Nondimensional Activation Energy Research Articles

Finite element analysis for sand and paraffin wax nanoparticles in propylene glycol–water mixture-based hybrid nanofluid flow over a swirling cylinder with Arrhenius kinetics

This study aims to investigate the impact of activation energy on the flow of a hybrid nanofluid over a rotating stretching cylinder with torsional motion and a heat source/sink. The paraffin wax-sand-propylene glycol–water-based hybrid nanofluid has been used in the study. By adopting appropriate similarity transformations, the modeled partial differential equations are transformed into a set of ordinary differential equations, which are then solved using the finite element method. The numerical integration’s validity and reliability, as well as the newly obtained discoveries, were thoroughly analyzed. Results reveal that the larger Reynolds number values enhance the system’s inertial force, which resists the liquid accelerating force and declines both velocities and heat transport. The heat source/sink parameter has a favorable impact on the thermal profile, but larger Schmidt number values restrict mass transfer. The improved values of the chemical reaction rate parameter augment the mass transport rate, but nondimensional activation energy parameter has negative impact on Sherwood number.

Numerical study on wave configuration of wedge-induced oblique detonation wave: Reactive boundary layer effect

A numerical simulation solving the Reynolds-averaged Navier–Stokes equation is presented to investigate the initiation and evolution of the wedge-induced oblique detonation wave (ODW) with emphasis on the effects of the burning boundary layer. The nondimensional activation energy (Ea) is selected as the bifurcate parameter, which varies from 30 to 50. The largest induction ignition length behind the oblique shock/detonation wave is shown to be proportional to the Ea. The initiation of ODW can be attributed to the collision and diffraction of reactive waves. The wave configuration, a series of compression waves (or shock wave), is observed at the conjunction point of the burning boundary layer and combustion wave, which intensifies the pressure jump as increasing the Ea. The polar line analysis demonstrates that the pressure jump triggers the transition from regular reflection to Mach reflection near triple-point. The oscillations of the ODW wave structures, for example, the triple-point and Mach stem, can be attributed to the Rayleigh–Taylor instabilities developed on the reaction front of the boundary layer, which shall be appropriately suppressed to remain the steadiness of the ODW and flow configuration.

Dynamics of Cattaneo-Christov Double Diffusion (CCDD) and arrhenius activation law on mixed convective flow towards a stretched Riga device

Background Current paper elaborate the impact of MHD flow of Newtonian liquid over a extendable Riga sheet. Cattaneo-Christov (CC) heat and mass flux models in formulation are taken here. Fluid filling porous medium is considered. Influences of activation energy is also considered. Boundary layer approximation is used in obtaining partial differential equations (PDEs). Applying suitable transformation to reduce the given PDEs into ordinary differential (ODEs) system. Method Homotopy method is utilized to solve non-linear differential system. Results The impacts of influencing parameters like modified Hartman number, mixed convection parameter, inverse Darcy parameter, non-dimensional parameter, Biot number, non-dimensional activation energy, Eckert number, thermal relaxation and solutal concentration variables are examined through graphs. Conclusions Velocity profile enhances for larger estimation of ratio parameter and modified Hartman number. Temperature distribution is higher for Eckert and Biot number. Concentration profile is enhancing for more values of nondimensional activation energy.

MHD Darcy-Forchheimer flow of Casson nanofluid due to a rotating disk with thermal radiation and Arrhenius activation energy

In this research article, three-dimensional Casson nanofluid under influences of Arrhenius stimulation energy and thermal radiation is considered. The flow is induced by a turning disk. Temperature, velocity, and concentration slips at the outward of the turning disk are deliberated. The effect of Brownian movement and thermophoresis is examined due to the nanosized particles in a Casson fluid dispersed over the turning disk. The appropriate transformation methods for reducing a set of Partial differential equations (PDEs) to nonlinear Ordinary differential equations (ODEs) and further solved by the homotopy analysis method (HAM). Numerical simulation using Schmidt number, magnetic, Casson, Brownian movement, and thermophoresis parameters on outspread, temperature, tangential velocities, and nanoparticles are portrayed. Local Nusselt number, Skin friction, and Sherwood number are plotted and investigated. The graphical results show that the tangential velocity of nanofluids decreases because of an addition in Reynolds’ number, while the radial velocity displays the converse patterns. The tangential and radial velocities reduce with the increment magnetic factor. It is also perceived that an augmentation in estimations of radiation parameters enhances the heat transfer rate. Increasing the values of non-dimensional activation energy raises the mass transfer rate.

Hydromagnetic Carreau Nanoliquid in Frames of Dissipation and Activation Energy

The novel characteristics of magnetic field and entropy generation in mixed convective flow of Carreau fluid towards a stretched surface are investigated. Buongiornio nanoliquid model consists of thermophoresis and Brownian movement aspects is opted for analysis. Energy expression is modeled subject to thermal radiation and viscous dissipation phenomenon. Concentration by zero mass flux condition is implemented. Consideration of chemical reaction and activation energy characterizes the mass transfer mechanism. Total entropy generation rate and Bejan number is formulated. The utilization of transformation variables reduces the PDEs into non-linear ODEs. The obtained nonlinear complex problems are computed numerically through Shooting scheme. The impact of involved variables like local Weissenberg number, magnetic parameter, thermal radiation parameter, Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, mixed convection parameter, Prandtl parameter, Eckert number, Schmidt number, non-dimensional activation energy parameter, chemical reaction parameter, Brinkman number, dimensionless concentration ratio variable, diffusive variable and dimensionless temperature ratio variable on velocity, temperature, nanoparticles concentration, entropy generation, Bejan number, surface drag force and heat transfer rate are examined through graphs and tables.

Heat transfer on the cross flow of micropolar fluids over a thin needle moving in a parallel stream influenced by binary chemical reaction and Arrhenius activation energy

Emerging engineering and industrial needs made the prime concern of this article to investigate the thermal management on the cross flow of micropolar fluids over a thin needle moving in a parallel stream. The flow is subject to binary chemical reaction and Arrhenius activation energy. The mathematical model of the considered physical problem consists of coupled nonlinear partial differential equations: conservation of mass, momentum, energy, and concentration equation. The dimensionless transformed governing equations subject to the given boundary conditions have been solved directly by the Runge-Kutta Fehlberg fourth- fifth-order method followed by the shooting technique. Graphical results relative to the interaction effects of dynamic thermo-physical dimensionless parameters such as Richardson parameter, Dufour number, Soret number, Prandtl number, temperature ratio parameter, nondimensional activation energy, chemical reaction parameter and velocity ratio parameter controlling the flow, heat and mass transfer features are presented and analyzed. It can be seen, from the study, that the skin friction due to angular velocity reduces with increase in size of the needle and it upsurges due to the increase in material parameter. The obtained numerical results revealed that the augmented Richardson parameter is in favor of a greater heat transfer enhancement. The obtained results show a better agreement of this model with the previously published results.

Numerical simulation for Darcy-Forchheimer 3D rotating flow subject to binary chemical reaction and Arrhenius activation energy

Three-dimensional Darcy-Forchheimer nanoliquid flow in the presence of rotating frame and activation energy is inspected. Flow is developed through linearly stretching of the surface. Convection of heat and mass exchange is given due consideration. The novel characteristics in regards to Brownian dispersion and thermophoresis are retained. The variation in partial differential framework (PDEs) to nonlinear ordinary differential framework (ODEs) is done through reasonable transformations. Governing differential frameworks have been computed in edge of NDSolve. Discussion regarding thermal field and concentration distribution for several involved parameters is pivotal part. Physical amounts like surface drag coefficients, transfer of heat and mass rates are portrayed by numeric esteems. It is noticed that impacts of porosity parameter and Forchheimer number on the thermal and concentration fields are quite similar. Both temperature and associated thermal layer thickness are enhanced for larger porosity parameter and Forchheimer number. Temperature and concentration fields exhibit similar trend for the higher values of rotational parameter. Effects of thermal and concentration Biot numbers on the temperature and concentration fields are qualitatively similar. Higher Prandtl and Schmidt numbers correspond to stronger temperature and concentration fields. Larger nondimensional activation energy, temperature difference parameter and fitted rate constant yield weaker concentration field. Brownian motion parameter for temperature and concentration has reverse effects while similar trend is observed via thermophoresis parameter.

Chapman–Jouguet deflagrations and their transition to detonation

We study experimentally fast flames and their transition to detonation for five different hydrocarbons, namely methane, ethane, ethylene, acetylene, and propane with oxygen as the oxidizer. Following the interaction of a detonation wave with a column of cylinders of varying blockage ratio, the experiments demonstrate that the fast flames established are Chapman–Jouguet deflagrations, in excellent agreement with the self-similar model of Radulescu et al. (2005). The experiments indicate that these Chapman–Jouguet deflagrations dynamically restructure and amplify into fewer stronger modes until the eventual transition to detonation. The transition length to a self-sustained detonation was found to correlate very well with the mixtures’ sensitivity to temperature fluctuations, reflected by the χ parameter introduced by Radulescu, which is the product of the non-dimensional activation energy Ea/RT and the ratio of chemical induction to reaction time ti/tr. Correlation of the measured deflagration to detonation transition (DDT) lengths determined that the relevant characteristic time scale from chemical kinetics controlling DDT is the energy release or excitation time tr. Correlations with the cell size also capture the dependence of the DDT length on χ for fixed blockage ratios.

Unsteady features on one-dimensional hydrogen-air detonations

The features of one-dimensional unsteady detonations are studied numerically using a hydrogen-air detailed chemical reaction model. A series of simulations are carried out while degree of overdrive, initial pressure, initial temperature, and equivalence ratio are varied. The oscillation modes and mechanisms of the one-dimensional detonations are discussed with reference to shock pressure histories and x-t diagrams of density distributions. As the degree of overdrive is reduced with a stoichiometric mixture of hydrogen-air at P0=0.421atm and T0=293K, a steady state appears, along with a high-frequency mode and a low-frequency mode. The oscillation mechanism of the high-frequency mode is the same as that of the regular regime of unsteady shock-induced combustion observed around a spherical projectile flying at hypersonic velocity in detonable gases. The degree of overdrive threshold between the steady and unsteady region increases monotonically with initial pressure and decreases monotonically with initial temperature. When the equivalence ratio is changed, the threshold has a minimum value around ϕ=1. We focus attention on a nondimensional effective activation energy, which is generally used for linear stability analysis. The oscillation mode depends highly on the nondimensional effective activation energy. The oscillation of the detonation front appears as the nondimensional effective activation energy goes past a threshold value of 5.2. Furthermore, we investigate the failed regime and possible reignition in this regime. In the failed regime, a detonation wave breaks up into a leading shock, a contact discontinuity, and a rarefaction wave. When the shock is weak, reignition time becomes very long. Therefore, the reignition after the failed regime is difficult to reproduce in the restricted computational domain. The reignition process in the failed regime is investigated by means of analysis consisting of integration along the point of intersection between a Rayleigh line for weak leading shock and a partially burnt Hugoniot curve. The reignition time increases dramatically with decreasing temperature behind the shock wave, when the gas condition goes past the second explosion limit. The second explosion limit is one of the characteristics of the hydrogen-air detailed chemical reaction model and does not exist in the one-step chemical reaction model. Lastly, the reignition time obtained by the analysis is compared with that obtained by the simulation results. The simulation results agree well with the analytical results.

One-dimensional overdriven detonations with branched-chain kinetics

The dynamics of time-dependent, planar propagation of gaseous detonations is addressed on the basis of a three-step chemistry model that describes branched-chain processes. Relevant nondimensional parameters are the ratio of the heat release to the thermal enthalpy at the Neumann state, the nondimensional activation energies for the initiation and branching steps, the ratio of the branching time to the initiation time and the ratio of the branching time to the recombination time. The limit of strong overdrive is considered, in which pressure remains constant downstream from the leading shock in the first approximation, and the ratio of specific heats γ is taken to be near unity. A two-term expansion in the strong overdrive factor is introduced, and an integral equation is derived describing the nonlinear dynamics and exhibiting a bifurcation parameter, the reciprocal of the product of (γ−1), the nondimensional heat release and the nondimensional branching activation energy, with an acoustic correction. A stability analysis shows that, depending on values of the parameters, either the mode of lowest frequency or a mode of higher frequency may be most unstable. Numerical integrations exhibit different conditions under which oscillations die, low-frequency oscillations prevail, high-frequency oscillations prevail, highly nonlinear oscillations persist, or detonation failure occurs. This type of parametric analysis is feasible because of the relative simplicity of the model, which still is more realistic than a one-step, Arrhenius chemical approximation. In particular, by addressing the limit of slow radical recombination compared with branching, explicit results are derived for the critical value of the bifurcation parameter, involving the ratio of the recombination time to the induction time. The results help to clarify the general nature of one-dimensional detonation instability and provide simplifications that can be employed in efficiently relating gaseous detonation behavior to the true underlying chemistry.

The Ignition of Solids: An Asymptotic Analysis

The ignition of a solid exposed to a step in surface temperature, including the effect of the curvature, is analyzed by means of large activation energy asymptotics in the whole range of values of the Damköhler number, Da , which lead to a thermal runaway. For very large values of Da the chemical reaction takes place in a surface boundary layer. The evolution of the temperature in this layer is described by a universal problem. Its solution contains a mathematical singularity, which identifies the ignition event occuring at an ignition time much smaller than the conduction time through the solid. When Da is large but of the same order that the square of the nondimensional activation energy, the ignition time becomes of the order of the conduction time. The structure of the ignition problem is identical to that in the previous case, but its solution depends on the body size and shape. In both cases an initial quasisteady stage is followed by a transition stage in which the nonsteady effects must be retained. Finally, for Da of order unity the chemical reaction extends over the whole solid, and the ignition process can be described in terms of a first inert heating stage and a second reacting stage in which the temperature evolves according a nonsteady Frank-Kamenetskii equation.

A new heterogeneous burning velocity formula for the propagation of a laminar flame front through a polydisperse spray of droplets

A new burning velocity formula for the heterogeneous mode of laminar combustion of a premixed polydisperse spray of droplets is derived, using activation energy asymptotics and the method of multiple scales. For a mass fractional flux of fuel vapor, G F of O(1) at the homogeneous reaction zone the homogeneous burning velocity formula obtained by Silverman et al. [ Combust. Flame 93:97–118 (1993)] is applicable. Here, it is shown that for G F of O( θ −1) (where θ the nondimensional activation energy) heterogeneous combustion is predominant, whence the new formula is developed. The spray of droplets is modelled with the sectional approach, so that an arbitrary initial multisize distribution of droplets may be considered. Calculated results show that the behavior of the heterogeneous burning velocity as a function of the Sauter mean diameter is in qualitative accord with experimental data from the literature. For a polydisperse tetralin spray of low volatility the theory produces evidence suggesting a critical initial SMD at which a switchover from the homogeneous to the heterogeneous mode of flame propagation occurs that is in agreement with independent experimental and theoretical predictions for monodisperse sprays.

Effect of gas-phase thermal expansion on stability of deflagrations in porous energetic materials

Deflagration waves propagating through porous energetic materials are known to be subject to intrinsic diffusional/thermal instabilities that are associated with the onset of various oscillatory modes of combustion. A few theoretical analyses to explain these combustion phenomena have been published in the literature, and the present contribution extends these results. In particular, we reconsider our previous asymptotic analysis of non-steady, non-planar deflagration, which postulated a constant-density gas phase, to take into account the effects of quasi-steady thermal expansion of an ideal gas. With relative motion between gaseous and condensed phases included, a time-dependent, multidimensional asymptotic model is derived through the application of activation-energy asymptotics. Analyzing this model, an explicit solution corresponding to steady, planar deflagration is obtained as a special case, and a dispersion relation is derived describing its linear stability. In the plane defined by the non-dimensional activation energy and the disturbance wavenumber, a pulsating neutral stability boundary is calculated, beyond which non-steady, non-planar solutions are expected. The effects of porosity and gas-phase thermal expansion are shown to be generally destabilizing, suggesting that degraded propellants, which exhibit greater porosity than the pristine material, may be more readily subject to combustion instability and non-steady deflagration.

Ignition of catalytic reactions in a vertical wall immersed in a combustible gas

We study in this paper the steady-state ignition of a catalytic vertical plate immersed in a combustible gas. The set of governing equations are elliptic, including the energy equation for the plate as well as the balance equations for the laminar natural convective boundary layer. The influence of the longitudinal heat conduction through the plate is clarified, showing well-defined ignition and extinction conditions (S-shaped curve) for high activation energy. The parameter that measures the influence of the longitudinal heat conduction is the heat conduction parameter α for moderate values of the nondimensional activation energy (Ze) of the overall reaction or α ˜ = α Z e 1 / 4 for high activation energies ſ e →∞. The longitudinal heat conduction is important for large values compared with unity of the heat conduction parameter α or α ˜ for moderate or large values of the nondimensional activation energies, respectively. The heat conduction parameter can be very large compared with unity for metallic plafes or very small compared with unity for ceramic plates. Numerical and asymptotic, techniques have been used, to evaluate the ignition conditions for very good ( α , α ˜ → ∞ ) and poor ( α , α ˜ → 0 ) conducting plates. Very well-defined ignition and extinction conditions are obtained for large values of α or α ˜ and large values of the nondimensional activation energy. For small values of α or α ˜ , there is not an S-shaped, curve. The catalytic ignition is easier to achieve as the value of α increases.

The Linearised Response of the Mass Burning Rate of a Premixed Flame to Rapid Pressure Changes

ABSTRACT An investigation is made into the response of the mass burning rate of a premixed flame to small but sharp changes in pressure. In this paper a fast time scale is considered such that (K1 = thermal diffusivity, u01 1 = initial burning velocity, l1 a = a typical acoustic length, a01 1 = frozen sound speed, θ = nondimensional activation energy). Previous studies by the author (Mclntosh 1990)and by other researchers (e.g. Ledder and Kapila 1991) have considered the case of r = 1 which is the usual value corresponding to audible resonance of flames in tubes, burner ports etc. However the case r = Θ2 (Mclntosh 1991)is a most interesting and distinct case since then the fast time scale alters the inner reaction zone which consequently obeys a different and essentially unsteady diffusion-reaction equation. The mass burning rate is then on an appreciably larger scale. The time response of the mass burning rate to pressure fluctuations at this fast time scale is governed in general by a non-linear partial...

Period Doubling Gained, Period Doubling Lost

Pulsating solutions to a model of gasless condensed phase combustion are studied numerically as a function of a parameter $\mu $, which is proportional to the nondimensional activation energy. Due to the exothermic reaction, a combustion wave propagates into the fresh fuel mixture. Below a critical value $\mu _1 $ the wave propagates at a uniform velocity. For $\mu > \mu _1 $, periodic pulsations occur of period $T = T( \mu )$. That is, the velocity of the combustion wave increases and decreases periodically. The pu rations are sinusoidal for $\mu $ near $\mu _1 $, and then develop into relaxation oscillations as $\mu $ is increased. A transition to a doublyperiodic (period $2T$) solution branch is found at a value $\mu _2 > \mu _1 $. Stable doubly periodic solutions can no longer be computed beyond a third critical point $\mu _3 > \mu _2 $. For $\mu > \mu _3 $, there is a return to the T periodic solution branch, with an interval of bistability ($ \mu^* < \mu < \mu _3 $, with $\mu _2 < \mu ^ * < \mu _3 $) in which both singly and doubly periodic solutions stably coexist, each with its own domain of attraction.

The Influence of the Lewis Numbers of the Reactants on the Asymptotic Structure of Counterflow and Stagnant Diffusion Flames

Abstract The asymptotic structure of counterflow and stagnant diffusion flames are analyzed in the limit for large values of the overall, nondimensional activation energy, Ta , characterizing the rate of the reaction and results are given for small values of the stoichiometric fuel to oxygen mass ratio. The chemical reaction between the fuel and the oxidizer is represented by a one-step, irreversible process. A new approach is developed to characterize the influence of the Lewis number of the fuel, LF and the Lewis number of the oxidizer, L0 , on the outer and inner structure of near equilibrium diffusion flames. Explicit algebraic formulas to predict the critical conditions of flame extinction are also given. For counterflow diffusion flames at fixed values of L0 , the flame moves significantly toward the oxidizer stream and the heat losses toward the oxidizer region of the flame increase significantly with decreasing values of LF . The value of the maximum flame temperature is relatively insensitive to ...

Damköhler-Number Ratio Asymptotics of the Zeldovich-Liñán Model

Abstract A new asymptotics exploiting the disparity of the orders of magnitude of Damkohler numbers is uncovered in complex kinetics. In contrast to the conventional activation energy asymptotics where the non-dimensional activation energy 0 is algebraically large, the new asymptotics here only requires 0 to be logarithmically large, and is therefore a more appropriate approach for the analysis of problems where the activation energy 0 is not very large. The two-step Zeldovich-Linan model with a chain-branching and a chain-breaking step is chosen to demonstrate the use of this new asymptotics.

Local Nonlinear Stability of the Steady State in an Isothermal Catalyst

A first-order, irreversible, exothermic reaction in a bounded porous catalyst is considered, with smooth boundary, of one, two, or three dimensions. For small Prater and Nusselt numbers, $\beta $ and $\nu $, and a large Sherwood number, $\sigma $, two isothermal models are derived. An analysis of linear stability of the steady states of such models shows that oscillatory instabilities appear for appropriate values of the Damkohler number if the nondimensional activation energy is larger than $\gamma ^ * $ and the Lewis number is sufficiently large, where $\gamma ^ * = 4$ if $m = \nu /\beta \sigma \leqq 1$ and $\gamma ^ * = (m + 1)^2 / m$ if $m < 1$. A local Hopf bifurcation analysis is carried out at neutral stability points in order to ascertain whether such bifurcation is subcritical or supercritical.

Cumulative effects of weak pressure waves during the induction period of a thermal explosion in a closed cylinder

It is shown that the accumulation of small-amplitude gasdynamic perturbations is able to accelerate the process of self-ignition of a homogeneous explosive mixture. For analytical simplicity, the chemical kinetics are represented by a one-step irreversible reaction with a large activation energy. A one-dimensional piston-cylinder geometry is considered, which allows a slow compression of the gas during the induction period. It is assumed that the rates of temperature increase due to the reaction and due to the compression are comparable. A two-timescale asymptotic expansion for small Mach numbers is performed considering the distinguished limit ME = O(1), where E is the non-dimensional activation energy, and M is the Mach number based on a characteristic speed of the gas motion. Gasdynamic-chemical interaction is observed at the second order, where the secular equations describing the evolution on the slow timescale explicitly show a cumulative influence.