Reaction Rate Parameters Research Articles

Electrochemical Studies of the Cycloaddition Activity of Bismuth(III) Acetylides Towards Organic Azides Under Copper(I)-Catalyzed Conditions.

Time-dependent monitoring of the reactive intermediates provides valuable information about the mechanism of a synthetic transformation. However, the process frequently involves intermediates with short lifetimes that significantly challenge the accessibility of the desired kinetic data. We report in situ cyclic voltammetry (CV) and nuclear magnetic resonance (NMR) spectroscopy studies of the cycloaddition reaction of organobismuth(III) compounds with organic azides under the copper(I)-catalyzed conditions. A series of bismuth(III) acetylides carrying diphenyl sulfone scaffolds have been synthesized to study the underlying electronic and steric effects of the tethered moieties capable of transannular oxygen O···Bi interactions and para-functionality of the parent phenylacetylene backbones. While belonging to the family of copper-catalyzed azide-alkyne cycloaddition reactions, the reaction yielding 5-bismuth(III)-triazolide is the sole example of a complex catalytic transformation that features activity of bismuth(III) acetylides towards organic azides under copper(I)-catalyzed conditions. Stepwise continuous monitoring of the copper(I)/copper(0) redox activity of the copper(I) catalyst by cyclic voltammetry provided novel insights into the complex catalytic cycle of the bismuth(III)-triazolide formation. From CV-derived kinetic data, reaction rate parameters of the bismuth(III) acetylides coordination to the copper(I) catalyst (KA) and equilibrium concentration of the copper species [cat]eq. are compared with the overall 5-bismuth(III)-triazolide formation rate constant kobs obtained by 1H-NMR kinetic analysis.

RETRACTED: Formation of hydrogen bonding during the Homann flow over a cylindrical disk of variable visco-elastic nano-materials in presence of activation energy

The goal of this study is to deliberate the flow, heat, and mass transfer of Walter's B nanofluid over a cylindrical disk in the existence of a non-uniform heat source/sink. Unsteadiness, fluctuating thermal conductivity, activation energy and binary chemically reactive species are all taken into account. Additionally, momentum, temperature and concentration are expressed with new parameters in the form of combined parameter, Lewis number, activation parameter, temperature difference parameter, Biot number, heat source parameters and reaction rate parameter. Furthermore, the problem is represented applying non-linear PDE's, which are then transformed to ODE's using geometric conditions provided. However, when the momentum equation is exposed to inadequate boundary conditions, the order of the ODE is reduced using the perturbation approach. As [Formula: see text]., it is seen that displacement thicknesses increase and tend to their asymptotic value. For the same increasing values of the viscoelastic parameter, the displacement thickness [Formula: see text] is obtained in reverse trends. With an upward trend, the skin friction f″(0) variation is seen versus the viscoelastic parameter when [Formula: see text] and vice versa for [Formula: see text].

A comparative study of unsteady MHD Falkner–Skan wedge flow for non-Newtonian nanofluids considering thermal radiation and activation energy

Boundary layer flow is very important in many engineering applications, such as thermal padding, oil bed retrieval, percolation, heat exchangers, and geothermal analysis. In this study, we explore unsteady magnetohydrodynamic bioconvective stagnation-point boundary layer flow over a wedge. The heat and mass transfer in Jeffrey and Oldroyd-B nanofluids in the presence of chemical reactions and under radiation effects are considered to develop a system of equations. The governing equations are transformed to a system of ordinary differential equations by employing suitable transformations, and the reduced system of equations is solved using the finite element technique (FEM). The effect of various parameters on the velocity, microrotation, temperature, microbe compactness, and concentration of nanoparticles are determined. The Nusselt number increases with the Brownian motion parameter (Nb) and thermophoresis parameter (Nt). The Nusselt number is higher for elongating wedges than shrinking wedges. The Sherwood number increases with the reaction rate (Ω) and activation energy parameter. A detailed parametric study is carried out, and the results are presented in graphical and tabular forms. The code performance and the exactness of the numerical scheme are verified by comparing our results with those in the literature.

Investigation of Arrhenius activation energy and convective heat transfer efficiency in radiative hybrid nanofluid flow

The global energy need the development and functioning of heat exchangers and thermal systems for the use and resuscitation of thermal energy. Because of the heat transfer enrichment properties of nanoparticles, industries including nuclear reactors, biological sensing, gas sensing, solar synthesis, the chemical industry, and others have considered using nanoparticles in their respective fields to advance the thermal efficiency of normal liquids. In connection with this, we have envisioned a mathematical model that illustrates the flow and radiative heat transfer of a hybrid nanofluid over a curved stretching sheet with the injection/suction and Arrhenius activation energy. A numerical solution is attained using the Runge–Kutta–Fehlberg fourth, fifth-order and the shooting process. The solution is established through the graphs, which explain each profile in terms of involved parameters. Results reveal that the velocity of the liquid decreases as suction upsurges. The heat transfer enhances for rising values of radiation parameter and Biot number for injection and suction cases. The rate of mass transfer decreases for a rise in values of activation energy parameter, but the differing movement is detected for increasing values of chemical reaction rate parameter.

Intra-cardiac transfer of fatty acids from capillary to cardiomyocyte.

Blood-borne fatty acids (Fa) are important substrates for energy conversion in the mammalian heart. After release from plasma albumin, Fa traverse the endothelium and the interstitial compartment to cross the sarcolemma prior to oxidation in the cardiomyocytal mitochondria. The aims of the present study were to elucidate the site with lowest Fa permeability (i.e., highest Fa resistance) in the overall Fa trajectory from capillary to cardiomyocyte and the relative contribution of unbound Fa (detach pathway, characterized by the dissociation time constant τAlbFa) and albumin-bound Fa (contact pathway, characterized by the membrane reaction rate parameter dAlb) in delivering Fa to the cellular membranes. In this study, an extensive set of 34 multiple indicator dilution experiments with radiolabeled albumin and palmitate on isolated rabbit hearts was analysed by means of a previously developed mathematical model of Fa transfer dynamics. In these experiments, the ratio of the concentration of palmitate to albumin was set at 0.91. The analysis shows that total cardiac Fa permeability, Ptot, is indeed related to the albumin concentration in the extracellular compartment as predicted by the mathematical model. The analysis also reveals that the lowest permeability may reside in the boundary zones containing albumin in the microvascular and interstitial compartment. However, the permeability of the endothelial cytoplasm, Pec, may influence overall Fa permeability, Ptot, as well. The model analysis predicts that the most likely value of τAlbFa ranges from about 200 to 400 ms. In case τAlbFa is fast, i.e., about 200 ms, the extracellular contact pathway appears to be of minor importance in delivering Fa to the cell membrane. If Fa dissociation from albumin is slower, e.g. τAlbFa equals 400 ms, the contribution of the contact pathway may vary from minimal (dAlb≤5 nm) to substantial (dAlb about 100 nm). In the latter case, the permeability of the endothelial cytoplasm varies from infinite (no hindrance) to low (substantial hindrance) to keep the overall Fa flux at a fixed level. Definitive estimation of the impact of endothelial permeability on Ptot and the precise contribution of the contact pathway to overall transfer of Fa in boundary zones containing albumin requires adequate physicochemical experimentation to delineate the true value of, among others, τAlbFa, under physiologically relevant circumstances. Our analysis also implies that concentration differences of unbound Fa are the driving force of intra-cardiac Fa transfer; an active, energy requiring transport mechanism is not necessarily involved. Membrane-associated proteins may facilitate Fa transfer in the boundary zones containing albumin by modulating the membrane reaction rate parameter, dAlb, and, hence, the contribution of the contact pathway to intra-cardiac Fa transfer.

Simplification of full homogenized macro-scale model for lithium-ion batteries

A simplified model based on the novel full homogenized macro-scale model (FHM) is proposed to reduce the computational time of the FHM model with trivial loss of fidelity. The simplified FHM model is compared with a simplified model based on the pseudo-two-dimensional (P2D) model. The FHM model is based on the homogenization theory, while the volume averaging technique is the basis of the P2D model. Diffusion Partial differential equations (PDEs) are approximated by ordinary differential equations with time-varying coefficients. The intercalation current and conduction equation are also approximated to develop variants of the simplified model. The diffusion and reaction rate parameters of the FHM model are more accurate at high temperatures than the parameters based on the empirical Bruggeman method, as the FHM model parameters are based on the numerical model of the electrode structure. The simulations results verify that, compared with a similar simplified model based on the P2D model, the proposed simplified FHM model is more accurate at 318 K and higher temperature. The output voltage predicted by the proposed simplified model and the simplified P2D model has a root mean square (RMS) tracking error of 0.6% and 2%, respectively, at 1 C input current and 318 K temperature. The computational time of the proposed simplified model is reduced by 35% compared with that of the FHM model, highlighting its superior performance. Discretization of the model is accomplished using orthogonal collocation.

Synovial Joint Study

The impact of certain separate characteristics, including the porosity parameter, reaction rate parameter, and viscoelastic parameters of steady convective diffusion across a rectangular channel, has been investigated in this article. The model’s momentum and concentration equations were developed using the similarities technique, and the numerically finite volume method was combined with the Beavers and Joseph slip conditions. Various graphs have been used to get insight into various parameters of the problem on velocity and concentration. The cartilage surfaces are assumed to be porous, and the viscosity of synovial fluid varies with hyaluronate (HA) content.

Analysis of a Stagnation Point Flow With Hybrid Nanoparticles over a Porous Medium

The unsteady stagnation-point flow of a hybrid nanofluid over a stretching/shrinking sheet embedded in a porous medium with mass transpiration and chemical reactions is considered. The momentum and mass transfer problems are combined to form a system of partial differential equations, which is converted into a set of ordinary differential equations via similarity transformation. These ordinary differential equations are solved analytically to obtain the solution for velocity and concentration profiles in exponential and hypergeometric forms, respectively. The concentration profile is obtained for four different cases namely constant wall concentration, uniform mass flux, general power law wall con-centration and general power law mass flux. The effect of different physical parameters such as Darcy number (Da-1), mass transpiration parameter (VC), stretching/shrinking parameter (d), chemical reaction parameter (β) and Schmidt number (SC) velocity and concentration profile is examined. Results show that, the axial velocity will decreases as the shrinking sheet parameter increases, regardless of whether the suction or injection case is examined. The concentration decreases with an increase in the shrinking sheet parameter and the chemical reaction rate parameter.

Bioconvection and activation energy dynamisms on radiative sutterby melting nanomaterial with gyrotactic microorganism

Mechanism of pharmaceutical procedures, nuclear reactor cooling, pace technology, thermal insulation, crushing, geothermal reservoirs and enhanced oil recovery involving chemically reactive systems has a significance in mass transport. Additionally, nanofluids with swimming microorganisms have great significance in medicine, cancer therapy, micro fluidics devices and enzyme biosensor. Main focus of present communication is to analyze the impact of melting phenomena and nonlinear chemical reactions aspects on transient bioconvection flow of sutterby nanoliquid with gyrotactic microorganisms and heat source/sink. Additionally, activation energy and nonlinear radiations influences are invoked. Furthermore, a novel revised nanofluid model disclosed by Kuznetsov and Nield is applied to measure heat and mass transport. The basic PDEs embodying the conservation of microorganisms, nanoparticle concentration, energy, momentum and mass are persuaded into highly nonlinear coupled ODEs. Numerical solutions are executed via Runge-Kutta Fehlberg (RK45) scheme for the presence and absence of melting process. Comparative analysis with existing study are performed and reflected in excellent agreement. It is interesting to notice that microorganism field and nanoparticle concentration are depressed due to augmentation of reaction rate parameter for M=0.0 and M=0.5. It is also pointed out that heat transfer rate is better for the case M=0.5 when compared to the case.

RETRACTED: Passive control of nanoparticles in stagnation point flow of Oldroyd-B nanofluid with aspect of magnetic dipole

The present research focuses on nanoparticle suspensions and flow properties in the context of their applications. The application of these materials in biological rheological models has piqued the attention of many researchers. Magneto nanoparticles have an important function in controlling the viscoelastic physiognomies of ferrofluid flows. Having such substantial interest in the flow of ferroliquids our vision is to discuss the stagnation point flow of ferromagnetic Oldroyd-B nanofluid through a stretching sheet. The Buongiorno nanofluid model with Brownian motion and thermophoretic properties is examined. A chemical reaction effect and porous medium is also taken into account. Moreover, the modelled equations are changed to ordinary differential equations (ODEs) using suitable similarity transformations. Which are then solved using classical Runge-Kutta (RK) process with shooting technique. The solutions for the flow, thermal, concentration, skin friction, rate of heat and mass transfer features are attained numerically and presented graphically. The significant results of the current study are that, the growing values of ferromagnetic interaction parameter and porosity parameter declines the velocity profile. The rising values of chemical reaction rate parameter and Brownian motion parameter declines the mass transfer but inverse behaviour is seen for augmented values of thermophoresis parameter.

Effect of Metal Sequestrants on the Decomposition of Hydroxylammonium Nitrate

Hydroxylammonium nitrate (HAN) is an energetic salt used in flight-proven green monopropellants such as ASCENT (formerly AF-M315E), flown in NASA’s 2019 Green Propellant Infusion Mission, and SHP163, flown in JAXA’s Rapid Innovative Satellite Technology Demonstration-1. The decomposition of HAN is catalyzed by metals commonly found in storage tanks, a factor limiting its use. This work investigates the ability of metal-sequestering chelating agents to inhibit the decomposition of HAN. Isothermal and dynamic thermogravimetric analysis (TGA) were used to find isothermal decomposition rates, decomposition onset temperatures, and first-order Arrhenius reaction rate parameters. In the present research, 2,2′-bipyridine (Bipy), triethanolamine (TEA), and ethylenediaminetetraacetic acid (EDTA) were studied as 0.05, 0.1, 0.5, 1, and 5% by weight additives in 90% aqueous HAN. An isothermal decomposition rate of 0.137%/h at 348 K was observed for HAN. The addition of 1% Bipy and 1% TEA reduced the isothermal decomposition rate by 20.4% to 0.109%/h, and by 3.65% to 0.132%/h, respectively, showing that Bipy can inhibit decomposition. The addition of 1% EDTA increased the isothermal decomposition rate by 12.4% to 0.154%/h. Bipy was found to increase the decomposition onset temperature from 454.8 K to 461.8 K, while the results for TEA and EDTA were inconclusive. First order reaction rates calculated by the Ozawa-Flynn-Wall method were found to be insufficient to capture the effects of the tested additives. Bipy was found to inhibit the decomposition of HAN, while TEA and EDTA produced little or negative effect, a result believed to be due to poor metal complex stability at low pH and high acidity, respectively. Spectrophotometry, used for colorimetric analysis of Bipy+iron complexes, showed that Bipy forms chelate complexes with trace iron impurities when added to HAN solutions.

Construction of simplified combustion mechanism of diesel from direct coal liquefaction-PODE3

DDCL (Diesel from Direct Coal Liquefaction) and PODEn (Polyoxymethylene Dimethyl Ethers) are alternative fuels commonly used for Diesel engines. Their blend has close cetane number to diesel fuel. N-dodecane and decalin were selected as model fuels of DDCL. Based on the decoupling method, initial simplified combustion mechanism reaction paths were constructed, and the sensitive reaction rate parameters were optimized by PSO (Particle Swarm Optimization). Then the simplified combustion mechanism of DDCL was constructed by combining the mechanisms of the two fuels, and the NOx mechanism was combined to form the DDCL-PODE3-NOx mechanism. Moreover, the prediction performance of the simplified mechanism was verified via JSR (Jet Stirred Reactor) test, and the results proved that it can provide a reliable prediction of the ignition delay time and species concentration distribution. Eventually, the DDCL simplified mechanism contains 156 components and 617 reactions. The PODE3 mechanism contains 149 components and 597 reactions, and the DDCL-PODE3-NOx simplified mechanism contains 171 components and 642 reactions. Constructing fuel combustion mechanism is the basis of fuel combustion research. Most significantly, the simplified combustion mechanism shows excellent prediction in the basic combustion test data.

The Impact of Cattaneo–Christov Double Diffusion on Oldroyd-B Fluid Flow over a Stretching Sheet with Thermophoretic Particle Deposition and Relaxation Chemical Reaction

The current study focuses on the characteristics of flow, heat, and mass transfer in the context of their applications. There has been a lot of interest in the use of non-Newtonian fluids in biological and technical disciplines. Having such a substantial interest in non-Newtonian fluids, our goal is to explore the flow of Oldroyd-B liquid over a stretching sheet by considering Cattaneo–Christov double diffusion and heat source/sink. Furthermore, the relaxation chemical reaction and thermophoretic particle deposition are considered in the modelling. The equations that represent the indicated flow are changed to ordinary differential equations (ODEs) by choosing relevant similarity variables. The reduced equations are solved using the Runge–Kutta–Fehlberg fourth–fifth order technique (RKF-45) and a shooting scheme. Physical descriptions are strategized and argued using graphical representations to provide a clear understanding of the behaviour of dimensionless parameters on dimensionless velocity, concentration, and temperature profiles. The results reveal that the rising values of the rotation parameter lead to a decline in the fluid velocity. The rise in values of relaxation time parameters of temperature and concentration decreases the thermal and concentration profiles, respectively. The increase in values of the heat source/sink parameter advances the thermal profile. The rise in values of the thermophoretic and chemical reaction rate parameters declines the concentration profile.

Study on MHD Flow over a Stretching Surface with Convective Boundary Condition by Numerical Method

The thermal and mass diffusive MHD flow through a stretching sheet has been inspected in the presence of a chemically reactive solute under convective boundary conditions in the present paper. The non-linear PDEs of the system concerning the flow, temperature, and species are recasted into a set of non-linear ODEs using ST. The consequential system of the differential equations is numerically resolved by using an implicit FDS in combination with the QL technique. The velocity ratio factor plays an important role in reducing the thickness of the velocity boundary layer, whereas the presence of magnetic parameters decreases the thickness of the velocity boundary layer profile. The study reveals that the fluid moves away from the surface during injection, resulting in a fall of the velocity gradient, whereas the opposite effect is observed in suction. The thermal and concentration boundary layer thicknesses are influenced by non-dimensional numbers, namely Prandtl and Schmidt numbers. The reaction rate parameter acts as a decelerating agent, and it thins the solute boundary layer formed in the neighborhood of the sheet. An increase in the convective parameter leads to an increase in the plate surface temperature. The present results of the paper are compared with the existing one, and good agreement is found between them.

Simulating single-cell metabolism using a stochastic flux-balance analysis algorithm

Stochasticity from gene expression in single cells is known to drive metabolic heterogeneity at the level of cellular populations, which is understood to have important consequences for issues such as microbial drug tolerance and treatment of human diseases like cancer. Despite considerable advancements in profiling the genomes, transcriptomes, and proteomes of single cells, it remains difficult to experimentally characterize their metabolism at the genome scale. Computational methods could bridge this gap toward a systems understanding of single-cell biology. To address this challenge, we developed stochastic simulation algorithm with flux-balance analysis embedded (SSA-FBA), a computational framework for simulating the stochastic dynamics of the metabolism of individual cells using genome-scale metabolic models with experimental estimates of gene expression and enzymatic reaction rate parameters. SSA-FBA extends the constraint-based modeling formalism of metabolic network modeling to the single-cell regime, enabling simulation when experimentation is intractable. We also developed an efficient implementation of SSA-FBA that leverages the topology of embedded flux-balance analysis models to significantly reduce the computational cost of simulation. As a preliminary case study, we built a reduced single-cell model of Mycoplasma pneumoniae and used SSA-FBA to illustrate the role of stochasticity on the dynamics of metabolism at the single-cell level.

Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

Highly production of dihydroxystrearic acid from catalytic epoxidation process by in situ peracid mechanism

AbstractEpoxidized vegetable oils are great concern as they are obtained from sustainable, and renewable natural resources. The epoxidation of palm oil‐derived oleic acid was carried out by using in situ generated performic acid to produce epoxidized palm oil‐derived oleic acid. The maximum conversion of palm oil‐derived oleic acid into oxirane was 86% by applying the in situ peracid mechanism. Based on the Fourier‐transform infrared spectrum, the hydroxyl group was observed within a wavenumber range of 1210–1320 cm−1. Last, a mathematical model was developed using Runge–Kutta method and after 100 iterations, the reaction rate parameters were obtained as follows:= 0.046 mol·L−1·min−1,= 39.058 mol·L−1·min−1,= 2.789 mol·L−1·min−1, and= 0.0235 mol·L−1·min−1for of dihydroxystearic acid production.

Numerical modelling of activation energy and hydromagnetic non-Newtonian fluid particle deposition flow in a rotating disc

This mathematical model explains the three-dimensional flow of Casson liquid through a stretchable rotating disk. In momentum equation magnetic effect and in mass equation Arrhenius chemical reaction and activation energy effects are incorporated. The equation which represents the described flow pattern is reduced to ordinary differential equations (ODEs) by using apposite similarity transformations and then they are tackled with the RKF45 method with shooting proficiency. The impact of pertinent parameters on thermal, mass and velocity curves are deliberated graphically. Further statistical values of skin friction, Nusselt number and Sherwood number are portrayed in table format. The result outcome reveals that, increase in the values of a magnetic parameter reduces velocity gradient. The concentration profile declines for augmented values of chemical reaction rate parameter, but a contrasting trend is seen in the concentration gradient for increased values of activation energy. Further, upsurge in thermophoretic and Brownian motion parameter reduces the mass transfer.

Impacts of activation energy and binary chemical reaction on MHD flow of Williamson nanofluid in Darcy–Forchheimer porous medium: a case of expanding sheet of variable thickness

An expanding sheet problem is more relevant when the thickness of the sheet is variable and it bears frequent applications in polymer press, paper production, metallic plate cooling, etc. On the other hand, activation energy is an important phenomenon of chemical reaction in flow dynamics of Newtonian and non-Newtonian fluids. The activation energy and chemical reaction have vital applications in food preparing, the mechanism of water and oil emulsions, chemical engineering, and more. So in this project, the impacts of activation energy and binary chemical reaction on MHD two-dimensional boundary layer flow of Williamson nanofluid on an expanding surface of variable thickness embedded in Darcy–Forchheimer porous medium are investigated. Using suitable transformations, the governing equations are transformed into a set of non-linear ordinary differential equations (ODEs). Later, numerical solutions have been achieved by well-known MATLAB inbuilt function ‘bvp4c’. Several vital results are explored for variations of involved physical parameters and those are presented in graphical and tabular modes. The achieved results suggest that when wall thickness parameter increases, there is a contrast in behaviors of velocity, temperature and nanoparticle concentration if there is a condition that the shape parameter is greater than or less than unity. For the former case, the above flow properties reduce with wall thickness parameter, whereas, for the latter case, those are showing significant growth. The Brownian motion of nanoparticles causes an increase in temperature and a reduction in nanoparticle concentration, whereas due to thermophoretic force, both temperature and nanoparticle concentration rise. Due to the presence of activation energy in chemical reaction, the nanoparticle concentration enhances, while, temperature decreases(increases) near(away from) the sheet. With increasing reaction rate parameters, nanoparticle concentration diminishes, but temperature increases near the sheet. The surface drag force decreases with Williamson fluid parameter, while it increases with the magnetic parameter, inverse Darcy number, and Forchheimer parameter. On the other hand, the surface heat flux and surface mass flux are decreasing functions of Williamson fluid parameter, magnetic parameter, inverse Darcy number, and Forchheimer parameter. It also reveals that surface heat flux reduces with increasing reaction rate parameters, whereas surface mass flux increases. Finally, for the growth of activation energy parameter, initially surface heat flux rises and surface mass flux declines, but for its larger values, the quantities turn out to be constants. Also, the surface heat and mass fluxes are decreasing functions of thermophoresis parameter.

A third-order two-step numerical scheme for heat and mass transfer of chemically reactive radiative MHD power-law fluid

A two-stage third-order numerical scheme is proposed for solving ordinary differential equations. The scheme is explicit and implicit type in two stages. First, the stability region of the scheme is found when it is applied to the linear equation. Further, the stability conditions of the scheme are found using a linearized homogenous set of differential equations. This set of equations is obtained by applying transformations on the governing equations of heat and mass transfer of incompressible, laminar, steady, two-dimensional, and non-Newtonian power-law fluid flows over a stretching sheet with effects of thermal radiations and chemical reaction. The proposed scheme with an iterative method is employed in two different forms called linearized and non-linearized. But it is found that the non-linearized approach performs better than the linearized one when residuals are compared through plots. Additionally, the proposed scheme is compared to the second-order central finite difference method for second-order non-linear differential equations and the Keller-Box/trapezoidal method for a linear differential equation. It is determined that the proposed scheme is more effective and computationally less expensive than the standard/classical finite difference methods. Moreover, the impact of magnetic parameter, radiation parameter, modified Prandtl and Schmidt numbers for power-law fluid, and chemical reaction rate parameter on velocity, temperature, and concentration profiles are displayed through graphs and discussed. The power-law fluid’s heat and mass transfer simulations are also carried out with varying flow behavior index, sheet velocity, and mass diffusivity. We hoped that this effort would serve as a guide for investigators tasked with resolving unresolved issues in the field of enclosures used in industry and engineering.