Increasing Schmidt Number Research Articles

Thermal study of MHD hybrid nano fluids confined between two parallel sheets: Shape factors analysis

This article discusses the heat and air transfer characteristics of stable magnetohydrodynamic nanofluid flow between two interconnected sheets under the influence of a magnetic field. The nanofluid is a mixture of equal proportions of ethylene glycol and water. This study examined hybrid nanoparticles containing multi-walled carbon nanotubes (MWCNT) and silver (Ag). This research presents, for the first time, a new method for solving nonlinear equations using HPM Python and AGM Python. In addition, the symbolic solution to HPM and AGM has been attained by employing SymPy and SciPy libraries in Python. The results are presented graphically by comparing them with the fourth-order Runge-Kutta number. The final results reflect a high level of agreement between the analytical and numerical methods on the one hand and HPM Python and AGM Python on the other hand. This examination also investigates the effect of various parameters, including magnetic properties, viscosity coefficients, thermophoretic parameters, Brownian parameters, and nanofluid parameters such as velocity, temperature, and concentration. The results prove that velocity and concentration increase as the magnetic field decreases, whereas the temperature displays an opposite trend. As the Schmidt number increases, both the Nusselt number and concentration decrease. The relationship between concentration and temperature with respect to the Prandtl number indicates that when the Prandtl number decreases, the temperature increases while the concentration declines. It is important to note that the employment of hybrid nanofluids leads to an increase in velocity, temperature, and concentration.

Unsteady magnetohydrodynamic bioconvection Casson fluid flow in presence of gyrotactic microorganisms over a vertically stretched sheet

The free convective, unsteady, two-dimensional (2D) magnetohydrodynamic (MHD) Darcy–Forchheimer Casson fluid flow via a vertical stretching sheet containing gyrotactic microorganisms was the novel aspect of this investigation. We rewrote the collection of partial differential equations (PDEs) as nonlinear ordinary differential equations (ODEs) by considering an appropriate similarity variable. We solved the overhaul of nonlinear ODEs using MATLAB’s bvp4c approach. This study rigorously investigates the significance of gyrotactic microorganisms for Casson fluid motility. Additionally, this work investigates the impact of various parameters, including magnetic parameters, thermophoresis, Brownian motion, and radiation parameters, on temperature, motile microorganisms, velocity, and concentration profiles. We use graphs to illustrate the outcomes of various fluid flow parameters. Numerical tables display the effects of different parameters on skin friction, Sherwood number, Nusselt number, and the quantity of motile microorganisms. The unsteady parameter causes a drop in the velocity, temperature, concentration, and the density profile of microorganisms. Additionally, the Casson parameter leads to a decrease in the flow profile, while simultaneously increasing the heat, concentration, and microorganism density profiles. The microorganism density profile decreases as the bioconvection Schmidt number, Peclet number, and motile microbe parameter increase. We deem the new results extremely satisfactory when compared to earlier research. The fields of environmental remediation, biomedical sciences, and engineering may find this examination useful.

Soret Effect of Unsteady Parabolic Flow Past an Accelerated Vertical Plate with Constant Temperature and Mass Diffusion in t he Presence of Rotation

Objective: Circular force's detrimental effects on inhomogeneous parabola circulation over an upright slab that rapidly accelerates in uniform temperature and continuous mass dispersion are discussed. There is no electrical conductivity in the liquid in question. Methods: The solutions for the temperature, concentration, and velocity profiles were identified through the Laplace transformation methodology. Findings: Graphical drawings displaying several specifications, include the acceleration parameter, Schmidt value, Soret value, Hartmann number, thermal Grashof number are used to illustrate the results that were obtained. It is noted that as the values - thermal Grashof number -increase, speed also increases. Regarding Schmidt and Prandtl numbers, the tendency is the opposite. Novelty: The unique aspect of this work is its thorough analysis of the Soret Effect in an erratic, rotating, parabolic flow past an accelerating vertical plate with mass diffusion and constant heat. The work closes gap in the literature by addressing these particular conditions and offers insightful conclusions and useful techniques that may be used to a variety of scientific and engineering issues. This study investigates the impact of rotating effects and Soret impact on erratic convective movement in a vertical plate. Results show that Schmidt number and wall thickness increase over time, while temperature patterns rise with increasing Sr and Sc levels. The Prandtl number depends on air and water temperatures. The study fills a literature gap and provides valuable insights for various scientific and practical applications. Keywords: Soret effect, Turning, Mass dissemination, Parabolic, Vertical surface

Analysis of MHD third-grade hybrid nanofluid model in Darcy-Forchheimer porous medium: Evaluation of the thermal performance of [formula omitted]-[formula omitted] cylindrical nanoparticles dispersed in ethylene glycol fluid

Researchers and scientists became interested in the newly developed idea of hybrid nanofluids because of their exceptional thermal conductivities, which resulted in enhanced thermal performance. These fluids have a wide range of uses in the industrial and technical fields. This novel class of fluids is playing a vital role in solar energy, automotive industry, cooling of the machine and manufacturing, heating and ventilation systems, electronic cooling, nuclear systems cooling, biomedical fields, space, ships, and defense systems. In light of the physical significance of the above-mentioned class of fluids, the current investigations are carried to examine the thermal performance of the mixture of cylindrical shaped aluminum oxide Al2O3 and copper Cu nanoparticles suspended in ethylene glycol using third-grade non-Newtonian fluid flow model. The fluid flow is induced by the stretching of the permeable sheet in exponential manner that is embedded in a Dacry-Forchheimer porous medium. The effects of Lorentz force applied normal to the flow and suction impacts have been incorporated in the current proposed model. The solutions of the flow model transformed to ordinary differential equations are computed using MATLAB built-in solver bvp4c. The solutions are presented in graphical representations. Graphical solutions reflect that fluid velocity slows down by growing the volume fractions of the nanoparticles. Increasing values of viscoelastic parameters reflect that there is a reduction in velocity and intensification in profiles of temperature and concentration have been noted. Rising values of cross-diffusion parameter is leading to the reduction in magnitude of velocity, and augmenting behavior of temperature and concentration has been seen. Observations indicate rising third-grade fluid parameter and porosity parameter lead to reduction in velocity. Increasing Schmidt number gives reduced Sherwood number, and magnetic field parameter improves the rate of hear transfer (Nusselt number) and skin friction coefficient for both Al2O3/ethylene glycol nanofluid and Al3O3-Cu/ethylene glycol-based hybrid nanofluid. The suggested model's validity is confirmed through comparison with previously released findings. Additionally, a grid independence test (sensitivity analysis) has been performed to verify the accuracy and verification of the numerical model.

Double diffusive mixed convective flow over a wedge and cone in the presence of Brownian diffusion and thermophoresis parameter

The present article examines the double diffusion mixed convective nanofluid flow over a wedge and cone in which slip effects as Brownian motion and the thermophoretic parameter are considered. Mixed convective flow over wedges and cones is applied in different technical fields such as fiber technology, nuclear cooling systems, surface treatment, spray deposition techniques, and polymer production. Double diffusion is increasingly significant in scientific fields like astronomy, geosciences, oceanography, and chemical processes. Mixed convection occurs in several applications such as electric devices, solar panels, nuclear power plants, heat exchangers, radiators, and atmospheric boundary layer fluxes. The governing equations of the study are highly coupled nonlinear partial differential equations with surface constraints. The process of similarity transformation used to converts partial differential equations into nondimensional ordinary differential equations, which can be resolved using the MATLAB Bvp5c function. The graphical representation and detailed analysis of variations in velocity, temperature, and concentration distributions of nanofluids are presented. As the mixed convection parameter increases, the fluid’s velocity rises, with a more pronounced effect observed in the cone compared to the wedge. As the Brownian diffusion parameter grows, the fluid temperature increases, and velocity is more pronounced in the wedge scenario compared to the cone. Moreover, an increase in the thermophoresis parameter results in an elevation in the fluid’s temperature. Additionally, the wedge has a higher concentration of fluid and nanoparticles compared to the wedge. Fluid concentration falls with increasing Schmidt number, but fluid nanoparticle concentration decreases with increasing Lewis number.

Influence of Chemical and Radiation on an Unsteady MHD Oscillatory Flow using Artificial Neural Network (ANN)

This paper delves into the intricate interplay between chemical and thermal radiation in the context of an unstable magnetohydrodynamic(MHD) oscillatory flow through a porous medium. The fluid under investigation is presumed to be incompressible, electrically conductive, and radiating with the additional influence of a homogeneous magnetic field applied perpendicular to the channel’s plane. Analytical closedform solutions are derived for the momentum, energy, and concentration equations providing a comprehensive understanding of the system’s behavior. The investigation systematically explores the impact of various flow factors, presenting their effects through graphical representations. The governing partial differential equations (PDE) of the boundary layer are transformed into a set of coupled nonlinear ordinary differential equations (ODE) using a closed-form method. Subsequently, an artificial neural network (ANN) is applied to these ODEs, and the obtained results are validated against numerical simulations. The temperature profiles exhibit oscillatory behavior with changes in the radiation parameter (N), revealing insights into the system’s dynamic response. Furthermore, the paper uncovers that higher heat sources lead to increased temperature profiles. Additionally, concentration profiles demonstrate a decrease with escalating chemical reaction parameters, with a reversal observed as the Schmidt number (Sc) increases. This study highlights the efficacy of an ANN model in providing highly efficient estimates for heat transfer rates from an engineering standpoint. This innovative approach leverages the power of artificial intelligence to enhance our understanding of complex fluid magnetohydrodynamics and porous media flows.

Numerical comparison of nonlinear thermal radiation and chemically reactive bio-convection flow of Casson-Carreau nano-liquid with gyro-tactic microorganisms: Lie group theoretic approach

The current research presents a mathematical model to study the flow of a non-Newtonian magnetohydrodynamics (MHD) Casson-Carreau nanofluid (CCNF) over a stretching porous surface, considering mass and heat transport rates with Stefan blowing, non-linear thermal radiation, heat source-sink, chemical reaction, thermophoretic and Brownian motions, convective heating, Joule heating, motile microorganisms, and bio-convection. The presence of microorganisms is utilized to control the suspension of nanomaterials within the nanofluid. The current flow model has been rendered by the boundary layer approximation and we get the highly nonlinear partial differential equations (PDEs). These nonlinear PDEs are simplified by the novel Lie group theoretic method. The one-parameter Lie scaling method simplified the PDEs and convert it into the ordinary differential equations (ODEs). Numerical solutions for these ODEs are obtained using the bvp4c scheme built-in function in MATLAB, ensuring reliable outcomes for temperature, velocity, concentration, and motile microorganism density profiles. The numerical results are presented through graphs and compared with available data, showing good agreement. These numerical outcomes reveal several important flow characteristics. Rates of change for Nr are 0.0007 and 0.0005, and for Ω, they are −0.0754 and −0.0536, respectively. Similarly, the rate of change for Rb in both models is −0.002 and −0.0002. Analysis shows a positive impact of the bioconvection Rayleigh number in both models, notably higher for the Casson fluid compared to the Carreau fluid model. Buoyancy ratio parameter exhibits consistent rates of change, while the reduction in impact is more pronounced for the Casson fluid model in the case of the mixed bioconvection parameter. The mixed bio-convection parameter reduces momentum velocity for both Casson and Carreau fluids, whereas the Darcy parameter boosts fluid velocity. As the Newtonian heating parameter increases, the temperature velocity distribution of both fluids also increases. The concentration profile of both Casson-Carreau fluid phases declines as the heat source-sink parameter and Schmidt number increase. Microbial velocity shows a decrease with increasing R values, whereas the opposite trend is observed for the Peclet number Pe.

Numerical investigation of mixed convective Williamson nanofluid flow over a stretching/shrinking wedge in the presence of chemical reaction parameter and liquid hydrogen diffusion

The numerical simulation of mixed convective Williamson nanofluid flow over a stretching/shrinking wedge with chemical reaction parameters and liquid hydrogen diffusion is studied. The usage of Williamson fluid in industry has had a considerable impact on industrial processes. Chemical reactions substantially impact heat and mass transfer in hydrometallurgical industries and chemical technology. The governing equations of the inquiry are nonlinear partial differential equations with surface constraints. The similarity transformation transforms partial differential equations into nondimensional ordinary differential equations that may be solved with the MATLAB bvp5c function. Variations in nanofluid velocity, temperature, and concentration patterns are graphically represented and thoroughly examined. In the case of a stretching/shrinking wedge, the liquid velocity decreases as the Williamson nanofluid parameter values increase. The dual nature solution for the skin friction coefficient is obtained when the Williamson nanofluid parameter increases. The liquid’s temperature rises proportionately to the thermophoresis and Williamson nanofluid parameters. As the Schmidt number increases, the fluid concentration improves while the chemical reaction parameter decreases.

Non-similar analysis of bio-convective micropolar nanofluid flow including gyrotactic microorganisms across a stretched geometry

This study explores the novel interaction of gyrotactic microorganisms within a two-dimensional bioconvective micropolar nanofluid flow along a stretched surface, employing the Tiwari-Das nanofluid model. Uniquely, blood is modeled as a micropolar fluid incorporating titanium dioxide ( Ti O 2 ) and silver ( Ag ) nanoparticles. The analysis incorporates influential factors such as viscous dissipation, magnetic field, and heat source effects. By converting the control system into dimensionless nonlinear coupled differential equations, a complete understanding of the system is attained through the application of the local non-similarity approach and bvp4c (MATLAB tool). Particularly, the study provides valuable insight into the influence of dimensionless control parameters on key profiles such as velocity, microrotation, temperature, concentration, and microbial profiles. The findings show that temperature, microrotation, and velocity profiles are all improved by raising the values of micropolar parameters. Furthermore, the microbe profile shows an inverse connection with the Lewis number and a positive association with the Peclet number, whereas the concentration profile declines with increasing Schmidt number values. Furthermore, the study provides a quantitative analysis through tables, revealing variations in the drag coefficient and Nusselt number. This innovative exploration sheds light on the unique behavior of micropolar bioconvective nanofluids, offering valuable contributions to the field of fluid dynamics and bioengineering.

A Numerical approach of activation energy and gyrotactic effects on MHD Carreau Nanofluid flow over plate, wedge and stagnation point

This study numerically investigates the steady two-dimensional flow of a Carreau nanofluid with activation energy and motile microorganisms over a plate, wedge and stagnation point. The effects of the magnetic field, the Brownian motion, the viscous dissipation and the thermophoresis examined for both shear-thinning and the shear-thickening fluids. The similarity transformations are implemented to convert the governing equations into a non-dimensional form for easier analysis. The Runge–Kutta Method and the shooting technique are employed for finding numerical solutions using MATLAB plot form. The obtained numerical results were analyzed for a broad spectrum of dimensionless parameters and are discussed through graphs. These encompass 0.1≤M≤0.4,0.2≤We≤0.8,0.1≤S≤0.4,0.1≤Ec≤0.4,5≤Sc≤20,0.01≤R≤0.04,1≤Nb≤4,0.1≤Nt≤0.4,0.1≤Pe≤0.4,0.01≤Pr≤2and 1≤Ec≤2.5. These ranges were explored concerning velocity, temperature, concentration, diffusion, wall frictional factor and heat transfer rate, both through numerical computations and graphical representations. A decreasing trend in profiles is observed except for velocity, as the magnetic field parameter increases. The flow over a plate exhibits lower skin friction, heat transfer, mass transfer and gyrotactic microorganism compared to other geometries. The Brownian motion leads to a decreased nanoparticle concentration and motile microorganism density, while increasing thermophoresis has the opposite effect. The suction/injection parameter increases fluid velocity but decreases the temperature, the concentration and the motile microorganism density. The shear-thinning nanofluids demonstrate higher rates of the heat transfer, the mass transfer and the motile microorganism compared to shear-thickening fluids. Furthermore, the present analysis demonstrates that as the Peclet number and bioconvective Schmidt number increase, there is a corresponding decrease in microorganism concentration. Additionally, the higher activation energy E is found to enhance the concentration field due to the reduced chemical reaction rates.

Modelling heat-mass transport for MHD Eyring-Powell hybrid nanofluid over an expanding surface laden by autocatalytic chemical reaction and nanoparticles diffusion

Prior hybrid nanofluid research is restricted to single or two-phase models, which were dominated by homogeneous nanofluid models. These models adhere a serious flaw with the heat-mass transfer indices. To handle this problem, we develop an entirely novel hybrid nanofluid models based on the fundamental slip mechanisms of nanofluids induced by Brownian and thermophoretic diffusion as well as the chemical reaction of binary species. The laminar flow of MHD rheological model with suspended nanoparticles is striking at the stagnation region laden over a stretching surface. In order to reach the real world scenario, the expression of radiative heat, non-uniform heat source and frictional heating are all included. The coupled Buongiorno's model and Tiwari-Das mixtures models incorporate the effect of particles diffusion and volumetric friction, respectively. It is hypothesized that first order kinetics can describe homogeneous events in the immediate proximity, while isothermal cubic autocatalysis kinetics frequently describe heterogeneous reactions occur on the sheet surface. The restructured mathematical equations are solved with a proficient Runge Kutta Fehlberg technique together with the shooting procedure. According to the outcomes, the presence of higher magnetic field diminished the flow and velocity gradient. The effect of elastic parameters is diminishing frictional coefficient. The effect of first and second Brownian (Nb1, Nb2) and thermophoretic parameters (Nt1, Nt2) are similar for temperature. The mass-heat transfer rate is significant with higher estimations of diffusivity ratio Nbt. The momentum rate of diffusion outweighs the species diffusion rate as the Schmidt number increases, resulting in a decrease in concentration values. Higher intensities of Lorentz's force results in denser streamlines. The streamlines split into an opposite direction because of stagnation point.

Development of an automated reliable method to compute transport properties from DPD equilibrium simulations: Application to simple fluids

Dissipative particle dynamics (DPD) is a promising candidate technique for modeling rheological properties of soft matter systems. However, several methodological issues inhibit its exploitation as a computational rheology tool. In this work, we focus on the development of an automated method to compute transport properties from equilibrium simulation with particular attention to the assessment of the Green-Kubo approach reliability and computational feasibility for a large set of simple DPD systems with increasing Schmidt number. Furthermore, we investigate the time step size dependency of dynamic properties and the role of different time integration schemes. In particular, we assess the performance of the Shardlow-splitting algorithm against the most popular modified velocity-Verlet algorithm. We consider, for the first time, application of the Shardlow-splitting algorithm to the transverse DPD thermostat in different friction regimes relying on systematic numerical experiments. In addition, we make use of these findings to perform a multi-parametric study aiming to investigate the Schmidt number relationship with the effective friction coefficient.

Schmidt-number effects on the flow past a sphere moving vertically in a stratified diffusive fluid: Revisited

The effects of the Schmidt number (Sc) on the flow past a sphere descending in a stratified fluid are investigated using high-resolution numerical simulations over a wide range of Sc(0.7≤Sc≤2000). The results indicate that the buoyant jet appearing above the sphere is strongly influenced by density diffusion as well as buoyancy, and it becomes stronger and thinner with increasing Schmidt number. Scaling laws are derived and validated for the radius of the buoyant jet and thickness of the density boundary layer on the sphere. The former, characterized by significant density diffusion, is proportional to Fr/(ReSc), where Re[=W*(2a*)/ν*] is the Reynolds number and Fr[=W*/(N*a*)] is the Froude number (a* is the radius of the sphere, W* is the descending velocity of the sphere, ν* is the kinematic viscosity of the fluid, and N* is the Brunt–Väisälä frequency). The latter is similar to that of the passive scalar with a high Schmidt number (∝Re−1/2Sc−1/3), but a better estimate Re−1/2Fr1/4Sc−3/8 can be obtained by assuming a balance between buoyancy and viscous forces in the velocity boundary layer.

Thermodynamical study of chemically-reactive and thermal-radiative magnetized oscillatory Couette flow in a porous medium filled channel

The thermodynamical study of a mathematical model of unsteady natural convective MHD oscillatory flow through a porous medium-filled channel of infinite plates with chemical reaction and thermal radiation effect is taken into account in this respective research. The time-dependent flow governing equations (PDEs); comprises momentum, energy and concentration equations are derived for the concerned physical model and converted into dimensionless second-order ordinary differential equations (ODEs) for fluctuation of small amplitude. Further, the set of ODEs is solved by MATLAB's built-in dsolve function. The graphical analysis of fluid velocity, temperature and concentration profiles has been explicated for flow parameters. According to the results, the transient velocity and concentration profiles expand when the chemical reaction parameter and Schmidt number increase, whereas a strong magnetic field retards the transient velocity profile. In addition, the velocity, temperature, and concentration profiles decline whenever the frequency of oscillation is increased. The elucidated flow model and mathematical results are significant to be used in real-life applications, including packed bed reactors, chemical reactors, cooling the towers and rocket engines, designing of heat exchangers, sewage and wastewater treatment, chemical and magnetic filtration, and separation etc.

Effects of Thermal Radiation and Chemical Reaction on Hydromagnetic Fluid Flow in a Cylindrical Collapsible Tube with an Obstacle

The aim of this research is to study the effects of thermal radiation and chemical reaction on hydromagnetic fluid flow in a cylindrical collapsible tube with an obstacle. The fluid flow is governed by continuity, momentum, energy, and concentration equations. Similarity transformation has been used to convert the obtained PDEs into ODEs. The collocation method has been used to numerically solve the ODEs. The method has been implemented in MATLAB using the bvp4c inbuilt function. The effects of the nondimensional parameters on velocity, temperature, and concentration have been presented graphically. Additionally, the skin‐friction coefficient, the Nusselt number, and the Sherwood number have been discussed and are presented in a tabular form. The findings demonstrated that increasing the Reynolds number causes a rise in the fluid temperature and velocity. The fluid velocity decreases as the Hartmann number and the weight of the obstacle increase but increases with increasing Grashof numbers. The temperature of the fluid increases as the radiation parameter, or Eckert number, increases, but decreases as the Prandtl number increases. As the Soret number rises, so do the fluid’s temperature and concentration distribution. With an increase in the unsteadiness parameter, the fluid velocity and the concentration distribution decrease, whereas the opposite is seen in temperature. As the Schmidt number, the concentration Grashof number, and the chemical reaction parameter increase, the fluid’s concentration decreases. There is an increase in skin‐friction coefficient with increasing Prandtl number, Eckert number, Soret number, thermal Grashof number, concentration Grashof number, thermal radiation parameter, Hartmann number, and unsteadiness parameter, while a decrease is observed with increasing Reynolds number. The Nusselt number increases with an increase in the Prandtl number, Eckert number, thermal radiation parameter, Hartmann number, and unsteadiness parameter. A slight decrease in the Nusselt number has been observed with increasing thermal Grashof number. The Sherwood number decreases with increasing Prandtl number, chemical reaction parameter, and thermal radiation parameter but increases with increasing Schmidt number, Eckert number, and Soret number. The research has the potential for a wide range of applications including but not limited to the medical field and other physical sciences.

MATHEMATICAL MODELING OF THERMO-SOLUTAL TRANSPORT IN PULSATING FLOW IN THE HYDROCEPHALUS

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Hydrocephalus is an asymmetric and unusual cerebrospinal fluid flow in the lateral ventricular portions. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. Mathematical models of transport in the hydrocephalus, which constitutes an excess of fluid in the cavities deep within the brain, enable a better perspective of how this condition contributes to disturbances of the CSF flow in the hollow places of the brain. Recent approaches to brain phase spaces reinforce the foremost role of symmetries and energy requirements in the assessment of nervous activity. Thermophysical and mass transfer effects are therefore addressed in this paper to quantify the transport phenomena in pulsatile hydrocephalus CSF transport with oscillating pressure variations that characterize general neurological activity and transitions from one functional state to another. A new mathematical model is developed which includes porous media drag for brain tissue and solutal diffusion (concentration) effects. A classical Laplace transform method is deployed to solve the dimensionless model derived with appropriate boundary conditions. The analysis reveals that with increasing permeability of the subarachnoid space, the CSF velocity is increased, and a significant fluid flux enhancement arises through the brain parenchyma as the pressure of the fluid escalates drastically due to hydrocephalus disorder. Stronger thermal buoyancy (Grashof number) also results in deceleration in the flow. CSF temperature is reduced with progression in time. Particle (e.g. ion) concentration is suppressed with increasing Schmidt number. As heat conduction parameter increases, there is a substantial depletion in CSF velocity with respect to time. Increasing Womersley parameter displaces the CSF velocity peaks and troughs. The present effects are beneficial in determining the thermo-fluidic transport mechanism of the pathological disorder hydrocephalus. Also, the present results are compared with those clinical studies for some cases. We have confirmed that our validity provides a decent justification with the neurological studies.

Impact of exponential form of internal heat generation on water-based ternary hybrid nanofluid flow by capitalizing non-Fourier heat flux model

The flow of fluids containing nanoparticles is important in industrial applications, particularly in nuclear reactors and nuclear system cooling to enhance energy efficiency. In connection to this, the convective boundary layer flow of ternary hybrid nanofluid (water-based graphene-CNT-Silver) flow over a curved stretching sheet with activation energy is investigated in this article. In addition, the non-Fourier heat flux model is taken into account. The use of similarity variables transforms the existing partial differential equations into an ordinary differential equation, which is then numerically solved using the Runge-Kutta-Fehlberg fourth and fifth order (RKF-45) method combined with a shooting approach. The set of graphical results for the significant parameters on thermal, concentration, and velocity profiles is explored. Results reveal that the heat transport in ternary hybrid nanoliquid rises as the thermophoresis and Brownian motion parameters rise. The Biot number influences the thermal profile positively, whereas the increasing Schmidt number and Stefan blowing parameter values reduce mass transport. The curvature parameter has positive impact on skin friction and mass transport rate but negative impact on heat transport rate. The concentration profile rises with increased activation energy parameter, but declines with increased chemical reaction rate parameter.

Heat transfer and double sampling of stratification phenomena in non-Newtonian liquid suspension: A comparative thermal analysis

The heat transfer with double sampling of stratification in magnetized non-Newtonian fluid flow towards inclined stretched surfaces is debated in the presence of first order chemical reaction, stagnation point, thermal radiations, and heat absorption/generation effects. The simultaneous existence of fluid over inclined surfaces results in coupled non-linear differential equations and hence the numerical solution is obtained. For seeking solution, we used the self-coded shooting method along with the Runge-Kutta scheme. We perform comparative analysis for the influence of these flow variables on Jeffrey fluid velocity, Jeffrey fluid temperature, and Jeffrey fluid concentration. For several significant physical domains, such as thermally stratified flow field, non-stratified flow field, chemically reactive, and non-reactive fields, the surface variables namely Nusselt and Sherwood numbers are evaluated. Line graphs and discrete data are used to present the comparison observations. It is observed that the Nusselt number admits direct relation towards temperature stratification parameter for both surfaces and the mass transfer rate increases as the Schmidt number increases. We are trustful that the comparative outcomes on the heat transfer with a double sampling of stratification in non-Newtonian fluid flow towards inclined surfaces will be helpful for readers having affiliation with heat transfer discipline.

Newtonian Heating Effect on Heat Absorbing Unsteady MHD Radiating and Chemically Reacting Free Convection Flow Past an Oscillating Vertical Porous Plate

In this article, we have discussed in detail the effect of Newtonian heating on MHD unsteady free convection boundary layer flow past an oscillating vertical porous plate embedded in a porous medium with thermal radiation, chemical reaction and heat absorption. The governing PDEs of the model together with related initial and boundary conditions have been solved numerically by the finite element method. The dimensionless velocity, temperature and concentration profiles are analyzed graphically due to the effects of key parameters in the concerned model problem. Computed results for the skin friction coefficient, Nusselt number and Sherwood number are put in tabular form. It is observed that the thermal and mass buoyancy effects support the velocity whilst a reverse effect is noticed when the strength of the magnetic field is increased. The velocity and temperature enhances with an increase in the Newtonian heating and thermal radiation whilst a reverse effect is observed with an increase in the Prandtl number and heat absorption parameter. Increasing Schmidt number and chemical reaction parameter tends to depreciate both velocity and concentration. The Newtonian heating, thermal radiation and magnetic field tends to decrease in the skin friction. The Nusselt number increases with increasing Newtonian heating and heat absorption parameters. An increase in the Schmidt number and chemical reaction rate tends to improve the Sherwood number.

Direct numerical simulation of turbulent mass transfer at the surface of an open channel flow

We present direct numerical simulation results of turbulent open channel flow at bulk Reynolds numbers up to 12 000, coupled with (passive) scalar transport at Schmidt numbers up to 200. Care is taken to capture the very large-scale motions which appear already for relatively modest Reynolds numbers. The transfer velocity at the flat, free surface is found to scale with the Schmidt number to the power ‘$-1/2$’, in accordance with previous studies and theoretical predictions for uncontaminated surfaces. The scaling of the transfer velocity with Reynolds number is found to vary, depending on the Reynolds number definition used. To compare the present results with those obtained in other systems, we define a turbulent Reynolds number at the edge of the surface-influenced layer. This allows us to probe the two-regime model of Theofanouset al.(Intl J. Heat Mass Transfer, vol. 19, 1976, pp. 613–624), which is found to correctly predict that small-scale vortices significantly affect the mass transfer for turbulent Reynolds numbers larger than 500. It is further established that the root mean square of the surface divergence is, on average, proportional to the mean transfer velocity. However, the spatial correlation between instantaneous surface divergence and transfer velocity tends to decrease with increasing Schmidt number and increase with increasing Reynolds number. The latter is shown to be caused by an enhancement of the correlation in high-speed regions, which in turn is linked to the spatial distribution of surface-parallel vortices.