In this paper we use an approximate analytical method for numerical solution of one dimensional moving boundary problem. We consider the oxygen diffusion problem where the oxygen is allowed to ...diffuse into a sick cell which absorbs and immobilizes oxygen at a constant rate. Our main problem consists in tracking the moving boundary that represents the oxygen penetration depth inside the sick cell. We can find an accurate solution which is obtained by a polynomial of third and fourth degree and we show some mistakes in the paper published by Seval Çatal in (App.Math.Comput 145:361-369, 2003).
In this article it is proved the existence of similarity solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The ...temperature distribution is obtained through a generalized modified error function which is defined as the solution to a nonlinear ordinary differential problem of second order. It is proved that the latter has a unique non-negative bounded analytic solution when the parameter on which it depends assumes small positive values. Moreover, it is shown that the generalized modified error function is concave and increasing, and explicit approximations are proposed for it. Relation between the Stefan problem considered in this article with those with either constant thermal conductivity or a temperature boundary condition is also analysed.
The permafrost in the Qilian Mountains (QLMs), the northeastern margin of the Qinghai–Tibet Plateau, changed dramatically in the context of climate warming and increasing anthropogenic activities, ...which poses significant influences on the stability of the ecosystem, water resources, and greenhouse gas cycles. Yet, the characteristics of the frozen ground in the QLMs are largely unclear regarding the spatial distribution of active layer thickness (ALT), the maximum frozen soil depth (MFSD), and the temperature at the top of the permafrost or the bottom of the MFSD (TTOP). In this study, we simulated the dynamics of the ALT, TTOP, and MFSD in the QLMs in 2004–2019 in the Google Earth Engine (GEE) platform. The widely-adopted Stefan Equation and TTOP model were modified to integrate with the moderate-resolution imaging spectroradiometer (MODIS) land surface temperature (LST) in GEE. The N-factors, the ratio of near-surface air to ground surface freezing and thawing indices, were assigned to the freezing and thawing indices derived with MODIS LST in considerations of the fractional vegetation cover derived from MODIS normalized difference vegetation index (NDVI). The results showed that the GEE platform and remote sensing imagery stored in Google cloud could be quickly and effectively applied to obtain the spatial and temporal variation of permafrost distribution. The area with TTOP < 0 °C is 8.4 × 104 km2 (excluding glaciers and lakes) and accounts for 46.6% of the whole QLMs, the regional mean ALT is 2.43 ± 0.44 m, while the regional mean MFSD is 2.54 ± 0.45 m. The TTOP and ALT increase with the decrease of elevation from the sources of the sub-watersheds to middle and lower reaches. There is a strong correlation between TTOP and elevation (slope = −1.76 °C km−1, p < 0.001). During 2004–2019, the area of permafrost decreased by 20% at an average rate of 0.074 × 104 km2·yr−1. The regional mean MFSD decreased by 0.1 m at a rate of 0.63 cm·yr−1, while the regional mean ALT showed an exception of a decreasing trend from 2.61 ± 0.45 m during 2004–2005 to 2.49 ± 0.4 m during 2011–2015. Permafrost loss in the QLMs in 2004–2019 was accelerated in comparison with that in the past several decades. Compared with published permafrost maps, this study shows better calculation results of frozen ground in the QLMs.
A one-phase Stefan problem in which the latent heat is a power function of position with a positive exponent is investigated. The Stefan problem involves a nonlinear boundary condition of the second ...type. The physical rational of the problem can be found in the context of both the shoreline movement and the soil freezing process. An exact solution is constructed using the similarity transformation technique and the theory of the Kummer functions. The existence and the uniqueness of the solution are proved. Computational examples of the solution provide useful data for verifying general numerical algorithms of Stefan problems. In the end, the solution for a similar Stefan problem involving a nonlinear boundary condition of the first type is also presented.
The present study analyzes the forced convective boundary layer flow of viscous incompressible time-established fluid. The base fluid containing water-based nanoparticles and gyrotactic microbes. The ...flat surface is considered with leading-edge accretion (or) ablation. Characteristics of flow are explored by the impacts of thermal radiation and constructive/destructive chemical reaction. The present flow problem is formed with the partial differential equations, and transformed nonlinear boundary value problems are solved mathematically by the finite difference with the collocation method. There is a good correlation between present work and previous work. Results of selected parameters on velocity, temperature, nanoparticles volume fraction, and microbe density function are discovered. Skin friction, heat transport, mass transfer, and microbes transfer rates are tabular. Efforts of the current work rise in progressive microflow devices to bio-modified nanomaterial dispensation.
•A simulation approach for transient freezing under thermal gradients is introduced.•Assessment of continuum theory to study transient freezing at the nanoscale.•A method to infer the enthalpy of ...freezing from the freezing speeds is presented.•Freezing under homogenous temperature much faster than under temperature gradients.
In this work we investigate the transient solidification of a Lennard-Jones liquid using non-equilibrium molecular dynamics simulations and continuum heat transfer theory. The simulations are performed in slab-shaped boxes, where a cold thermostat placed at the centre of the box drives the solidification of the liquid. Two well-defined solid fronts propagate outwards from the centre towards the ends of the box until solidification is completed. A continuum phase change model that accounts for the difference between the solid and the liquid densities is formulated to describe the evolution of the temperature and the position of the solidification front. Simulation results for a small and a large nanoscale system, of sizes 30.27 nm and 60.54 nm, are compared with the predictions of the theoretical model. Following a transient period of ~ 20-40 ps and a displacement of the solidification front of 1-2.5 nm we find that the simulations and the continuum theory show good agreement. We use this fact to combine the simulation and theoretical approaches to design a simple procedure to calculate the latent heat associated to the liquid-solid phase transition. We also perform simulations of the homogeneous freezing process, i.e. in the absence of a temperature gradient and at constant temperature, by quenching the liquid at supercooled temperatures. We demonstrate that, for comparable temperature conditions, the solidification rate of homogenous freezing is much faster than the one obtained under a thermal gradient. Our study and conclusions should be of general interest to a wide range of atomistic solids.
A polymer distribution is usually represented by its moments. Thus, to calculate transport in a polymer system, a formulation for the transport of moments of the polymer is needed. This is only ...possible if the moments close or if there is a suitable closing condition. To archive this, two simplifications of the Stefan–Maxwell diffusion are derived, which convert the transport equation of polymeric species to a closed set of transport equations for the polymer moments. The first approach corresponds to an infinitely diluted polymer system, whereas the second one describes a highly concentrated polymer system. Both formulations are compared with the full Stefan‐Maxwell model of a ternary mixture of a solvent and two polymer species of different chain length.
To describe a polymer distribution by its moments, a formulation for the transport is needed. This is only possible if the moments close. Two different simplifications of the Stefan–Maxwell diffusion are derived. The first approach corresponds to an infinitely dilute polymer system, while the second approach describes an infinitely concentrated polymer system. Both formulations are validated for different cases.
We introduce a Darcy‐scale model to describe compressible multicomponent flow in a fully saturated porous medium. In order to capture cross‐diffusive effects between the different species correctly, ...we make use of the Maxwell–Stefan theory in a thermodynamically consistent way.
For inviscid flow, the model turns out to be a nonlinear system of hyperbolic balance laws. We show that the dissipative structure of the Maxwell‐Stefan operator permits to guarantee the existence of global classical solutions for initial data close to equilibria. Furthermore, it is proven by relative entropy techniques that solutions of the Darcy‐scale model tend in a certain long‐time regime to solutions of a parabolic limit system.
The Maxwell–Stefan (M–S) formulation is shown to be the most convenient and general way of describing diffusion within zeolite structures. This theory goes a long way to explain the observed various ...types of dependencies of the Fick diffusivity with sorbate loading. For mixture diffusion within zeolites, the M–S theory provides clues for the development of novel separation techniques that rely on diffusion selectivity. We illustrate this aspect by considering a number of practical applications in membrane permeation and chromatographic separations.
Maintenance of the proteome, ensuring the proper locations, proper conformations, appropriate concentrations, etc., is essential to preserve the health of an organism in the face of environmental ...insults, infectious diseases, and the challenges associated with aging. Maintaining the proteome is even more difficult in the background of inherited mutations that render a given protein and others handled by the same proteostasis machinery misfolding prone and/or aggregation prone. Maintenance of the proteome or maintaining proteostasis requires the orchestration of protein synthesis, folding, trafficking, and degradation by way of highly conserved, interacting, and competitive proteostasis pathways. Each subcellular compartment has a unique proteostasis network compromising common and specialized proteostasis maintenance pathways. Stress-responsive signaling pathways detect the misfolding and/or aggregation of proteins in specific subcellular compartments using stress sensors and respond by generating an active transcription factor. Subsequent transcriptional programs up-regulate proteostasis network capacity (i.e., ability to fold and degrade proteins in that compartment). Stress-responsive signaling pathways can also be linked by way of signaling cascades to nontranscriptional means to reestablish proteostasis (e.g., by translational attenuation). Proteostasis is also strongly influenced by the inherent kinetics and thermodynamics of the folding, misfolding, and aggregation of individual proteins, and these sequence-based attributes in combination with proteostasis network capacity together influence proteostasis. In this review, we will focus on the growing body of evidence that proteostasis deficits leading to human pathology can be reversed by pharmacologic adaptation of proteostasis network capacity through stress-responsive signaling pathway activation. The power of this approach will be exemplified by focusing on the ATF6 arm of the unfolded protein response stress responsive-signaling pathway that regulates proteostasis network capacity of the secretory pathway.
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