Delay time of gases's catalytic heterogeneous ignition on various sizes's catalyst particles

In this work, catalytic ignition delay time of combustible gas's small impurities in air on a spherical metal particle of various diameters is analytically determined by the example of gas-air mixtures's flameless combustion with hydrogen impurities on a platinum particle. It is shown that stable flameless combustion is observed after an induction period for particles of a certain range. It has been established that catalytic ignition time of gases is divided into three stages: 1. inert heating, the duration of which still depends on the combustible gas concentration; 2. the stage of self-acceleration and catalyst temperature rise during the course of the catalytic reaction in the transition region; 3. stage of diffusion inhibition and reaching stable catalytic combustion. The characteristic relaxation time was used in a dimensionless form. To determine the duration of the second stage, a modified Frank-Kamenetsky approach is applied. The duration of diffusion inhibition stage in the dimensionless form is practically independent of catalyst particle's diameter, although the catalytic combustion temperature decreases with an increase in the catalyst diameter. Heat transfer by radiation, the role of which increases with the growth of the catalyst size, is included in the effective heat transfer coefficient, which allows maintaining the classical ideology to solving the problem of the induction period.

Theoretical insights from upscaling Michaelis–Menten microbial dynamics in biogeochemical models: a dimensionless approach

Leading an effective response to the accelerating crisis of anthropogenic climate change will require improved understanding of global carbon cycling. A critical source of uncertainty in Earth system models (ESMs) is the role of microbes in mediating both the formation and decomposition of soil organic matter, and hence in determining patterns of CO2 efflux. Traditionally, ESMs model carbon turnover as a first-order process impacted primarily by abiotic factors, whereas contemporary biogeochemical models often explicitly represent the microbial biomass and enzyme pools as the active agents of decomposition. However, the combination of non-linear microbial kinetics and ecological heterogeneity across space and time guarantees that upscaled dynamics will violate mean-field assumptions via Jensen's inequality. Violations of mean-field assumptions mean that parameter estimates from models fit to upscaled data (e.g., eddy covariance towers) are likely systematically biased. Likewise, predictions of CO2 efflux from models conditioned on mean-field values will also be biased. Here we present a generic mathematical analysis of upscaling Michaelis–Menten kinetics under heterogeneity and provide solutions in dimensionless form. We illustrate how our dimensionless form facilitates qualitative insight into the significance of this scale transition and argue that it will facilitate cross-site intercomparisons of flux data. We also identify the critical terms that need to be constrained in order to unbias parameter estimates.

Effects of radiation and magnetohydrodynamic on unsteady Casson fluid over accelerated plate

The effects of radiation and magnetohydrodynamic on unsteady Casson fluid through an accelerated plate is analysed. The problem is formulated in the form of Partial Differential Equations (PDE) with imposed initial and boundary conditions. The Partial Differential Equations are transformed into dimensionless form by introducing suitable non-dimensional variables. Laplace transform method is used to derive the exact solutions for temperature and velocity profiles, fulfilling all initial and boundary conditions. The effects of parameters are depicted and illustrated graphically for radiation, Casson fluid and time, as well as Magnetohydrodynamics (MHD). It is found that the thermal radiation rises due to an increase in temperature. Besides, the increasing of Casson fluid and MHD parameter has decreasing effect on velocity. Finally, the influence of time will increase the velocity of the fluid.

Interaction of multiple slip features of magnetized Casson nanofluid over a wedge

The intention of this exertion is to inspect the flow heat and mass transfer of unsteady magnetite Casson nanofluid over a wedge. The peak theme of thermal radiation and chemical reaction are also incorporated. Slip effects are also assumed near the surface of the wedge along with the convective boundary restrictions. The governing equations are transmuted into dimensionless form first, the famous shooting technique is implemented. The obtained numerical outcomes are exhibited through graphs and tables. Fascinating features of various emerging parameters in flow, heat and nanoparticle concentration are discussed.

PARTICULARITIES OF HYDRAULIC CALCULATION OF COLLECTING PREASSURE DRAINAGE PIPELINES

A system of two differential equations, which describes the fluid motion in a pipe with a variable flow rate and the conditions for fluid entry through the drainage pipelines walls from the surrounding soil, is considered. It is shown that for the studied case the second term in the original equation can be neglected without a significant error. The system is reduced to a dimensionless form by introducing the original variables. The solution of this equations system is given in a dimensionless form. Two main parameters are used in the analysis: the coefficient of collecting drainage pipeline resistance "ζl" and the generalized parameter "A", which takes into account the structural and hydraulic characteristics of the considered flow. Also, the concept of an infinitely long drainage pipeline or, which is the same, a pipeline with an infinite walls filtration capacity of the drainage pipeline is introduced in the article. It is noted that such pipeline will have a maximum throughput compared to pipes of the same diameter but limited length. Sufficiently simple and convenient calculated dependencies for the determination of the nature of flow rate variation and pressure drop along the length of the pipeline were obtained on the basis of the conducted analysis. Series of calculations of important characteristics for such pipes were carried out on the basis of offered formulas. Corresponding graphical dependencies were built for visibility. In particular, graphs of the flow rate variations at the end of the collector, depending on the design and filtration characteristics of the “soil-drain” system, are presented. Graph, that shows the dependence of the change in the flow rate connection unevenness along the length of the drainage pipeline at various hydraulic conductivity values of the surrounding soil, is important for understanding the drainage pipes particularity. The necessity to take into account the nature of the flow rate connection unevenness along the length for obtaining reliable results when calculating real drainage pipelines is shown in the article.

Theoretical insights from upscaling Michaelis-Menten microbial dynamics in biogeochemical models: a dimensionless approach

Leading an effective response to the accelerating crisis of anthropogenic climate change will require improved understanding of global carbon cycling. A critical source of uncertainty in Earth Systems Models (ESMs) is the role of microbes in mediating both the formation and decomposition of soil organic matter, and hence in determining patterns of CO2 efflux. Traditionally, ESMs model carbon turnover as a first order process impacted primarily by abiotic factors, whereas contemporary biogeochemical models often explicitly represent the microbial biomass and enzyme pools as the active agents of decomposition. However, the combination of non-linear microbial kinetics and ecological heterogeneity across space guarantees that upscaled dyamics will violate mean-field assumptions via Jensen’s Inequality. Violations of mean-field assumptions mean that parameter estimates from models fit to upscaled data (e.g. eddy covariance towers) are likely systematically biased. Here we present a generic mathematical analysis of upscaling michaelis-menten kinetics under heterogeneity, and provide solutions in dimensionless form. We illustrate how our dimensionless form facilitates qualitative insight into the significance of this scale transition, and argue that it will facilitate cross site intercomparisons of flux data. We also identify the critical terms that need to be constrained in order to unbias parameter estimates.

Sensitivity Analysis of Adjustable River Surf Waves in the Absence of Channel Drop

Most artificial river wave technologies require a drop in the riverbed to generate recreational surf waves; herein a new technology is introduced that can be used on a flat bed. The mechanism includes an adjustable ramp, transition and kicker, which can be independently manipulated to generate a surf wave. A 3-D numerical model of the described mechanism is developed based on a prototype Kananaskis River wave in Alberta, Canada, and is calibrated by means of physical model data. Numerical experiments are conducted to demonstrate sensitivity of the wave to geometric features of each element of the structure in different hydraulic conditions such as flowrate and tailwater depth. Results are presented in dimensionless form to be generalizable and describe the wave behavior. It is shown that the ramp slope, the heaviest and most expensive element of the structure, has a minimal effect on the wave profile, while the tailwater depth, kicker geometry and kicker position can significantly augment and accelerate the wave.

Common Microcirculatory Framework for Monitoring Integrated Microcirculation

Wide variation in magnitudes, units, and ranges of the microcirculatory variables brings hindrance in describing and evaluating the integrated microcirculatory function of tissues. We designed to establish common microcirculatory framework that contains microhemodynamic and microcirculatory oxygen parameters. To integrate microcirculatory information, demo microcirculatory permutations were generated by a computer algorithm based on microcirculatory characteristics. Four dimensionless methods (Z-score, Min-max, L2, and median scaling) were applied to transform microcirculatory data set into the dimensionless form. Three-dimensional (3-D) common microcirculatory framework was constructed and visualized by using Python and Apache ECharts. The performance of the four dimensionless methods in the pre-processing of multiple microcirculatory variables and the establishment of the common microcirculatory framework were compared. Microhemodynamic and microcirculatory oxygen parameters were embedded in the common microcirculatory framework. After processing by Min-max normalization, the transformed multiple microcirculatory values remained positive with fixed range mapping within [0, 1] and maintained the identity property of microcirculation both of microhemodynamic and microcirculatory oxygen variables in the common microcirculatory framework. Conclusively, Min-max normalization displays preferable integration efficiency, compatibility, and adaptability in the establishment of the 3-D visualized multiparametric common microcirculatory framework.

Fractional model of second grade fluid induced by generalized thermal and molecular fluxes with constant proportional caputo

In this research article, the constant proportional Caputo approach of fractional derivative is applied to derive the generalized thermal and molecular profiles for flow of second grade fluid over a vertical plate. The governing equations of the prescribed flow model are reduced to dimensionless form and then solved for temperature, concentration, and velocity via Laplace transform. Further graphs of field variables are sketched for parameter of interest. Comparison between present result and the existing results is also presented graphically.