heat transfer through a thin horizontal liquid film of a Newtonian nanofluid subjected to a magnetic field is considered.The physical boundary conditions are a variable surface heat flux and a uniform concentration along the sheet.Moreover,viscous dissipation is present and concentration is assumed to be influenced by both thermophoresis and Brownian motion effects.Using a similarity method to turn the underlying Partial differential equations into a set of ordinary differential equations(ODEs)and a shooting technique to solve these equations,the skin-friction coefficient,the Nusselt number,and the Sherwood number are determined.Among other things,it is shown that large values of the thermal radiation heat transfer rate,thermal conductivity parameter,and the Brownian motion parameter can enhance the cooling of the sheet.

Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect

Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work.With the reservation of the axial nonlinear strain,there are more coupling terms for axial and transverse deformations.The discretized dynamic governing equations are obtained by using the finite element method and Lagrange’s equations of the second kind.Time responses are conducted to compare the proposed model with other previous models.The stretching deformation due to rotating motion is observed and calculated by special formulations under dynamic equilibrium.The stretching deformation and the change of the associated equilibrium position are taken into account to analyze the free vibration and frequency response of the rotating beams.Analytical and numerical comparisons show that the proposed model can provide reliable results,while the previous models may lead to imprecise results,especially in high-speed conditions.

Coherent Chemical Variation Trends of the 55-25 Ma Magmatic Rocks in SE Tibet:N-S Direction Lithospheric Stretching of Eurasia during Early Stage of India-Eurasia Collision

The progressive indentation of India into Eurasia generated an E-W-trending orthogonal collision belt and a N-S-trending oblique collision belt.Compiling available data reveals that~70%of the Cenozoic igneous rocks in eastern and southeastern Tibet are concentrated within an ENE-trending,~550-km long and~250-km wide magmatic zone(CMZ)that once separated the orthogonal and oblique collision belts.The Latitude 26°N Line is now its southern boundary.The onset timing of magmatism of the CMZ varies gradually from~55 Ma in the westernmost part to~27 Ma in the easternmost.Then the magmatism successively occurred and suddenly stopped at~25 Ma.The segmented and coherent chemical variation trends found suggest that the CMZ magmatic rocks were formed due to partial melting of the heterogeneous upper mantle and crusts of Eurasia.Subduction of Paleo-and Neotethyan oceanic plates generated this compositional and mineralogical heterogeneity.Combined with available geophysical data,the CMZ was diachronously formed in response to asthenosphere upwelling induced by NNW-SSE-direction lithosphere stretching.The difference in responses of the orthogonal and oblique collision belts to the indentation of the Indian continent has led to this lithosphere stretching.

Influence of Thermophoresis and Brownian Motion of Nanoparticles on Radiative Chemically-Reacting MHD Hiemenz Flow over a Nonlinear Stretching Sheet with Heat Generation

In this study,a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered.Using a similarity method to reshape the underlying Partial differential equations into a set of ordinary differential equations(ODEs),the implications of heat generation,and chemical reaction on the flow field are described in detail.Moreover a Homotopy analysis method(HAM)is used to interpret the related mechanisms.It is found that an increase in the magnetic and velocity exponent parameters can damp the fluid velocity,while thermophoresis and Brownian motion promote specific thermal effects.The results also demonstrate that as the Brownian motion parameter is increased,the concentration values become smaller.

The Effects of Thermal Radiation and Viscous Dissipation on the Stagnation Point Flow of a Micropolar Fluid over a Permeable Stretching Sheet in the Presence of Porous Dissipation

In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.

Axisymmetric magnetohydrodynamic flow of micropolar fluid between unsteady stretching surfaces

This investigation examines the time dependent magnetohydrodynamic （MHD） flow problem of a micropolar fluid between two radially stretching sheets. Both strong and weak concentrations of microelements are taken into account. Suitable transformations are employed for the conversion of partial differential equations into ordinary differential equations. Solutions to the resulting problems are developed with a homotopy analysis method （HAM）. The angular velocity, skin friction coefficient, and wall couple stress coefficient are illustrated for various parameters.

Influences of Marangoni convection and variable magnetic field on hybrid nanofluid thin-film flow past a stretching surface

Investigations on thin-film flow play a vital role in the field of optoelectronics and magnetic devices.Thin films are reasonably hard and thermally stable but quite fragile.The thermal stability of a thin film can be further improved by incorporating the effects of nanoparticles.In the current work,a stretchable surface is considered upon which hybrid nanofluid thin-film flow is taken into account.The idea of augmenting heat transmission by making use of a hybrid nanofluid is a focus of the current work.The flow is affected by variations in the viscous forces,along with viscous dissipation effects and Marangoni convection.A time-constrained magnetic field is applied in the normal direction to the flow system.The equations governing the flow system are shifted to a non-dimensional form by applying similarity variables.The homotopy analysis method is employed to find the solution to the resultant equations.It is noticed in this study that the flow characteristics decline with augmentation of magnetic,viscosity and unsteadiness parameters while they increase with enhanced values of thin-film parameters.Thermal characteristics are supported by increasing values of the Eckert number and the unsteadiness parameter and opposed by the viscosity parameter and Prandtl number.The numerical impact of different emerging parameters upon skin friction and the Nusselt number is calculated in tabular form.A comparison of current work with established results is carried out,with good agreement.