Effects of chemical reaction and radiation on an unsteady MHD flow past an accelerated infinite vertical plate with variable temperature and mass transfer

This paper deals with the study of the effects of first order chemical reaction and radiation on an unsteady MHD flow of an incompressible viscous electrically conducting fluid past an accelerated infinite vertical plate with variable temperature and mass transfer. The resulting approximate dimensionless system of governing partial differential equations are integrated in closed form by the Laplace transform technique A uniform magnetic field is assumed to be applied transversely to the direction of the flow. Rosseland model of radiation has been chosen in the investigation, the expressions for the velocity field, temperature field and concentration field and skin-friction in the direction of the flow, coefficient of heat transfer and mass flux at the plate have been obtained in non-dimensional form and these are illustrated graphically for various physical parameters involved in the study. Investigation reveals that the fluid velocity is decelerated in the region adjacent to the plate, due to the effect of first order chemical reaction and the rate of heat transfer (from plate to the fluid) decreases due to the absorption of thermal radiation. The results obtained in this work are consistent with physical situation of the problem.     

Effects of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media with radiation

The effect of chemical reaction and variable viscosity on hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media has been studied in the presence of radiation and magnetic field. The plate surface is embedded in a uniform Darcian porous medium in order to allow for possible fluid wall suction or blowing and has a power-law variation of both the wall temperature and concentration. The similarity solution is used to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations, and an efficient numerical technique is implemented to solve the reduced system. Numerical calculations are carried out, for various values of the dimensionless parameters of the problem, which include a variable viscosity, chemical reactions, radiation, magnetic field, porous medium and power index of the wall temperature parameters. Comparisons with previously published works are performed and excellent agreement between the results is obtained. The results are presented graphically and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters.     

On the modeling of pedestrian motion

A model for the simulation of pedestrian flows and crowd dynamics has been developed. The model is based on a series of forces, such as: will forces (the desire to reach a place at a certain time), pedestrian collision avoidance forces, obstacle/wall avoidance forces; pedestrian contact forces, and obstacle/wall contact forces. Except for the will force, it is assumed that for any given pedestrian these forces are the result of only local (nearest neighbour) situations. The near-neighbour search problem is solved by an efficient incremental Delaunay triangulation that is updated at every timestep. In order to allow for general geometries a so-called background triangulation is used to carry all geographic information. At any given time the location of any given pedestrian is updated on this mesh. The results obtained to date show that the model performs well for standard benchmarks, and allows for typical crowd dynamics, such as lane forming, overtaking, avoidance of obstacles and panic behaviour.     

Unsteady state mathematical model of chemically reactive pollutants from an instantaneous line source into a stable atmospheric boundary layer

A time dependent atmospheric model represented for chemically reactive primary pollutants emitted from an elevated line source into a stable atmospheric boundary layer over a surface terrain. The model obtained from an analytical solution of the atmospheric diffusion equation with the quadratic diffusion coefficient (exchange coefficient) and the variable wind velocity taken to be of three different types’ viz. constant, constant shear and parabolic functions of vertical height. The pollutants considered to be of chemically reactive primary pollutants emitted from a time-dependent line source of Instantaneous type. In order to facilitate the application of the model the results for the general situation that includes chemical reaction rate & time dependent source incorporated in the model.     

Effective models for reactive flow under a dominant Péclet number and order one Damköhler number: Numerical simulations

The paper is devoted to the longitudinal dispersion of a soluble substance released in a steady laminar flow through a slit channel with heterogeneous reaction at the outer wall. The reactive transport happens in the presence of a dominant Péclet number and order one Damköhler number. In particular, these Péclet numbers correspond to Taylor’s dispersion regime. An effective model for the enhanced diffusion in this context was derived recently. It contains memory effects and contributions to the effective diffusion and effective advection velocity, due to the flow and chemistry reaction regime. In the present paper, we show through numerical simulations the efficiency of this new model. In particular, using Taylor’s ‘historical’ parameters, we illustrate that our derived contributions are important and that using them is necessary in order to simulate correctly the reactive flows. We emphasize three main points. First, we show how the effective diffusion is enhanced by chemical effects at dispersive times. Second, our model captures an intermediate regime where the diffusion is anomalous and the distribution is asymmetric. Third, we show how the chemical effects also slow down the average speed of the front.     

Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating

The combined effect of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid past a vertical permeable surface embedded in a porous medium is analyzed. The heat equation includes the terms involving the radiative heat flux, Ohmic dissipation, viscous dissipation and the internal absorption whereas the mass transfer equation includes the effects of chemically reactive species of first-order. The non-linear coupled differential equations are solved analytically by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field is to decrease the velocity, temperature and concentration profiles in the boundary layer. There is also considerable effect of magnetic field and chemical reaction on skin-friction coefficient and Nusselt number.     

Mathematical modelling of spark-ignition engines

The flow field, scavenging efficiency, power output, heat transfer losses, and unburned hydrocarbon emissions have been numerically studied by means of a two-equation model of turbulence in a four-stroke, homogeneous-charge, spark-ignition engine. The engine is equipped with an intake valve, an exhaust valve, and a constant rate heat source which simulates the spark plug. Combustion has been modelled by means of a one-step irreversible chemical reaction whose rate is controlled by an Arrhenius-type expression. The numerical results indicate that the intake stroke is characterized by the formation of two eddies which persist in the compression stroke. Turbulence is generated at the shear layers of the air jet drawn into the cylinder, but its level decreases in the compression stroke. Due to the heat released by the spark plug and the chemical reaction, a spherical flame kernel is formed. This kernel evolves into a cylindrical flame when the flame front reaches the piston. Fuel remains unburnt at the corner between the cylinder head and the cylinder wall due to heat transfer losses. The numerical results also indicate that despite uncertainties about the turbulence and heat transfer models, an engine model such as the one studied here can be used to understand the flow field, heat transfer losses, scavenging efficiency, and power output in conventional spark-ignition engines. Such capabilities are very helpful in the development and optimization stages of engines. For example, here the engine model thermal and scavenging efficiencies are 15.69% and 94%, respectively. The peak pressure is 33 atm and occurs at 6° ATDC. The unburnt hydrocarbon emissions are 7.41% of the total fuel admitted into the cylinder.     

Comparisons between thermodynamic and one-dimensional combustion models of spark-ignition engines

A one-dimensional combustion model, employing a constant eddy diffusivity and a one-step chemical reaction, has been developed and applied to study the flame propagation in a spark-ignition engine. Calculations have been made at 1600 and 4200 rev min⁻¹ under fuel rich conditions and compared with available engine pressure data. One- and two-zone thermodynamic models have also been developed and applied to study the combustion process in the engine. The thermodynamic models have been compared with the one-dimensional model results and comparisons include the average mixture temperature, the temperatures of the burned and unburned gases and the flame surface area. These comparisons indicate that the one-dimensional model predictions are very sensitive to the eddy diffusivity and reaction rate data. The two-zone thermodynamic model predicts, first, a monotonically increasing flame surface area with time and, then, a monotonically decreasing surface area, whereas the one-dimensional model always predicts a monotonically increasing flame surface area. The average mixture temperature predicted by the one-zone thermodynamic model is higher than those of the two-zone and one-dimensional models during the compression stroke, while that of the one-dimensional model is higher than the temperatures predicted by the one- and two-zone models during the expansion stroke. The one-dmensional model predicts an accelerating flame even when the front approaches the cold cylinder wall. This yields a faster fuel consumption rate than those predicted by the one- and two-zone thermodynamic models which predict smoother burned fuel mass profiles.     

Nonstationary mass transfer of a reacting spherical particle in laminar stream of a viscous fluid : PMM vol. 38, n 6, 1974, pp. 1041–1047

The process of the formation of a stationary mass transfer mode for a moving reacting particle is examined. An analytic expression valid for a nonstationary distribution of the concentration of matter in a steady stream of viscous fluid, flowing past a spherical particle, was obtained for the case when at a certain instant a chemical reaction of the first order begins at the surface of the sphere. The problem is solved for small finite Reynolds and Péclet numbers. The solution of the corresponding stationary problem has been obtained in [1]. Paper [2] examined a nonstationary heat transfer of a fluid spherical drop in an inviscid flow with spasmodic change of initial temperature at high Péclet numbers. Paper [3] contains an analysis of the problem of a nonstationary heat transfer of a rigid spherical particle for small Reynolds and Péclet numbers at spasmodic change of temperature of the particle surface. The results obtained in [3] can be used to describe the mass transfer for a moving reacting particle only in the case of a diffusion mode of the chemical reaction.     

Free localized vibrations of a long double-walled carbon nanotube introduced into an inhomogeneous elastic medium

Based on modified Flügge equations and nonlocal elasticity theory, free axisymmetric oscillations of a long double-walled carbon nanotube embedded into an inhomogeneous elastic medium is studied. The ambient medium is simulated by the Winkler foundation. Van der Waals forces are introduced in order to take into account the interaction between the nanotube walls. Using Tovstik’s asymptotic method, eigenmodes are constructed in the form of functions that decay far from the line on the surface of the outer wall, on which the modulus of subgrade reaction has a local minimum. Eigenmodes and eigenfrequencies corresponding to the coand counterdirected wall motions are found. It has been found that introducing a nonlocality parameter into the model results in eigenmodes that are not inherent in macroscale shells. In particular, an increase in the stretching force leads first to greater localization of vibrations and increase in the amplitudes of tangential atomic oscillations and, second, to reduction in the frequencies in the case when the tube lies in a sufficiently stiff medium.     

Effect of homogeneous and heterogeneous chemical reactions on peristaltic transport of an MHD micropolar fluid with wall effects

In this paper, the influence of magnetic field on the dispersion of a solute in peristaltic flow of an incompressible micropolar fluid is studied as a model of fluid transport in the human intestinal system with wall properties. Long wavelength approximation, Taylor's limiting condition, and dynamic boundary conditions at the flexible walls are used to obtain the average effective dispersion coefficient in the presence of combined homogeneous and heterogeneous chemical reactions. The effects of various pertinent parameters on the effective dispersion coefficient are discussed. Average effective dispersion coefficient increases with amplitude ratio, which implies that dispersion is more in the presence of peristalsis. It also increases with the cross‐viscosity coefficient, heterogeneous chemical reaction rate, and wall parameters. Further, dispersion decreases with micropolar parameter, magnetic parameter, and homogeneous chemical reaction rates. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of Hall currents and chemical reaction on hydromagnetic flow of a stretching vertical surface with internal heat generation/absorption

The problem of steady, laminar, hydromagnetic, simultaneous heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generating/absorbing fluid over a continuously stretching surface in the presence of the combined effect of Hall currents and mass diffusion of chemical species with first and higher order reactions is investigated. The fluid is permeated by a strong transverse magnetic field imposed perpendicularly to the plate on the assumption of a small magnetic Reynolds number. Certain transformations are employed to transform the governing differential equations to a local similarity form which are solved numerically. Comparisons with previously published work have been conducted and the results are found to be in good agreement. A parametric study is performed to illustrate the influence of the magnetic field parameter, Hall parameter, the coefficients of space-dependent and temperature-dependent internal heat generation/absorption, the chemical reaction parameter and order of reaction on the fluid velocity, temperature and concentration distributions. Numerical data for the local skin-friction coefficient, the local Nusselt number and the local Sherwood number have been tabulated for various values of parametric conditions.     

Exact solutions of potentiostatic current transients for a corrosion reaction under mixed charge transfer and diffusion control

An analytical solution has been obtained for the current response transients to a potentiostatic step for a corrosion reaction where a planar metal electrode is immersed in an acidic electrolyte. This solution can be used to provide values of important kinetic parameters of the reaction such as corrosion current and Tafel slopes. The model is derived for conditions of mixed charge transfer and diffusion control and includes the metal ion deposition partial reaction. A Nernstian diffusion model is used, where anodic and cathodic species diffuse in a finite diffusive layer. A numerical solution has previously been published [1], but it is believed that this is the first time an analytical solution has been presented. Transients obtained by including both the metal dissolution and metal-ion deposition (back) reactions, are compared to those obtained by neglecting the metalion deposition reaction. It is shown that neglecting the back reaction can cause significant errors especially when large cathodic potential steps are applied and as the corrosion current approaches the limiting current density of the cathodic reaction.     

Variable structure control for a class of nonlinear systems with mismatched uncertainties

A scheme to stabilize nonlinear time-varying systems with both matched and mismatched uncertainties is proposed in this paper by switching between two control laws: a first-order sliding-mode control and a second-order sliding-mode control. Based on this idea, a variable structure control algorithm is designed for a class of second-order systems. The closed-loop system is globally or locally asymptotically stable. It has been proven that the stability region has relation with the order of the boundary function and the region can be obtained by solving an inequality. The uncertainty considered in this work is also more general than those in the existing works.     

Microwave Assisted Ignition to Achieve Combustion Synthesis†

The use of microwave heating to initiate combustion synthesis has been increasingly investigated in recent years because of its advantages over traditional methods. A simple mathematical model is used to model these experiments. The microwave power absorption term is modelled as the product of an Arrhenius reaction term with a function that decays exponentially with distance. The former represents the temperaturedependent absorption of the microwaves whereas the latter describes the penetration of the material by the microwaves. Combustion kinetics are modelled as a first-order Arrhenius reaction.     

Effects of stenosis on arterial rheology through a mathematical model

The paper presents an analytical study of blood flow through a stenosed artery using a suitable mathematical model. The artery is modelled as an anisotropic viscoelastic cylindrical tube containing a non-Newtonian viscous incompressible fluid representing blood. The blood flow is assumed to be characterized by the Herschel–Bulkley model. The effect of the surrounding connective tissues on the motion of the arterial wall has been incorporated. Initially, the relevant solutions of the boundary value problem are obtained in the Laplace transform space, through the use of a suitable finite difference technique. Laplace inversion is carried out by employing suitable numerical techniques. Finally, the variations of the vascular wall displacements, the velocity distribution of the blood flow, the flux, the resistance to flow and the wall shear stress in the stenotic region are quantified through numerical computations and presented graphically.     

Multiple absorption-related blow-up rates to a coupled heat system

This paper deals with asymptotic behavior of solutions to a heat system with absorptions and coupling positive multi-nonlinearities. It is known that although absorption mechanisms may affect such as blow-up criteria, blow-up time, and initial data required for blow-up solutions, they cannot change blow-up rates of solutions in general. It has been reported in the current literature that blow-up rates for scalar equations with absorptions are all absorption-independent. In a previous paper of the authors, four absorption-independent simultaneous blow-up rates were obtained already for the same problem under weak absorptions. The present paper will furthermore prove that if the absorptions are unbalanced in the model (i.e., the absorption is stronger for one component and weaker for another), then there are in addition eight possible absorption-related blow-up rates for the model, besides the four absorption-independent ones. This exposes a significant difference between scalar and coupled nonlinear parabolic equations with absorptions.     

Mathematical modelling of flows in recessed wall flame holder

A finite difference procedure has been employed to predict the flow situation in a recessed wall flame holder with and without combustion. Turbulence has been modelled by an ad hoc effective viscosity law. A single step chemical reaction has been assumed in dealing with the flows involving combustion. The predicted physical parameters have been compared with the experimental results. It has been argued that with the simplifying assumptions on turbulence and chemical kinetics the numerical procedure is adequately accurate to predict the important design parameters such as flame length and blow-off velocity. However, there are significant discrepancies between the predicted and measured distribution of velocity and temperature which could be attributed mainly to the inadequate turbulence modelling.     

Effect of chemical reaction on the dispersion of a solute in a porous medium

A mathematical model is presented in this paper which describes the dispersion of a chemically active solute in the laminar flow in a sparsely packed porous medium. The validity of time-dependent dispersion coefficient is widened by using a generalized dispersion coefficient. The effect of porous parameter and chemical reaction on the dispersion coefficient is studied. The exact solution for the mean concentration distribution of a chemically active solute is obtained as a function of downwind distance and time. Results are also obtained for pure convection.     

Perturbation analysis of unsteady magnetohydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction

An analytical study for the problem of unsteady mixed convection with thermal radiation and first-order chemical reaction on magnetohydrodynamics boundary layer flow of viscous, electrically conducting fluid past a vertical permeable plate has been presented. Slip boundary condition is applied at the porous interface. The classical model is used for studying the effect of radiation for optically thin media. The non-linear coupled partial differential equations are solved by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field decreases the velocity, temperature and concentration profiles in the boundary layer. Also, the effects of the various parameters on the skin-friction coefficient and the rate of heat transfer at the surface are discussed.