Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations

<p style='text-indent:20px;'>In this paper, multidimensional stability of pyramidal traveling fronts are studied to the reaction-diffusion equations with degenerate Fisher-KPP monostable and combustion nonlinearities. By constructing supersolutions and subsolutions coupled with the comparison principle, we firstly prove that under any initial perturbation (possibly large) decaying at space infinity, the three-dimensional pyramidal traveling fronts are asymptotically stable in weighted <inline-formula><tex-math id="M1">\begin{document}$ L^{\infty} $\end{document}</tex-math></inline-formula> spaces on <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^{n}\; (n\geq4) $\end{document}</tex-math></inline-formula>. Secondly, we show that under general bounded perturbations (even very small), the pyramidal traveling fronts are not asymptotically stable by constructing a solution which oscillates permanently between two three-dimensional pyramidal traveling fronts on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R}^{4} $\end{document}</tex-math></inline-formula>.</p>

The New Equations for “Rate-Determining Chemisorption of Coal”

The purpose of the new formulas, Cml, CmlK, and CmlY, which express the slowest char combustion rate, is to show the controlling mechanism of single coal burning. Oxygen diffusion through the boundary layer (as a result of releasing volatile matter from coal) to the char surface is the slowest step rate and can also represent as the rate determining. This step has not yet been taken into account in the literature and may effect incomparable decisions between numerical and experimental results of coal combustion studies. In the 1920s, Wilhelm Nusselt found the coal combustion equation for a single coal, which is based on initial coal diameter, and its burning time, or Nusselt square law (NSL). Also, the burning constant in NSL expressed oxygen partial pressure and the ambient temperature level. Nevertheless, recent studies according to char combustion have explained the effect of coal density on char combustion. Consequently, to help understand the slowest rate of char combustion, NSL as well as ordinary char combustion equations can be used together to establish the rate-determining factor. For this purpose, in this study, the slowest step of the char reaction rate is given as “Cml” of stable position for single coal particle, “CmlK” and “CmlY” for a coal particle in a motion.

CO2 Emissions by Agricultural Machines in South Korea

The burning of fossil fuels and the resulting CO2 emissions are related to climate change and global warming. In order to help meet international goals of preventing irreversible climate change, South Korea must reduce its gross CO2 emission level from its 2015 level of 680 Mt. Knowing current sources of CO2 productions is essential for accomplishing this reduction. This study calculated the level of CO2 emissions by agricultural tractors, heaters, and dryers which are accounted for consuming 88.6% of the tax-free fuels allocated for agricultural use in South Korea. After the amount of fuel and electricity consumed by each machine was determined, CO2 emissions from each were estimated using the combustion equations. The total annual amount of CO2 emissions produced by these agricultural machines was estimated to be 4,334.2 kt which is less than 1% of the gross CO2 emissions in South Korea in 2015. Keywords: Agricultural dryer, Agricultural heater, Agricultural tractor, CO2 emissions.

Flame balls stabilized by suspension in fluid with a steady linear ambient velocity distribution

The ignition of lean H2/air mixtures under microgravity (μg) conditions can lead to the formation of spherical premixed flames (flame balls) with small Péclet number (Pe). A central question concerning these structures is the existence of appropriate stationary stable solutions of the combustion equations. In this paper we examine an individual flame ball that is suspended in a fluid whose velocity far from the flame is steady and varies linearly in space. Detailed results are obtained for simple shear flows and simple straining flows, both axisymmetric and plane.Convection enhances the flux of heat from the flame and the flux of mixture to the flame, but because the Lewis number (Le) is less than unity the relative impact on the former is greater than on the latter. Consequently, there is a net loss of energy from the flame to the far field, and if large enough this will quench the flame. For values of shear or strain less than the quenching value there are two possible stationary solutions, but one of these is unstable to spherically symmetric disturbances of the flame ball. The radius of the other solution is unbounded as Pe goes to zero. Examination of a class of three-dimensional disturbances reveals no additional instability when the energy losses are due only to convection, but sufficiently large flame balls are unstable when volumetric heat losses from radiation are accounted for. This last result is in agreement with previous results that have been obtained for zero Pe, albeit with inadequate accounting for the flow field generated by the perturbations.