Kinetic Study of Oxide Growth at High Temperature in Low Carbon Steel

High-temperature surface oxidation kinetics were determined for low-carbon steel using a Joule heating device on hollow cylindrical specimens. The growth of the oxide layer was measured in situ between 800 and 1050 ∘C under isothermal oxidation conditions and in an air laboratory atmosphere (O2 = 20.3% and humidity = 42%). Through a laser and infrared measuring system, the expansion and temperature were measured continuously. From the data acquired, the oxidation kinetic parameters were obtained at different temperatures with a parabolic-type growth model to estimate the rate of oxide layer generation. The convergence degree of the data fitted with the oxidation model was acceptable and appropriately correlated with the experimental data. Finally, comparisons were made between the estimated kinetic parameters and those reported in the literature, observing that the activation energy values obtained are in the range of the reported values.

Assessment of potential beach erosion risk and impact of coastal zone development: a case study on Bongpo–Cheonjin Beach

In many parts, coastal erosion is severe due to human-induced coastal zone development and storm impacts, in addition to climate change. In this study, the beach erosion risk was defined, followed by a quantitative assessment of potential beach erosion risk based on three components associated with the watershed, coastal zone development, and episodic storms. On an embayed beach, the background erosion due to development in the watershed affects sediment supply from rivers to the beach, while alongshore redistribution of sediment transport caused by construction of a harbor induces shoreline reshaping, for which the parabolic-type equilibrium bay shape model is adopted. To evaluate beach erosion during storms, the return period (frequency) of a storm occurrence was evaluated from long-term beach survey data conducted four times per year. Beach erosion risk was defined, and assessment was carried out for each component, from which the results were combined to construct a combined potential erosion risk curve to be used in the environmental impact assessment. Finally, the proposed method was applied to Bongpo–Cheonjin Beach in Gangwon-do, South Korea, with the support of a series of aerial photographs taken from 1972 to 2017 and beach survey data obtained from the period commencing in 2010. The satisfactory outcomes derived from this study are expected to benefit eroding beaches elsewhere.

Inverse problem of determining the coefficient and kernel in an integro - differential equation of parabolic type

This article is concerned with the study of the unique solvability of inverse boundary value problem for integro-differential heat equation. To study the solvability of the inverse problem, we first reduce the considered problem to an auxiliary system with trivial data and prove its equivalence (in a certain sense) to the original problem. Then using the Banach fixed point principle, the existence and uniqueness of a solution to this system is shown.

Analysis of Long-Term Shoreline Observations in the Vicinity of Coastal Structures: A Case Study of South Bali Beaches

Recently, many rigid structures have been installed to cope with and efficiently manage coastal erosion. However, the changes in the coastline or isocenter and the movements of coastal sediment are poorly understood. This study examined the equilibrium shoreline and isocenter lines by applying a Model of Estimating Equilibrium Parabolic-type Shoreline (MeEPASoL) as an equilibrium shoreline prediction model. In addition, the inverse method was used to estimate littoral drift sediment transport from long-term beach profile observations. The movement of coastal sediments was analyzed using long-term beach profile observation data for three Indonesian beaches, namely, Kuta Beach for 13 years, Karang Beach in Sanur for 15 years, and Samuh Beach in Nusa Dua for 18 years. The littoral drift at every site was dynamically controlled by seasonal changes in the monsoon, the erosion and deposition patterns coupled with the presence of coastal structures, and limited sediment movement. Shoreline deformation in Kuta is generally backward deformed, with a littoral drift from south to north. In Sanur, the littoral drift vector carries sediment from the right and left sides and forms a salient behind the offshore breakwater. The littoral drift at Nusa Dua is dominantly from south to north, but the force of sediment transport decreases near the breakwater towards the north. Furthermore, the methods applied herein could aid the development of strategic coastal management plans to control erosion in subcells of coastal areas.

A General Class of Differential Hemivariational Inequalities Systems in Reflexive Banach Spaces

We consider an abstract system consisting of the parabolic-type system of hemivariational inequalities (SHVI) along with the nonlinear system of evolution equations in the frame of the evolution triple of product spaces, which is called a system of differential hemivariational inequalities (SDHVI). A hybrid iterative system is proposed via the temporality semidiscrete technique on the basis of the Rothe rule and feedback iteration approach. Using the surjective theorem for pseudomonotonicity mappings and properties of the partial Clarke’s generalized subgradient mappings, we establish the existence and priori estimations for solutions to the approximate problem. Whenever studying the parabolic-type SHVI, the surjective theorem for pseudomonotonicity mappings, instead of the KKM theorems exploited by other authors in recent literature for a SHVI, guarantees the successful continuation of our demonstration. This overcomes the drawback of the KKM-based approach. Finally, via the limitation process for solutions to the hybrid iterative system, we derive the solvability of the SDHVI with no convexity of functions u↦fl(t,x,u),l=1,2 and no compact property of C0-semigroups eAl(t),l=1,2.

Mathematical model for calculating the temperature field of a direct-flow drying drum

In this paper, one parabolic-type boundary value problem is solved for determining the temperature field of the raw cotton and air components in drum dryers. In the proposed model, convective heat transfer is used according to Newton’s law, the terms describing the evaporation of moisture from the components of raw cotton (seeds, fiber) and the influence of air velocity are taken into account. The resulting system of Galerkin’s differential equations is solved by the finite-difference method in time. It is shown that the approximate solution is estimated according to Galerkin in Sobolev space.The numerical results of the considered problem are obtained by the Bubnov–Galerkin method. A comparative analysis is carried out with experimental data. It is shown that the proposed mathematical model and its numerical algorithm adequately describe the drying process of raw cotton.

Determination of Temperature of Components of Cotton-Raw Material in a Drum Dryer with a Constant

This article solves one parabolic-type boundary value problem for determining the heat-moisture state of raw cotton in drum dryers at a constant air temperature. Numerical results are obtained by the Bubnov – Galerkin method of the problem under consideration, a comparative analysis is carried out with experimental data. It is shown that the proposed mathematical model and its numerical algorithm adequately describe the drying process of raw cotton.

Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations

We consider the Dynamical Low Rank (DLR) approximation of random parabolic equations and propose a class of fully discrete numerical schemes. Similarly to the continuous DLR approximation, our schemes are shown to satisfy a discrete variational formulation. By exploiting this property, we establish stability of our schemes: we show that our explicit and semi-implicit versions are conditionally stable under a “parabolic” type CFL condition which does not depend on the smallest singular value of the DLR solution; whereas our implicit scheme is unconditionally stable. Moreover, we show that, in certain cases, the semi-implicit scheme can be unconditionally stable if the randomness in the system is sufficiently small. Furthermore, we show that these schemes can be interpreted as projector-splitting integrators and are strongly related to the scheme proposed in [29, 30], to which our stability analysis applies as well. The analysis is supported by numerical results showing the sharpness of the obtained stability conditions.