Reaction Rate Parameters Research Articles

Multivariate modeling of intrinsic kinetics for gas-solid heterogeneous photocatalytic reaction: A general method for different pollutant-photocatalyst systems

A reactor model that can interpret the effects of multiple variables on photocatalytic performance is crucial to bridging the gap between lab- and commercial-scale reactors. However, there is no explicit expression to simultaneously describe the relationships between reaction rate and operating parameters including initial concentration, flow rate, light intensity, relative humidity, and catalyst dosage. Therefore, this work presents a multivariate reactor model that extensively describes the effects of these quantities on reaction rate. First, the model is developed by resolving the Navier-Stokes equations coupled with the convection-diffusion equations and an improved reaction kinetics expression. Then, the particle swarm optimization (PSO) algorithm is integrated with the numerical simulation of velocity and concentration fields to determine intrinsic kinetic parameters. Subsequently, the multivariate model for NO degradation is experimentally validated. In addition, the versatility of the proposed modeling method is evidenced by the experimental data of different photocatalyst-pollutant systems from literature. The model predictions agree with experimental results well with the R2 values of 0.949–0.995. Furthermore, a CFD simulation is executed to understand the interactive effects of fluid flow, mass transfer, and kinetic reaction to guide reactor optimization. Finally, the model for NO removal using UiO-66-NH2 in the current study outperforms several reported NO removal models with the smallest RMSE of 2.57% and MAPE of 2.74%. It is concluded that the proposed modeling method could successfully predict the performance of different gas-solid or liquid-solid heterogeneous reactions.

MHD Boundary Layer Flow due to an Exponentially Stretching Surface Through Porous Medium with Radiation Effect and Chemical Reaction

In this study, the numerical solutions for an exponentially stretching sheet with radiation effects, chemical reaction and a heat sink is obtained for the problem of MHD boundary layer flow. By using similarity transformation, the PDEs ruling system is converted into an ODEs system. The resulting nonlinear equations governing the flow problem are numerically solved by a successive linearization method (SLM) using MATLAB software. The significance of this paper is to show and compare the results of solving velocity, temperature, and concentration equations in the existence of changes through SLM for presenting it as appropriate and accurate method for solving nonlinear differential equations. Tables with the numerical data are created for comparison and displayed graphically. Analysis and studies of the effects of different parameters are conducted. The numerical values for the local skin friction coefficient, local Sherwood number, and local Nusselt number are tabulated and explained. The study demonstrates that different parameters have a substantial impact on the fluid flow profiles. It was noted that the concentration patterns were impacted by the reaction rate parameter. In addition, it was found that as the magnetic and radiation parameters increase in value, the local heat transfer rate at the surface decreases.

Multilayer neural networks for studying three-dimensional flow of non-Newtonian fluid flow with the impact of magnetic dipole and gyrotactic microorganisms

The current paper explores the three-dimensional flow of an Oldroyd-B liquid with the impact of a magnetic dipole that occurred by stretching a flat surface placed in the plane with a linear velocity variation in two directions containing motile gyrotactic microorganisms. Using proper similarity transformations, the governing equations are reduced into nonlinear coupled ordinary differential equations (ODEs). The ODEs are then solved using Runge–Kutta-Fehlberg (RKF) method. The training, testing, and validation processes are carried out in parallel to adapt neural networks and calculate an approximate solution for the considered model. This helps to reduce the mean square error (MSE) function by Levenberg–Marquardt backpropagation. The efficiency of the suggested backpropagated neural networks methodology has been demonstrated by utilizing outcomes such as MSE, error histograms, correlation and regression. Results reveal that the heat transport augments for increased Biot number values. The mass transport declines for improved chemical reaction rate parameter values. A higher Peclet number will result in a lower motile diffusivity and result in a decline in the micro-organism’s density profile. For the least value of Mu and gradient, better convergence of the findings can be achieved with better network testing and training.

Quantification Method of Mass Transfer Resistance in Cathode Catalyst Layer in PEFC

The quantification method of mass transfer resistance in the cathode catalyst layer (CCL) should be established in order to appropriately evaluate the cell performance. Lots of PEFC research assumes that any resistances in PEFC are in series to reaction resistance. In this study, oxygen and proton transfer resistances in CCL were quantitatively separated from reaction resistance by applying the model where the through-plane mass- transport resistances were parallel to the reaction resistance. In order to evaluate oxygen and proton transfer resistance, a dimensionless cathode isothermal one-dimensional model was applied. The mass transfer resistance in CCL can be quantitatively evaluated by obtaining the value of five dimensionless moduli derived from mass balance. Polarization curves dependency on the oxygen partial pressure and relative humidity (RH) were measured at the temperature of 80 °C. Reaction rate parameters, effective oxygen diffusion coefficient, effective proton conductivity, and oxygen permeance through the ionomer layer were determined.

Heat and mass transfer analysis of assisting and opposing radiative flow conveying ternary hybrid nanofluid over an exponentially stretching surface

Access to dependable and environmentally friendly energy sources is critical to a country's economic growth and long-term development. As countries seek greener energy alternatives, the interaction of environmental elements, temperature, and sunlight becomes more critical in utilizing renewable energy sources such as wind and bioenergy. Solar power has received much attention due to extraordinary efficiency advances. under this context, the present work focus on solar radiation and chemical processes in the presence of modified ternary hybrid nanofluids (THNFs) circulating over an exponentially stretched surface in both aiding flow (A-F) and opposing flow (O-F) circumstances. The primary objective of this investigation is to dive into the complicated dynamics of these structures, which are distinguished by complex interactions involving radiation, chemical reactions, and the movement of fluids. We construct reduced ordinary differential equations from the governing equations using suitable similarity transformations, which allows for a more in-depth examination of the liquid's behavior. Numerical simulations using the Runge–Kutta Fehlberg (RKF) approach and shooting techniques are used to understand the underlying difficulties of these reduced equations. The results show that thermal radiation improves heat transmission substantially under O-F circumstances in contrast to A-F conditions. Furthermore, the reaction rate parameter has an exciting connection with concentration levels, with greater rates corresponding to lower concentrations. Furthermore, compared to the O-F scenario, the A-F scenario promotes higher heat transfer in the context of a modified nanofluid. Rising reaction rate and solid fraction volume enhanced mass transfer rate. The rate of thermal distribution in THNFs improves from 0.13 to 20.4% in A-F and 0.16 to 15.06% in O-F case when compared to HNFs. This study has real-world implications in several fields, including developing more efficient solar water heaters, solar thermal generating plants, and energy-saving air conditioners.

Performance of a pilot-scale BDD reactor by numerical analysis of reaction rate parameters and additional numbers for mass transfers

The performance of a pilot-scale boron-doped diamond (BDD) reactor through a numerical analysis of reaction rate parameters and enhanced mass transfer has been investigated. The main objective of this research is to evaluate the efficiency of the reactor in mineralizing and degrading caffeine as an emerging contaminant. Based on the kinetic mechanisms and mass transport correlations reported in the literature, two reaction rate kinetic models for caffeine degradation are proposed and analyzed. The models consider different electrolytes (NaCl and Na2SO4) and applied current densities. The kinetic fitting process utilizes the gradient-maximal electrochemical approach, together with orthogonal placement methods, fourth-order Runge-Kutta (RK4) methods, and Nelder & Mead methods for optimization of kinetic parameters and spatial discretization of the material balance. Experimental data obtained from a factorial design with four factors and two levels (24) validate the proposed kinetic models. Caffeine degradation is achieved with NaCl and Na2SO4 electrolytes at concentrations of 60 ppm and 100 ppm, respectively. The corresponding applied loads are 1.5 AhL−1 and 3 AhL−1. Na2SO4 exhibits superior performance with a total organic carbon (TOC) removal efficiency of 99.13%, while NaCl achieves 31.47% mineralization. The behavior of caffeine degradation under the operational and scale conditions demonstrates that NaCl, as a support electrolyte, enables controlled charge transfer (current density) during the degradation process. In contrast, Na2SO4 as a support electrolyte introduces a mixed control of charge and mass transfer. The pilot-scale kinetic parameters obtained in this study provide valuable insights into the support electrolyte dynamics and current density dynamics in BDD-based Electrooxidation (EO) systems, particularly in complex matrix applications. Furthermore, the observed electrical consumption supports the potential application of EO as a viable technology for industrial-scale tertiary wastewater treatment, specifically for caffeine removal.

Model Based Comparative Analysis of GDC and YSZ Based Solid Oxide Fuel Cells

Designing solid oxide fuel cell (SOFCs) stacks for transportation applications places new challenges on SOFC architecture and operation with respect to power density, dynamic response, and thermal management. Recent developments in SOFCs with either thin-film yttria stabilized zirconia (YSZ) electrolytes (thickness ≤ 5 μm) or highly conductive, gadolinia-doped ceria (GDC) electrolytes (thicknesses ≥10 μm) enable thigh-power-density stack operation at inlet temperatures well below 700ºC with the potential for using compliant seals and lower cost ferrous interconnect materials. Applications, such as hybridized aircraft engines, can use such SOFC stacks if they meet strict requirements with respect to specific power and thermal management. Highly conductive GDC-based electrolytes offer pathways to high power-density SOFCs at operating temperatures below 650ºC, but the rise in mixed ionic electronic conductivity (MIEC) above 650ºC reduces open circuit voltages and thus fuel cell efficiency [1,2]. This necessitates thermal management to maintain operating temperatures and mitigate thermo-mechanical stresses within an SOFC. Thin-film YSZ electrolytes offer lower power densities below 650ºC, but avoid the penalties associated with MIEC behavior at higher temperatures and therefore reduce the challenges associated with thermal management at high power densities. In this work, a model-based approach is used to compare SOFC stack operation with thin-film YSZ electrolytes and with GDC-based electrolytes for operation on hydrogen and reformate fuels at high-power densities relevant for transportation applications.To calibrate models to experimental cell performance, polarization curves of a commercially available YSZ-based cell operating between 600-750ºC and of a high-power-density GDC cell operating between 500-650ºC are used to fit electrochemical model parameters for both electrolytes. Modeling of the YSZ based cell can neglect electronic charge transfer through the membrane electrolyte, but GDC-cell modeling must account for the multiple charge carriers (ceria polarons and oxygen vacancies) in the electrolyte [3]. Electrochemical parameters for ionic conductivities and electrochemical reaction rate parameters for oxide cathodes and nickel-electrolyte-composite anodes are fit to the experimental polarization data over the broad range of operating temperatures. Global rate expressions to account for internal reforming on the active nickel surfaces of anode are adopted from literature [4,5]. The calibrated cell model for each cell type is adopted to a down-the-channel discretized cell simulation to predict heat loss and temperature gradients at high current densities.This presentation compares GDC- and YSZ-based SOFCs in high power-density applications from fundamental and practical perspectives. The open-circuit voltages for GDC-based cells drops with increasing temperature to about 0.85 V/cell at 650°C which is lower than the Nernst open-circuit voltage of YSZ-based cells (≥ 1.05 V/cell) at similar conditions. Both types of cells can sustain power densities around 1.0 W/cm2 with high excess cathode air ratios ≥ 5 to keep temperature gradients near 10°C/cm. These results show that GDC-based cells support higher power densities at lower cell flow inlet temperatures < 600°C, whereas thin-film YSZ cells provide superior performance at flow inlets that drive cell temperatures > 600°C. Higher stack power densities > 1.0 W/cm2 must be supported by stack designs that alleviate high thermal stresses and allow steeper gradients of temperature. A summary of stack design and operational strategies that meet the stringent requirements of high power-density operation will be presented in the light of the modeling resuls..

Modeling of electrocatalytic hydrogen evolution via high voltage alkaline electrolyzer with different nano-electrocatalysts

An energy system based on water for creating hydrogen energy might be less globally restricted than one that uses the available fossil fuels today. Therefore, creating an efficient catalyst and electrolyzer system is necessary to effectively convert renewable energy into chemical energy (hydrogen). In this study, a model based on kinetic reaction rate parameters is proposed for estimating energy efficiency and energy conversion for hydrogen generation in a high-voltage alkaline electrolyzer. Three complementary models, including the thermal, electrochemical, and thermodynamic, are conducted to forecast the thermal time constant, overall thermal resistance, operating temperature, electrolyzer voltage, energy consumption, and energy loss. To ensure that they can operate directly with renewable energy sources, the modeling was expanded to incorporate hydrogen production at a voltage level of 6 V. The model's various parameters were computed using non-linear regression presented in Engineering Equation Solver (EES) utilizing experimental data gathered in a high-voltage alkaline test rig. From their precursors and coated on Ti substrates, nanoparticles of Ag, TiO2, and Ag + TiO2 are created as electrocatalysts for the production of hydrogen. In comparison with the bare Ti electrode, the results revealed that energy efficiencies of the Ag, TiO2, and Ag + TiO2 electrodes have increased by 23%, 28%, and 28%, respectively. The largest improvement in hydrogen energy conversion achieved with TiO2 electrodes over Ti electrodes was 84%. Thermodynamic-thermal models that were integrated showed that the coated electrodes decreased the thermal energy loss (TΔS) and useable energy (ΔG) simultaneously during the electrolysis process. The electrochemical model demonstrated a strong fit to the data from those experiments, indicating that the coated nanomaterials are the most important factor in increasing the electrolyzer energy efficiency-based production of hydrogen. The models presented in this research offered a practical method for increasing hydrogen energy production and energy conversion using nanomaterial to build effective electrolyzer devices. The models described in this study are appropriate for the dynamic simulation of renewable energy-hydrogen systems. As a result, these models are easily connected to economic theories that account for both financial and operation expenses.

Significance of Arrhenius activation energy and binary chemical reaction in ternary hybrid nanofluid flow over a convectively heated porous curved surface: A passive control strategy

The convective flow of Jeffrey ternary hybrid nanoliquid over a curved stretching sheet, water-based aluminum oxide and graphene nanoparticles and single wall carbon nanotubes had been employed in this work to explore the hydrothermal variation. In the process of modeling the mechanism of mass transfer, activation energy and binary chemical processes are taken into consideration. The expressions of energy and mass are computed with the extra influence of Brownian diffusion and the thermophoresis characteristics. The initial step in evaluating leading equations involves transforming them into dimensionless forms through similarity transformations. To supplement the assessment, a diverse range of graphs and tables are utilized. The exploration and discussion of various parameters and their impact on involved fields are also presented. In ternary hybrid nanoliquids, an increase in thermophoresis and Brownian motion parameters positively impacts heat transfer capacity. The Biot number exhibits a positive influence on heat transport, while the Schmidt number reduces mass transfer. The curvature parameter has a beneficial impact on the heat transmission rate. Furthermore, as the activation energy parameter rises, the mass transport increases, while it decreases as the chemical reaction rate parameter increases.

Non-Newtonian Flow with Heat and Mass Transfer Over a Porous Stretching Sheet Under the Effects of Space Dependent and TGD Heat Sink, Non-Uniform Heat Source and Dissipation of Energy and CGD Mass Diffusion with Suction/Blowing

In the present paper, an analytical study of visco - elastic fluid flow with heat and mass transfer characteristics over a porous stretching sheet has been examined. Heat balance is maintained with space dependent and temperature gradient dependent heat sink/source, viscous dissipation, and non-uniform heat source on the non-Newtonian Walter’s liquid B' model. The mass balance is maintained with chemically reactive species of order I, variable mass diffusivity and concentration gradient dependent mass diffusion. Using similarity transformation technique on the highly non-linear differential equations, several closed form analytical solutions are obtained for non-dimensional temperature and concentration in both PST and PHF cases in the form of confluent hypergeometric (Kummar’s) functions. The effect of permeability parameter, viscoelastic parameter, suction parameter on velocity profiles and various physical fluid situations with different degrees of viscoelasticity, Prandtl number, Eckert number, heat source- sink strength, temperature field are discussed in detail and presented through graphs. Similarly in the mass transfer field the effects of Schmidt number, reaction rate parameters are discussed in detail and presented through graphs.

Effect of variable viscosity on oscillatory heat and mass transfer in mixed convective flow with chemical reaction along inclined heated plate under reduced gravity

Reduced gravity refers to the actual decline in the accelerated motion of gravitation that occurs when a particular fluid comes into contact with another fluid that has different densities as a result of buoyant effects. The reduced gravity mechanism is very affective along the inclined geometries to reduce more gravitational pressure. In comparison to ordinary action of gravity, reduced gravity was reported to demonstrate less heat transfer, which helped to thicken the liquid layers. The main objective of this study is to illustrate the effects of chemical reaction and variable viscosity on oscillatory behavior of heat and mass transfer along an inclined heated plate under reduced gravity. The viscosity of fluid is assumed as a function of temperature. The mathematical model is developed in terms of partial differential equations and converted into steady and oscillating part by using oscillating Stokes conditions. The primitive variable formulation is used to convert steady and oscillating part into convenient form for smooth algorithm. The numerical results are deduced in tables and graphs with the help of FORTRAN and Tecplot 360. The velocity, temperature distribution, concentration profile, oscillatory skin friction, heat transfer and mass transfer are plotted for various governing parameters. The range of parameters has selected according as Prandtl number 0.1≤Pr≤7.0, buoyancy parameter 0<λT,λC<∞, Schmidt number 1.0≤Sc≤6.0, 0.1≤Rg≤8.0 and the choice of reaction rate parameter set the effects of chemical reaction respectively. The results show that the velocity profile increases as viscosity decreases under reduced gravity. It can be seen that temperature profile decreases as reduced gravity increases with lower viscosity. It is noticed that the heat and mass transfer increases with significant amplitude in the presence of reduced gravity and chemical reaction.

Effect of homogeneous chemical reaction on the dispersion of a solute in a three – dimensional flow of a Newtonian liquid through a porous medium

All-Time dispersion of a reactive solute in a Newtonian fluid flow through a Darcy-Brinkman-Forchheimer Porous medium is carried out using the approach of Gill - Sankarasubramanian (1970) and Doshi et al. (1978). The velocity profile of the non - linear porous medium flow equation is solved using the Maclaurin series of two variables. The three - dimensional model brings into the focus the convective and dispersion coefficients. The chemical reaction is assumed to be homogeneous. The chemical reaction is shown to increase the value of the convective coefficient while it decreases with increase in the value of the reaction rate parameter. The effect of the presence of the porous medium is to decrease the flow and hence the convective coefficient. Similar effect of the porous parameter is seen on the dispersion coefficient. The reaction rate parameter and the porous parameter have opposite effect on the mean concentration distribution.

Influence of multi-stratification and multi-slip on the radiative MHD flow of Carreau fluid

In this paper, we scrutinize the impacts of multi-slip with multi-stratification on nanoparticles MHD Carreau fluid flow through a time-dependent stretching sheet with thermal radiation. We obtain the solution upon the application of the Keller-box scheme with an implicit finite-difference scheme. The influence of thermal stratification and concentration stratification is also being measured. The differentce parameters’ influence on the fluid flow is illustrated in diagrams and the quantitative numerical findings are well-argued. For increasing heavier species, fluid index and the reaction rate parameter with Prandtl number [Formula: see text], 10.0 and 15.0 will decrease the concentration of fluid within its boundary limits. Behavior of Weisenberg number on fluid velocity is studied. Moreover, fluid velocity declines as the unsteady parameter rises, while the temperature and concentration significantly decrease. Higher values of solutal and thermal stratification parameters result in decay of velocity and thermal boundary layer thickness while the fluid temperature reflects the opposite behavior.

Impact of Cattaneo–Christov double diffusion theory and Arrhenius pre-exponential factor law on flow of radiative Reiner–Rivlin nanofluid over rotating disk

Reiner–Rivlin nanofluid flow due to rotating disk has significance in manufacturing of computer disks, pumping of liquid metals, spin coating, centrifugal machinery, turbo-machinery, crystal growth and rotational viscometer. In light of such real and relevant industrial applications, this study deals with the numerical investigation of unsteady rotationally symmetric flow of Reiner–Rivlin nanofluid over a stretchable rotating disk. The purpose of this investigation is to explore heat transfer characteristics of Reiner–Rivlin nanofluid subject to radial stretched surface implementable in several thermal systems. For facilitation of heat transport in complex thermal systems, mathematical models, such as Cattaneo–Christov, Buongiorno and nonlinear thermal radiation models, are assumed to be introduced. Runge–Kutta–Fehlberg technique along with shooting method is used for numerical computation of the transformed equations. It is captivating that radial and circumferential velocities decelerate with rise in Reiner–Rivlin and stretching strength parameters, respectively. Amplified thermal relaxation and Reiner–Rivlin parameters led to diminution of wall temperature gradient. Nanoparticle concentration profiles exhibit opposite behavior in response to escalation of activation energy and reaction rate parameters.

Hydrogen photoproduction using Au promoted ZrOx-TiO2 composite catalysts

In this research study, the impact of adding zirconium oxide to titanium oxide-supported gold systems on photocatalytic hydrogen production was analyzed. The activity was evaluated as a function of the zirconium content, with up to 5 mol.% tested under UV, visible light, and sunlight illumination. It was found that the highest activity was achieved with a 1.75 mol.% zirconium oxide, as measured using reaction rate and quantum efficiency parameters under various illumination conditions. The results showed a quantum efficiency close to 1.9% under sunlight, which represents a substantial improvement of over two orders of magnitude compared to the original titanium system. The addition of zirconium influenced the recombination of charge carriers and boosted photoactivity through the interaction between gold and zirconium.

Effect of niobium on the performance of Pd-TiO2 photocatalysts for hydrogen production

A series of catalysts with growing quantities of Niobium were prepared using Pd as co-catalyst and a high surface area titania support. All samples displayed a constant Pd particle size of ca. 4.6 nm and a support where Niobium appears to be present in the pores of anatase without altering the main oxide primary particle size. The activity of the samples in the hydrogen production under UV and visible illumination was tested and measured using the reaction rate and quantum efficiency parameters. The optimum system has a 1 mol. % of Niobium and is particularly akin to profit from sunlight, showing a quantum efficiency value of 2.8%. The physico-chemical analysis of the activity ground unveils a direct correlation between change handling capability of the samples and the optimization of activity.

Comparison Theorems for Stochastic Chemical Reaction Networks

Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to understand the dependence of the stochastic behavior of these systems on the chemical reaction rate parameters. Towards solving this problem, in this paper we develop theoretical tools called comparison theorems that provide stochastic ordering results for SCRNs. These theorems give sufficient conditions for monotonic dependence on parameters in these network models, which allow us to obtain, under suitable conditions, information about transient and steady-state behavior. These theorems exploit structural properties of SCRNs, beyond those of general continuous-time Markov chains. Furthermore, we derive two theorems to compare stationary distributions and mean first passage times for SCRNs with different parameter values, or with the same parameters and different initial conditions. These tools are developed for SCRNs taking values in a generic (finite or countably infinite) state space and can also be applied for non-mass-action kinetics models. When propensity functions are bounded, our method of proof gives an explicit method for coupling two comparable SCRNs, which can be used to simultaneously simulate their sample paths in a comparable manner. We illustrate our results with applications to models of enzymatic kinetics and epigenetic regulation by chromatin modifications.

Investigating to chemically reactive and radiative Darcy/non-Darcy stagnation point flow of ternary composite nanofluids with moderate Prandtl numbers

ABSTRACT In this study, the Darcy or non-Darcy stagnation point flow and thermal analysis of ternary composite nanofluids with modest Prandtl numbers across stretched surfaces that are susceptible to slip or no-slip environments are examined. The concept of non-linear thermal radiation is brought into play. It has been decided to apply non-linear slip. Homogeneous and heterogeneous chemical reactions, or HHCRs, make the flow problem harder to solve. Along with the shooting method, the Runge–Kutta method of the fourth order is an important part of the numerical solution needed for the non-dimensional and non-linear system of partial differential equations. In slip and no slide, both the amplified porosity parameter and the Forchheimer number work to slow down the speed of the fluid. In a medium that may be Darcy or non-Darcy, an increase in the slip parameter causes the fluid velocity and temperature to sputter and stop. When Darcy and non-Darcy media and slip and no-slip conditions are taken into account, surface viscous drag goes down as the strength of the porous matrix goes up, heat transfer rate goes down as the Brinkman number goes up, and mass transfer rate goes up as the homogeneous reaction rate parameter goes up.

Chemical reaction effects on mhd heat and mass transfer of a Jeffrey fluid flow with viscous dissipation and joule heating through a porous stretching sheet

The effect of chemical reaction on heat and mass transfer of a Jeffrey fluid flow with viscous dissipation and joule heating over a porous stretching sheet in the presence of an external magnetic field and internal heat generation or absorption effects are examined. By applying similarity variables, the governing non-linear partial differential equations are converted into nonlinear ordinary differential equations. MATLAB BVP4c approach gets numerical solutions to these equations. The things of several constraints on velocity, temperature, and concentration flow are studied and shown graphically. Moreover, the consequence of system parameters on friction factor, Nusselt, and Sherwood numbers are also investigated and arranged for different values of Jeffrey parameter, reaction rate parameter, magnetic field, Prandtl number, suction parameter, porosity parameter, radiation parameter, internal heat generation or absorption, Eckert number and Schmidt number in tabular form. The findings of this study are very well-acknowledged with current research.

A Computational Scheme for Stochastic Non-Newtonian Mixed Convection Nanofluid Flow over Oscillatory Sheet

Stochastic simulations enable researchers to incorporate uncertainties beyond numerical discretization errors in computational fluid dynamics (CFD). Here, the authors provide examples of stochastic simulations of incompressible flows and numerical solutions for validating these newly emerging stochastic modeling methods. A numerical scheme is constructed for finding solutions to stochastic parabolic equations. The scheme is second-order accurate in time for the constant coefficient of the Wiener process term. The stability analysis of the scheme is also provided. The scheme is applied to the dimensionless heat and mass transfer model of mixed convective non-Newtonian nanofluid flow over oscillatory sheets. Both the deterministic and stochastic energy equations use temperature-dependent thermal conductivity. The stochastic model is more general than the deterministic model. The results are calculated for both flat and oscillatory plates. Casson parameter, mixed convective parameter, thermophoresis, Brownian motion parameter, Prandtl number, Schmidt number, and reaction rate parameter all impact the velocities, temperatures, and concentrations shown in the graphs. Under the influence of the oscillating plate, the results reveal that the concentration profile decreases with increasing Brownian motion parameters and increases with increasing thermophoresis parameters. The behavior of the velocity profile for the deterministic and stochastic models is provided, and contour plots for the stochastic model are also displayed. This article aims to provide a state-of-the-art overview of recent achievements in the field of stochastic computational fluid dynamics (SCFD) while also pointing out potential future avenues and unresolved challenges for the computational mathematics community to investigate.