A mathematical model for heterogeneous reactions with a moving boundary

AIChE Journal ◽  
1989 ◽  
Vol 35 (4) ◽  
pp. 625-634 ◽  
Author(s):  
Kareem I. Batarseh ◽  
Glenn P. Swaney ◽  
Alfred H. Stiller
Keyword(s):  
Mathematical Model ◽  
Moving Boundary ◽  
Heterogeneous Reactions

Homogeneous–Heterogeneous Reactions of Blasius Flow in a Nanofluid

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Hang Xu
Keyword(s):  
Mathematical Model ◽  
Diffusion Coefficients ◽  
Multiple Solutions ◽  
Transport Mechanism ◽  
Heterogeneous Reactions ◽  
Nonlinear Ordinary Differential Equations ◽  
Blasius Flow ◽  
Homogeneous And Heterogeneous Reactions ◽  
Heterogeneous Chemical ◽  
Heterogeneous Chemical Reactions

An investigation is made to study the Blasius flow of a nanofluid in the presence of homogeneous–heterogeneous chemical reactions. Here, the diffusion coefficients of the reactant and autocatalyst are considered to be in comparable sizes. The Buongiorno's mathematical model is applied in describing the behavior of nanofluids. Multiple solutions of the steady-state system of nonlinear ordinary differential equations are obtained. Results show that nanofluids significantly participate in the transport mechanism of the homogeneous–heterogeneous reactions, which play different roles in the procedures of homogeneous and heterogeneous reactions.

scholarly journals Modeling of Thermal Conductivity in a Medium with Phase Transition with a Moving Boundary of Phase Change

2021 ◽  
pp. 53-61
Author(s):  
Vadim Mizonov ◽  
◽  
Andrei Tikhonov ◽  
Elena Basova ◽  
Andrei Mitrofanov ◽  
...  
Keyword(s):  
Phase Transition ◽  
Thermal Conductivity ◽  
Heat Treatment ◽  
Mathematical Model ◽  
Numerical Experiments ◽  
Moving Boundary ◽  
Phase Interface ◽  
Significant Feature ◽  
Engineering Practice ◽  
Interface Motion

This work is devoted to the theoretical study of the effect of the phase interface motion on thermal conductivity in a liquid-solid nonlinear medium with a phase transition. The problem under consideration deals with the Stefan problems. Its most significant feature is the jump in the phase properties at separation of their moving boundaries. The objective was achieved by solving the following tasks: the construction of the process mathematical model based on its cell representation and with the use of the Markov chain theory mathematical apparatus, performing numerical experiments with the developed model, demonstrating its operability and the possibility to achieve the set goal. The most significant scientific results were as follows. First was an algorithm for the construction of a cell mathematical model of nonlinear thermal conductivity in a phase transitions medium with a moving phase interface for domains of a canonical shape (plane wall, cylinder, ball). Second, the results of the numerical experiments, showing that the jump of properties affected greatly the kinetics of the process. The significance of the results obtained consisted in the development of a simple but informative mathematical model of the media heat treatment kinetics with phase transformations, available for a direct use in the engineering practice. The proposed algorithm for constructing the model can be effectively used in prediction the open water pipes freezing in cold regions, in modeling the heat treatment of metals, in choosing the freezing modes of food products for a long-term storage, and other thermo-physical processes.

scholarly journals Modelling cell guidance and curvature control in evolving biological tissues

2020 ◽  
Author(s):  
Solene G.D. Hegarty-Cremer ◽  
Matthew J. Simpson ◽  
Thomas L. Andersen ◽  
Pascal R. Buenzli
Keyword(s):  
Mathematical Model ◽  
Moving Boundary ◽  
Particle Method ◽  
Biological Tissues ◽  
Tissue Growth ◽  
Tissue Properties ◽  
Front Tracking Method ◽  
Cell Guidance ◽  
Cell Motion ◽  
Curvature Control

AbstractTissue geometry is an important influence on the evolution of many biological tissues. The local curvature of an evolving tissue induces tissue crowding or spreading, which leads to differential tissue growth rates, and to changes in cellular tension, which can influence cell behaviour. Here, we investigate how directed cell motion interacts with curvature control in evolving biological tissues. Directed cell motion is involved in the generation of angled tissue growth and anisotropic tissue material properties, such as tissue fibre orientation. We develop a new cell-based mathematical model of tissue growth that includes both curvature control and cell guidance mechanisms to investigate their interplay. The model is based on conservation principles applied to the density of tissue synthesising cells at or near the tissue’s moving boundary. The resulting mathematical model is a partial differential equation for cell density on a moving boundary, which is solved numerically using a hybrid front-tracking method called the cell-based particle method. The inclusion of directed cell motion allows us to model new types of biological growth, where tangential cell motion is important for the evolution of the interface, or for the generation of anisotropic tissue properties. We illustrate such situations by applying the model to simulate both the resorption and infilling components of the bone remodelling process, and provide user-friendly MATLAB code to implement the algorithms.

scholarly journals Mathematical Model of Pipeline Abandonment and Recovery in Deepwater

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xia-Guang Zeng ◽  
Meng-Lan Duan ◽  
Chen An
Keyword(s):  
Mathematical Model ◽  
Boundary Condition ◽  
Oil And Gas ◽  
Moving Boundary ◽  
Mechanical Analysis ◽  
Contact Analysis ◽  
Moving Boundary Condition ◽  
Pipeline Segment ◽  
Pi Theorem ◽  
Offshore Oil And Gas

In offshore oil and gas engineering the pipeline abandonment and recovery is unavoidable and its mechanical analysis is necessary and important. For this problem a third-order differential equation is used as the governing equation in this paper, rather than the traditional second-order one. The mathematical model of pipeline abandonment and recovery is a moving boundary value problem, which means that it is hard to determine the length of the suspended pipeline segment. A novel technique for the handling of the moving boundary condition is proposed, which can tackle the moving boundary condition without contact analysis. Based on a traditional numerical method, the problem is solved directly by the proposed technique. The results of the presented method are in good agreement with the results of the traditional finite element method coupled with contact analysis. Finally, an approximate formula for quick calculation of the suspended pipeline length is proposed based on Buckingham’s Pi-theorem and mathematical fitting.

Two methods to solve a fractional single phase moving boundary problem

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Xicheng Li ◽  
Shaowei Wang ◽  
Moli Zhao
Keyword(s):  
Mathematical Model ◽  
Exact Solution ◽  
Heat Equation ◽  
Fractional Derivative ◽  
Boundary Problem ◽  
Single Phase ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Moving Boundary Problems ◽  
Boundary Problems

AbstractA moving boundary problem of a melting problem is considered in this study. A mathematical model using the Caputo fractional derivative heat equation is proposed in the paper. Since moving boundary problems are difficult to solve for the exact solution, two methods are presented to approximate the evolution of the temperature. To simplify the computation, a similarity variable is adopted in order to reduce the partial differential equations to ordinary ones.

scholarly journals Analytical Solutions for Non-Darcy Transient Flow with the Threshold Pressure Gradient in Multiple-Porosity Media

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Erhui Luo ◽  
Xiaodong Wang ◽  
Yongle Hu ◽  
Jianjun Wang ◽  
Li Liu
Keyword(s):  
Mathematical Model ◽  
Pressure Gradient ◽  
Transient Response ◽  
Moving Boundary ◽  
Low Permeability ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
Pressure Transient ◽  
Multiple Porosity ◽  
Low Permeability Reservoirs

Low-velocity non-Darcy flow can be described by using the threshold pressure gradient (TPG) in low-permeability porous media. The existence of the TPG yields a moving boundary so that fluid starts to flow inside this boundary when the pressure gradient overcomes the viscous forces, and beyond this boundary, there will be no flow. A mathematical model of considering the TPG is developed to describe the flow mechanism in multiple-porosity media. By defining new dimensionless variables, the nonlinear mathematical model can be solved analytically. This new approach has been validated with several approximate formulas and numerical tools. The diffusion of the moving boundary varying with time is analyzed in detail in multiple-porosity media, and then the effect of the moving boundary on pressure transient response is investigated and compared with that of the traditional three boundary types (closed boundary, infinite-pressure boundary, and constant-pressure boundary). Sensitivity analysis is conducted to study the effect of the TPG on pressure and pressure derivative curves and rate decline curves for single-porosity media, dual-porosity media, and triple-porosity media, respectively. The results show that the moving boundary exerts a significant influence on reservoir performance at a relatively early time, unlike the other three boundary types, and only a boundary-dominated effect at the late time. The larger the threshold pressure gradient, the smaller the diffusion distance of the moving boundary and the rate of this well at a given dimensionless time. At the same time, the pressure transient response exhibits a higher upward trend because of a larger TPG. All behavior response might be explained by more pressure drop consumed in low-permeability reservoirs. The finding is helpful to understand the performance of low-permeability multiple-porosity media and guide the reasonable development of low-permeability reservoirs.

A Mathematical Model for Li-Air Battery Considering Volume Change Phenomena

2014 ◽  
Author(s):  
Kisoo Yoo ◽  
Prashanta Dutta ◽  
Soumik Banerjee
Keyword(s):  
Mathematical Model ◽  
Volume Change ◽  
Moving Boundary ◽  
Cell Voltage ◽  
Storage Device ◽  
Volume Changes ◽  
Voltage Drops ◽  
Lithium Peroxide ◽  
Air Battery ◽  
Volume Method

Li-air battery has the potential to be the next generation energy storage device because of its much higher energy density and power density. However, the development of Li-air battery has been hindered by a number of technical challenges such as passivation of cathode, change in effective reaction area, volume change during charge and discharge, etc. In a lithium-air cell, the volume change can take place due to Li metal oxidation in anode during charge as well as due to the solubility of reaction product (lithium peroxide) in the electrolyte at cathode. In this study, a mathematical model is developed to study the performance of lithium-air batteries considering the significant volume changes at the anode and cathode sides using moving boundary technique. A numerical method was introduced to solve moving boundary problem using finite volume method. Using this model, the electric performance of lithium-air battery is obtained for various load conditions. Numerical results indicate that cell voltage drops faster with increase in load which is consistent with experimental observations. Also, the volume changes significantly affect the electric performance of lithium-air cell.

scholarly journals Verification of Frost Penetration Mathematical Model with Conjugate Equation in Moving Boundary

2016 ◽  
Vol 9 (1) ◽  
pp. 24-31
Author(s):  
Valentin M. Juravlev ◽  
◽  
Pavel E. Khagleev ◽  
Evgeny P. Khagleev ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Moving Boundary ◽  
Conjugate Equation ◽  
Frost Penetration
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