Heterogeneous Reaction Parameter Research Articles

Homogeneous-heterogeneous reactions in MHD flow due to an unsteady curved stretching surface

This article addresses the homogeneous-heterogeneous reactions effects in magnetohydrodynamic (MHD) flow of viscous fluid flow by a curved stretching surface. Fluid is electrically conducting in the presence of an applied magnetic field. System of ordinary differential equations is obtained by appropriate transformations. Convergent series solutions are computed for the resulting nonlinear differential system. Impact of different parameters on the velocity, temperature and concentration profiles is examined. Computations for pressure, surface drag force and heat transfer rate are presented and examined for the influences of pertinent parameters. It is noted that fluid velocity enhances when curvature parameter is increased. Surface heat transfer rate enhances for larger Prandtl number. Further, the concentration distribution decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter.

Spectral Quasi-linearization Method for Homogeneous-Heterogeneous Reactions on Nonlinear Convection Flow of Micropolar Fluid Saturated Porous Medium with Convective Boundary Condition

Abstract Based on the nonlinear variation of density with temperature (NDT) in the buoyancy term, the mixed convection flow along a vertical plate of a micropolar fluid saturated porous medium is considered. In addition, the effect of homogeneous-heterogeneous reaction and convective boundary condition has been taken into account. Using lie scaling group transformations, the similarity representation is attained for the system of partial differential equations, prior to being solved by a spectral quasilinearization method. The results show that in the presence of aiding and opposing flow situations, both the species concentration and mass transfer rate decreases when the strength of homogeneous and heterogeneous reaction parameters are enhanced.

Effects of homogeneous–heterogeneous reactions in flow of magnetite-Fe3O4 nanoparticles by a rotating disk

This article addresses the flow of ferrofluid due to a rotating disk in the presence of homogeneous–heterogeneous reactions. The disk rotates with constant angular velocity about the z-axis. Water is used as base fluid while magnetite-Fe3 O4 as nanoparticle. Fluid is electrically conducting in the presence of an applied magnetic field. Effects of viscous dissipation are also considered. The disk is kept at uniform temperature while there is ambient temperature away from the disk. In view of the rotational symmetry, the derivatives in the azimuthal direction are neglected. Appropriate transformations reduce the system of nonlinear partial differential equations to system of ordinary differential equations. Convergent series solutions are computed using homotopy analysis method (HAM) for the resulting nonlinear problems. Effects of different parameters on the velocity, temperature and concentration profiles are shown and analyzed. Computations for skin friction coefficient and Nusselt number are presented and examined for the influences of pertinent parameters. It is noted that concentration distribution decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter. Skin friction coefficient and rate of heat transfer are enhanced when the strength of magnetic field is increased.

Unequal diffusivities case of homogeneous–heterogeneous reactions within viscoelastic fluid flow in the presence of induced magnetic-field and nonlinear thermal radiation

This article presents the effects of nonlinear thermal radiation and induced magnetic field on viscoelastic fluid flow toward a stagnation point. It is assumed that there exists a kind of chemical reaction between chemical species A and B. The diffusion coefficients of the two chemical species in the viscoelastic fluid flow are unequal. Since chemical species B is a catalyst at the horizontal surface, hence homogeneous and heterogeneous schemes are of the isothermal cubic autocatalytic reaction and first order reaction respectively. The transformed governing equations are solved numerically using Runge–Kutta integration scheme along with Newton’s method. Good agreement is obtained between present and published numerical results for a limiting case. The influence of some pertinent parameters on skin friction coefficient, local heat transfer rate, together with velocity, induced magnetic field, temperature, and concentration profiles is illustrated graphically and discussed. Based on all of these assumptions, results indicate that the effects of induced magnetic and viscoelastic parameters on velocity, transverse velocity and velocity of induced magnetic field are almost the same but opposite in nature. The strength of heterogeneous reaction parameter is very helpful to reduce the concentration of bulk fluid and increase the concentration of catalyst at the surface.

Impact of Cattaneo-Christov Heat Flux in Jeffrey Fluid Flow with Homogeneous-Heterogeneous Reactions.

Two-dimensional stretched flow of Jeffrey fluid in view of Cattaneo-Christov heat flux is addressed. Effects of homogeneous-heterogeneous reactions are also considered. Suitable transformations are used to form ordinary differential equations. Convergent series solutions are computed. Impact of significant parameters on the velocity, temperature, concentration and skin friction coefficient is addressed. Analysis of thermal relaxation is made. The obtained results show that ratio of relaxation to retardation times and Deborah number have inverse relation for velocity profile. Temperature distribution has decreasing behavior for Prandtl number and thermal relaxation time. Also concentration decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter.

Modeling and analysis for three-dimensional flow with homogeneous-heterogeneous reactions

This work addresses the steady three-dimensional boundary layer flow of Maxwell fluid over a bidirectional stretching surface with homogeneous-heterogeneous reactions. A system of ordinary differential equations is obtained by using suitable transformations. Convergent series solutions are derived by homotopic procedure. Impact of various pertinent parameters on the velocity and concentration is discussed. It is noted that an increase in the Deborah number decreases both the velocity components. Also concentration distribution decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter.

Impact of magnetohydrodynamics in bidirectional flow of nanofluid subject to second order slip velocity and homogeneous–heterogeneous reactions

This paper addresses the steady three-dimensional boundary layer flow of viscous nanofluid. The flow is caused by a permeable stretching surface with second order velocity slip and homogeneous–heterogeneous reactions. Water is treated as base fluid and copper as nanoparticle. An incompressible fluid fills the porous space. The fluid is electrically conducting in the presence of an applied magnetic field. A system of ordinary differential equations is obtained by using suitable transformations. Convergent series solutions are derived. Impact of various pertinent parameters on the velocity, concentration and skin friction coefficient is discussed. Analysis of the obtained results shows that the flow field is influenced appreciably by the presence of velocity slip parameters. Also concentration distribution decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter.

Simultaneous effects of Hall current and homogeneous/heterogeneous reactions on peristalsis

This article first time addresses the effects of homogeneous–heterogeneous reactions on peristaltic transport of third order fluid in a channel with convective boundary conditions. Mathematical modelling and analysis have been carried out in the presence of Hall current and Joule heating. The partial differential equations are constructed using lubrication approach. Results of temperature, heat transfer coefficient and homogeneous–heterogeneous reactions are analyzed for the influential parameters entering into the problems. It is noted that temperature of the fluid decays due to increase in Biot number. Also the effects of Hartman number and Hall parameter are quite opposite on temperature profile. It is worth mentioning that homogeneous and heterogeneous reaction parameters have opposite effects on concentration profile.

Homogeneous-heterogeneous reactions in micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium

Abstract The effects of a homogeneous-heterogeneous reaction on steady micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium are numerically investigated in this paper. The model developed by Chaudhary and Merkin (Fluid Dyn. Res. 16:311-333, 1995) for a homogeneous-heterogeneous reaction in boundary layer flow with equal diffusivities for reactant and autocatalysis is used and extended in this study. The uniqueness of this problem lies in the fact that the solutions are possible for all values of the stretching parameter λ > 0 , while for λ < 0 (shrinking surface), solutions are possible only for a limited range of values. The effects of physical and fluid parameters such as the stretching parameter, micropolar parameter, permeability parameter, Schmidt number, strength of homogeneous and heterogeneous reaction parameter on the skin friction, velocity and concentration are analyzed, and these results are presented through graphs. The solute concentration at the surface is found to decrease with the strength of the homogeneous reaction, and to increase with heterogeneous reactions, the permeability parameter and stretching or shrinking parameters. The velocity at the surface was found to increase with the micropolar parameter.

Computational thermal and kinetic analysis

A software package to determine the non-isothermal kinetic parameters of heterogeneous reactions has been developed. The dynamic handle of conversion degree step and ranges, heating rates and kinetic models makes the evaluation of the activation parameters much faster. The standard procedure: ‘model-free’ kineitc, IKP and Perez-Maqueda et al. methods, is applied for the determination of the kinetic triplet corresponding to thermal induced transformations. The software is designed mainly for thermogravimetric, temperature programmed reduction and dilatometry data processing, but may also import already transformed numeric data.

Kinetic analysis of nonisothermal solid-state reactions: determination of the kinetic parameters by means of a nonlinear regression method

A nonlinear regression method has been proposed for a simultaneous calculation of the activation energy, frequency factor, and reaction order from a single TG curve. This method was based on the new temperature integral approximation proposed in this paper and the Levenberg–Marquardt method. The newly proposed nonlinear regression method was applied for determining the kinetic parameters from two simulated TG curves. The results of the calculations were compared with values obtained by the traditional method. It can be concluded from this comparison that the new nonlinear regression method is more accurate than the traditional method for the determination of the kinetic parameters of solid-state heterogeneous reactions.

Simulation of the kinetics of complex heterogeneous catalytic reactions under diffusion limitations

A method is suggested for determining kinetic parameters of arbitrary complex heterogeneous catalytic reactions under conditions such that the reaction rate is significantly affected by heat and mass transfer to and in the catalyst pellets. Linear relationships are established between the concentrations of the key and dependent reactants (diffusion stoichiometry relationships) and between temperature and the concentrations of the key components. A solution procedure is suggested for the problems involved in the determination of kinetic parameters for reactions proceeding under diffusion limitations. The procedure is illustrated by analysis of data earlier reported for steam methane reforming over a nickel catalyst.

Nonlocal Effects and the Overscreening Effect in the Kinetics of Heterogeneous Charge Transfer Reactions

The effect of the spatial dispersion of the solvent on kinetic parameters of heterogeneous charge transfer reactions is considered by using the (Cp)2Co+/(Cp)2Co (Cp—cyclopentadienyl) reaction as the example and allowing for the effects of overscreening and field penetration into the metal. The calculations are based on an exactly solvable sharp-boundary model of the metal/polar solvent interface. Parameters of the analytical expression used for the dielectric function e(k) of the solvent are selected so as to reproduce the results of calculations of the e(k) function obtained by a molecular dynamics method. Acetonitrile and dimethyl sulfoxide are considered as the solvents. The reorganization free energy infinitely away from the electrode is calculated using a model of a smeared Born sphere for the reactant ion. The smearing parameters are selected so as to obtain the electrostatic part of the solvation free energy of the ion in the solvent bulk. A method of an effective Born sphere for the ion is suggested and substantiated. The method is intended for the description of reorganization and activation free energies near the electrode surface. The reorganization and activation free energies are shown to reduce with the reactant approaching the electrode. Numerical values of these energies are greater than those computed in the classic limit with the Marcus formula and nicely conform to the estimates obtained from experimental data.

Non-local and overscreening effects in the kinetics of heterogeneous charge transfer reactions

The effects of solvent spatial dispersion including the overscreening effect and field penetration into a metal on the kinetic parameters of heterogeneous charge-transfer reactions are studied. The calculations are based on the exactly solvable ‘sharp-boundary model’ of the interface. The analytical expressions derived using the mean-field theory for the phenomenological Hamiltonian of the liquid are adopted for the dielectric function of the solvent. The parameters entering these expressions are chosen to reproduce the results of molecular dynamics computer simulations presented in the literature. We consider the (Cp) 2Co +/(Cp) 2Co electrochemical reaction and acetonitrile (AN) and dimethyl sulfoxide (DMSO) as the solvents. The smeared Born sphere (SBS) model of an ion is used for calculations of the reorganization Gibbs energies at infinite electrode–reactant separation. The extent of the smearing of the ion excess charge is fitted to obtain the electrostatic part of the solvation Gibbs energy of an ion in the bulk of the solvent. The effective Born sphere (EBS) and renormalized smeared Born sphere (RSBS) models of an ion are suggested for calculations of the reorganization and activation Gibbs energies near an electrode. It is shown that the reorganization Gibbs energy and the activation Gibbs energy decrease with decrease of the electrode–reactant separation in accordance with Marcus theory (in which the non-local effects are neglected). However, the reorganization and activation Gibbs energies are found to be larger than those given by the Marcus formula and agree rather well with the estimates obtained from the experimental data.

Influence of Nonlocal Effects on Kinetic Parameters of Heterogeneous Charge Transfer Reactions

The influence of the spatial dispersion of the solvent and of the effect of the electrical field penetration into a metal on the free energy of the solvent reorganization and the activation free energy for heterogeneous charge transfer reactions is studied. The calculations are based on the exactly solved model of a sharp metal/electrolyte interface, the model of a Born sphere for the ion, and the three-mode approximation for the dielectric function of the solvent. In the sharp-interface model, in the case of a mirror reflection, a relationship for the dielectric tensor of a heterogeneous system comprising two contacting media with a plane interface is obtained, along with an expression for the potential created by a point charge. This expression formally coincides with the expression derived earlier by Vorotyntsev and Kornyshev, but it contains true bulk dielectric functions of contacting media. In the model of the Born sphere for the ion and the three-mode approximation for the dielectric function of the solvent, an expression for the potential of image forces, which determines the dependence of the solvent reorganization energy on the distance from the reacting ion to the electrode, is obtained. It is shown that both the reorganization energy and the activation free energy decrease with decreasing distance from the ion to the electrode. The calculation results are compared with estimates of the reorganization energy obtained from experimental data for the reaction Fe3+/Fe2+ and the reaction of the hydronium ion discharge.

A Monte Carlo uncertainty analysis of ozone trend predictions in a two‐dimensional model

We use Monte Carlo analysis to estimate the uncertainty in predictions of total O3 trends between 1979 and 1995 made by the Goddard Space Flight Center (GSFC) two‐dimensional (2‐D) model of stratospheric photochemistry and dynamics. The uncertainty is caused by gas phase chemical reaction rates, photolysis coefficients, and heterogeneous reaction parameters which are model inputs. The uncertainty represents a lower bound to the total model uncertainty assuming the input parameter uncertainties are characterized correctly. Each of the Monte Carlo runs was initialized in 1970 and integrated for 26 model years through the end of 1995. This was repeated 419 times using input parameter sets generated by Latin hypercube sampling. The standard deviation (σ) of the Monte Carlo ensemble of total O3 trend predictions is used to quantify the model uncertainty. The 34% difference between the model trend in globally and annually averaged total O3 using nominal inputs and atmospheric trends calculated from Nimbus 7 and Meteor 3 total ozone mapping spectrometer (TOMS) version 7 data is less than the 46% calculated 1σ model uncertainty, so there is no significant difference between the modeled and observed trends. In the northern hemisphere midlatitude spring the modeled and observed total O3 trends differ by more than 1σ but less than 2σ, which we refer to as marginal significance. We perform a multiple linear regression analysis of the runs which suggests that only a few of the model reactions contribute significantly to the variance in the model predictions. The lack of significance in these comparisons suggests that they are of questionable use as guides for continuing model development. Large model/measurement differences which are many multiples of the input parameter uncertainty are seen in the meridional gradients of the trend and the peak‐to‐peak variations in the trends over an annual cycle. These discrepancies unambiguously indicate model formulation problems and provide a measure of model performance which can be used in attempts to improve such models.

Convective diffusion of power law fluids inside ducts with consecutive homogeneous and catalytic wall reactions

Analytical and exact solutions for the concentration distribution and Sherwood number of the reactant and the intermediate product in convective diffusion of power law fluids in parallel plates and tubular reactors with consecutive homogeneous and catalytic wall reactions are developed. Closed-form expressions have also been obtained for the conversion of the reactant as well as the yield of the intermediate product. The problem of solving the equation of conservation of mass for each component was transformed to that of solving an eigenvalue problem using the finite-integral transform technique, and as many eigenvalues and eigenfunctions as needed are determined using the sign-count method. The accuracy of the solutions is established and the effects of power law index, and the homogeneous and heterogeneous reactions parameters on mass transfer variables are examined.

Convective diffusion of power-law fluids inside ducts with single homogeneous and catalytic wall reactions

Analytical solutions are developed for the convective diffusion of power-law fluids in parallel plate and tubular reactors with single homogeneous and catalytic wall reactions. Closed-form expressions for the concentration distribution and Sherwood number valid from the entrance to the exit of the reactors are presented. The problem of solving the equation of conservation of mass was transformed to that of solving an eigenvalue problem using the finite integral transform technique; as many eigenvalues and eigenfunctions as needed are determined using the sign count method. The accuracy of the solutions is established and the effects of the power-law index and homogeneous and heterogeneous reactions parameters on the mass transfer variables are examined.

A comparison of some integral methods

The integral methods proposed to compute the kinetic parameters of heterogeneous reactions under non-isothermal conditions are usually worked by the help of the least squares method and the obtained correlation coefficient is taken as a criterion to choose the best integral method. An analysis of several experimental data by mean of three different integral methods was performed by us and the results pointed out that this criterion, by itself, is not enough to provide reliable information on the kinetic parameters. It appears, thus, that the use of an integral method or another is a simple matter of researcher's choice.

Immobilization of denatured DNA to macroporous supports: II. Steric and kinetic parameters of heterogeneous hybridization reactions

The accessibility of immobilized DNA has been shown to depend more crucially on the method of immobilization than on the type of support used for fixation. When sonicated denatured DNA is coupled via diazotization or via cyanogen bromide reaction to solid Sephadex G-25 and Cellex 410 or to macroporous Sephacryl S-500 and Sepharose C1-6B its accessibility varies from 100 to 24 percent. Generally the loss of accessibility is linked to a depression of the melting temperature of DNA helices formed on the support. This correlation shows a characteristic course for a particular coupling method. DNA coupled under denaturing conditions may become totally inaccessible when only 3 percent of its bases are involved in the covalent linkage. Kinetic experiments with sonicated E.coli DNA have shown that the rate constants for renaturation or hybridization reactions are very similar for DNA immobilized by different methods to solid or macroporous supports. Generally the second order rate constant for a heterogeneous reaction (between mobile and immobilized DNA) is about one order of magnitude smaller than that of the analogous homogeneous reaction (in solution).