One-dimensional Finite Difference Research Articles

Numerical investigation of ionic transport and overpotential effects in the electrolyte of the lithium-ion battery

ABSTRACT In this study, we numerically investigated the electrochemical performance of a CGR 17,600 lithium-ion battery (LIB), focusing on lithium-ion transport dynamics within the electrolyte. Using a one-dimensional Nernst-Planck model and finite difference method, we simulated ion diffusion and migration during galvanostatic charge-discharge cycles. Our model predicts concentration profiles, overpotentials, and resistances, identifying a maximum safe operating current of 0.8271 A. The analysis reveals that diffusion dominates during discharge, while migration prevails during charging. The study also characterises ohmic resistance of 0.0497 Ω and steady-state resistance of 0.1904 Ω, underscoring their importance in battery efficiency. Additionally, a transference coefficient of 0.4 highlights effective ion transport, critical for optimising LIB design and performance.

Optimization of Geothermal Heat Pump Systems for Sustainable Urban Development in Southeast Asia

This study examines the optimization of ground source heat pump (GSHP) systems and energy piles for sustainable urban development, focusing on Southeast Asia. GSHPs, which utilize geothermal energy for indoor HVAC needs, offer a sustainable alternative to traditional systems by utilizing consistent subsurface temperatures for heating and cooling. The study highlights the importance of understanding thermal movement within the soil, especially in soft marine clays prevalent in Southeast Asia, to improve GSHP system efficiency. Using a one-dimensional finite difference model, the study examines the effects of soil thermal conductivity and density on system performance. The results show that GSHP systems, especially when integrated with energy piles, significantly reduce electricity consumption and greenhouse gas emissions, underscoring their potential to mitigate the urban heat island effect in densely populated areas. Despite challenges posed by the region’s hot and humid climate, which could affect long-term effectiveness, the study highlights the need for further study, including field experiments and advanced modeling techniques, to optimize GSHP configurations and fully exploit geothermal energy in urban environments. The study’s insights into soil thermal dynamics and system design optimization contribute to advancing sustainable urban infrastructure development.

Long-term “memory” of extraordinary climatic seasons in the hysteretic seepage of an unsaturated infinite slope

AbstractThis paper presents a study of the hydraulic response of an infinite unsaturated slope exposed to a perturbation of the ordinary seasonal climatic cycle. The ground flow is modelled via a simplified one-dimensional finite difference scheme by decomposing the two-dimensional slope seepage into antisymmetric and symmetric parts. The numerical scheme incorporates two distinct hysteretic and non-hysteretic soil water retention laws, whose parameters have been selected after a preliminary sensitivity analysis. Results indicate that, in the hysteretic case, the “memory” of the perturbation takes a long time to fade, and the ordinary soil saturation cycle is only restored after several years of normal weather. Instead, in the non-hysteretic case, the recovery of the ordinary saturation regime is almost immediate after the perturbation. In contrast with the markedly different predictions of degree of saturation, both hysteretic and non-hysteretic slope models predict virtually identical evolutions of negative pore water pressures, with an almost immediate restoration of the ordinary cycle after the perturbation.

Finite Difference Method for Solving Parabolic-Type Integro-Differential Equations in Multidimensional Domain with Nonhomogeneous First-Order Boundary Conditions

Introduction. We investigate a multidimensional (in terms of spatial variables) parabolic-type integro-differential equation with nonhomogeneous first-order boundary conditions. The locally one-dimensional finite difference scheme developed herein can be applied to solve various applied problems leading to multidimensional parabolic-type integro-differential equations. Examples include mathematical modelling of cloud processes, addressing the issue of active intervention in convective clouds to prevent hail and artificially enhance precipitation, as well as describing the droplet mass distribution function due to microphysical processes such as condensation, coagulation, fragmentation, and freezing of droplets in convective clouds.Materials and Methods. In this study, an approximate solution to the initial-boundary value problem is constructed using the locally one-dimensional scheme of A.A. Samarsky with a specified order of approximation О(h2 +τ). The primary research method employed is the method of energy inequalities.Results. A priori estimates have been obtained in the discrete interpretation, from which uniqueness, stability, and convergence of the solution of the locally one-dimensional difference scheme to the solution of the original differential problem follow, with a convergence rate equal to the order of approximation of the difference scheme.Discussion and Conclusions. The research findings can be utilized for further development of boundary value problem theory for parabolic equations with variable coefficients. Additionally, they may find applications in the fields of difference scheme theory, computational mathematics, and numerical modelling.

Estimation of Electromagnetic Radiation Distribution in the Human Heart Rate at Different Frequencies‏‏

The health implications of electromagnetic radiation have been extensively debated due to the sharp increase in the usage of cell phones, Wi-Fi transmitters and other microwave equipment. Electromagnetic radiation affects the autonomic nervous system, heart rate, blood pressure and other cardiovascular functions. This study aims to present a Numerical Simulation of Electromagnetic Radiation (EMR) on the human heart tissue and to explore the effect of different frequencies in the spectral range (900, 1,800 and 2,400 MHz) on Specific Absorption Rate (SAR), power density, the Distribution of Electromagnetic Fields by Matlab program, and Finite-Difference Time-Domain (FDTD) method in One Dimension (1D). A 1-dimensional finite difference method was used to solve Maxwell’s equations in heart tissue. The heart model was subjected to electromagnetic radiation that has dielectric properties according to frequency. Frequency was chosen and the operation of the software program as Matlab and the dielectric attribute has been calculated. Concurring with the Frequency in a private program, are the conductivity, relative permittivity, wavelength and infiltration profundity. The amplitudes of the reflected and transmitted sinusoid waves, relative to the occurrence wave, were portrayed by the reflection coefficient and the transmission coefficient, which relate to the amplitudes of the electric field wave. The electric field, magnetic field and power density were simulated along the line X = Y = 0. The study showed that the impact of electromagnetic radiation depends on the frequency of the wave which hit the heart. It was found that the heart tissue reacts more at 900 MHz compared to 1,800 and 2,400 MHz, and the tissue absorption is higher at the lower frequency. There was a relation between the magnetic field in the y-dimension and the time step the in x-dimension. HIGHLIGHTS The effect of electromagnetic has been theoretically studied where the electromagnetic fields produced from electromagnetic radiation at 900 MHz,1800 MHz, and 2400 MHz on layered biological tissues (heart model) by the finite difference time domain (FDTD) method A one-dimensional finite difference method was used to solve Maxwell's equations in heart tissue The amplitudes of the reflected and transmitted sinusoid waves, relative to the occurrence wave, were portrayed by the reflection coefficient and the transmission coefficient, which relate to the amplitudes of the electric field wave The impact of electromagnetic radiation depends on the frequency of the wave which hit the heart. There was a relation between the magnetic field in the y-dimension and the time step the in x-dimension GRAPHICAL ABSTRACT

Using Phase Change Materials (PCM) to Reduce Energy Consumption in Buildings

The article discusses the use of phase change materials (PCM) to enhance thermal energy storage (TES) in residential buildings. The building sector consumes a significant amount of energy, and energy efficiency is crucial in reducing overall energy consumption. PCM has emerged as a promising approach to decrease energy consumption for space cooling and heating in buildings. The article uses DesignBuilder software to evaluate the energy consumption of a residential building. EnergyPlus is the calculation method used by DesignBuilder. The researchers considered a baseline dwelling house located in Moscow and used EnergyPlus, a simulation tool, to analyze the performance of building components integrated with PCM to reduce energy consumption while maintaining a comfortable indoor temperature. The study used the one-dimensional finite difference conductivity (CondFD) algorithm in EnergyPlus to simulate a building element with PCM. Using BioPCM M91/Q23 can significantly reduce heating and cooling costs. The article concludes that integrating PCM into building components can improve indoor thermal comfort, reduce energy demand for heating and cooling, and enhance occupant comfort. The use of PCM has the potential to mitigate the effects of outdoor temperature changes on indoor thermal comfort, making it a cost-effective and clean energy-saving material.

A Methodology to Reduce Thermal Gradients Due to the Exothermic Reactions in Resin Transfer Molding Applications

Resin transfer molding (RTM) is among the most used manufacturing processes for composite parts. Initially, the resin cure is initiated by heat supply to the mold. The supplementary heat generated during the reaction can cause thermal gradients in the composite, potentially leading to undesired residual stresses which can cause shrinkage and warpage. In the present numerical study of these processes, a one-dimensional finite difference method is used to predict the temperature evolution and the degree of cure in the course of the resin polymerization; the effect of some parameters on the thermal gradient is then analyzed, namely: the fiber nature, the use of multiple layers of reinforcement with different thermal properties and also the temperature cycle variation. The validity of this numerical model is tested by comparison with experimental and numerical results in the existing literature.

Trans-level multi-scale simulation of porous catalytic systems: Bridging reaction kinetics and reactor performance

Multi-scale porous structures inside and/or between the catalyst pellets or particles are found in many chemical processes, where strong coupling of reaction and transport results in complex apparent reaction kinetics influential to the reactor performance. Traditional continuum-based porous media models and simulation methods can hardly describe such structures and their scale effects faithfully. A trans-level multi-scale discrete computational framework is hence proposed to address this complexity and implemented for an olefin catalytic cracking (OCC) process. The apparent reaction kinetics at the REV (representative elementary volume) scale is obtained by hard-sphere pseudo-particle modeling (HS-PPM), and coupled with computational fluid dynamics / discrete element method (CFD-DEM) for the reactor-level hydrodynamics via a one-dimensional (1D) finite difference scheme for particle-level diffusion. The mesoscales of the REVs and the flow networks between the particles are thus covered by the framework, which are previously described by simple average quantities in the continuum methods. The reactant conversion rate and target product selectivity obtained agree well with experimental results, while a continuum approach may give significantly different and unreasonable results. The multi-scale method is, therefore, demonstrated to be necessary and effective for bridging the intrinsic reaction kinetics with the performance of porous catalytic reactors.

Graphene saturable absorber mirror for passive mode-locking of mid-infrared QCLs

Passive mode-locking in quantum cascade lasers (QCLs) remains one of the huge challenges because of the fast relaxation time of the excited carriers which is typically in the range of sub-picoseconds. The use of conventional techniques such as the semiconductor saturable absorber mirror is inefficient because the spatial hole burning effect dominates the carrier dynamics. To overcome this effect, longitudinal transition structures with relaxation time around $$50~\mathrm {ps}$$ were proposed. However, mode-locking is assured with an external modulation at a cavity roundtrip frequency. In this paper, we demonstrate that a single-layer graphene used as a saturable absorber permits to generate stable pulses in such structures. The graphene is integrated with a highly reflective mirror to increase the internal electric field and achieve the saturation intensity. The dynamic of the QCL is modeled with Maxwell-Bloch equations while Maxwell-Ampere equation is used for the graphene layer by considering a nonlinear conductivity. This system of equations is solved using the one-dimensional Finite-Difference Time-Domain ( FDTD) method. To model the single-layer graphene of a $$0.33~\mathrm {nm}$$ thickness, a specific sub-cell is implemented based on Maloney method. Simulation results of a $${\mkern 1mu} 6.2~\mu {\text{m}}$$ QCL with a diagonal radiative transition show a generation of isolated pulses with a peak electric field of $$80~\mathrm {MV.m^{-1}}$$ and a duration of $$51~\mathrm {fs}$$ . The mode-locking remains stable for QCLs with a vertical transition having a relaxation time below $$5~\mathrm {ps}$$ .

Integration of desiccant wheels and high-temperature heat pumps with milk spray dryers

Heat pump technologies are promising to decarbonise industrial drying processes by improving energy efficiency and shifting the energy source from fossil fuels to renewable-sourced electricity. While desiccant materials have proved effective in improving drying efficiency for dryers at temperatures < 120 °C, this paper focuses on the performance of desiccant wheel assisted high temperature heat pump (HTHP) technology to heat the dryer inlet air up to 150 °C using heat recovered from the dryer exhaust. Thermodynamic models of heat pump cycles were established to evaluate the performance of all the HTHP components. A one-dimensional finite difference model was used to simulate the dehumidification of exhaust air through the evaporator of the HTHP. The performance of the desiccant wheel was numerically simulated considering only the gas-side heat and mass transfer resistance. When compared with configurations of a simple HTHP, the desiccant wheel assisted HTHP requires a much smaller evaporator size (50–60 % less than the simple HTHP), similar to the HTHP with a heat recuperator. Its improvement in overall system coefficient of performance (COP), exergy efficiency and the drying capacity when applied to a spray dryer is marginal when compared to the model accuracy. However, comparisons between two cases with different ambient conditions (15 °C and 60 % RH vs 25 °C and 80 % RH) show that such improvement by the desiccant wheel assisted HTHP develops with increasing humidity in the incoming drying air.

Finite Difference Method Simulation on Effect of Blood Perfusion on Temperature Distribution of Female Human Skin

&lt;p&gt;&lt;span lang="EN-US"&gt;Bioheat&lt;/span&gt;&lt;span lang="EN-US"&gt; transfer is a combination of heat transfer and biology process comprising of transfer of heat from human living tissue to the environment. This study aims to estimate the temperature distribution of female human’s skin. In this study, effect of varied blood perfusions of 1.5, 2.0, 2.5 and 3.0 kg/s.m&lt;sup&gt;3 &lt;/sup&gt;on bioheat transfer of female human skin, which was modeled into four layers, was simulated. To address this issue, one-dimensional unsteady state finite difference method was applied in this study. Result of this study informed that the finite difference method can be used to solve the bioheat transfer equation and to estimate temperature distribution of different skin layers of female human. In this study, blood perfusion affects temperature distribution in the four layers of unstable women's skin. The highest blood perfusion of 3 kg/s.m&lt;sup&gt;3&lt;/sup&gt; resulted in more homogeny temperature distribution of different skin layers. This circumstance occurred since higher blood perfusion increases heat transfer between blood and skin layers.&lt;/span&gt;&lt;/p&gt;

Thermoplastic Composites: Modelling Melting, Decomposition and Combustion of Matrix Polymers

In thermoplastic composites, the polymeric matrix upon exposure to heat may melt, decompose and deform prior to burning, as opposed to the char-forming matrices of thermoset composites, which retain their shape until reaching a temperature at which decomposition and ignition occur. In this work, a theoretical and numerical heat transfer model to simulate temperature variations during the melting, decomposition and early stages of burning of commonly used thermoplastic matrices is proposed. The scenario includes exposing polymeric slabs to one-sided radiant heat in a cone calorimeter with heat fluxes ranging from 15 to 35 kW/m2. A one-dimensional finite difference method based on the Stefan approach involving phase-changing and moving boundary conditions was developed by considering convective and radiative heat transfer at the exposed side of the polymer samples. The polymers chosen to experimentally validate the simulated results included polypropylene (PP), polyester (PET), and polyamide 6 (PA6). The predicted results match well with the experimental results.

Performance analysis on combined heat and power of photovoltaic-thermal module integrated with phase change material-water storage

Use of phase change material (PCM) to generate temperature stratification in water storage tank coupled with unglazed photovoltaic-thermal (PVT) module for combined heat and power generation enhancement was investigated by experimental and numerical analyses. In the experiment, RT42 PCM having melting point of 38–43 °C was filled in a packed-bed of 40 mm diameter spherical capsules contained in a 220 L water storage tank connecting with four units of 200 Wp (watt peak) unglazed PVT module in series. The experiments were performed outdoor with the water mass flow rates of 2.4 and 5.8 LPM. One-dimensional finite difference enthalpy method was used to predict the water and PCM ball temperatures in the tank. The PVT thermal performance was evaluated similarly to that of solar thermal collector, and the electrical performance was calculated from nominal operating cell temperature (NOCT) approach. It could be noticed that the simulated results on the water and the PCM ball temperatures including the module temperature and the maximum generated electrical power of PVT modules agreed well with the experimental data. The model was used to predict the electrical and overall (both thermal and electrical) efficiencies of the PVT modules by considering the positions of the PCM packed-bed, the PCM amount, the circulating water mass flow rate, and the PCM type. It could be found that the position of the packed-bed did not give effect on the PVT module performances but increase of the PCM amount generated higher water temperature stratification in the storage tank which resulted in higher PVT module efficiencies especially in the afternoon. The circulating water also did not give strong effect on the total PVT module performances. For PCM with low melting point, the PVT module performances were higher but the water temperature in the storage tank might be too low for hot water utilization.

Study Of Various Thermal Conductivity Layers in Bioheat Transfer Against Thermal Distribution on Human Skin with Finite Difference Method (FDM)

Development of science are often found with the connection between science and another that forms a brands newscience.one among the new sciences is biomechanics with one among its scientific fields is bioheat transfer which is applied to human skin.one among the factors that influence the heat propagation of skin tissue is thermal conductivity because theability of materials to conduct heat. the aim of this study was to work out the mathematical model of bioheat transfer with a one-dimensional finite difference method and therefore the effect of thermal conductivity on its temperature distribution. The modelis often made with combine the Pennes H.H equation to the steady state then the chosen parameter entered into it. The results of the study were compared between the finite difference method and therefore the analytic method. The results of comparative studies indicate a rise in temperature distribution but between the 2still have differences (error).Changes in environmental temperature affect the temperature distribution in human skin. While the thermal conductivity of various layers has no significant effect, the worth of temperature distributed between points increases regularly from the core of the body to the outer layer of human skin.

Approximation Solution of the Fractional Parabolic Partial Differential Equation by the Half-Sweep and Preconditioned Relaxation

In this study, the numerical solution of a space-fractional parabolic partial differential equation was considered. The investigation of the solution was made by focusing on the space-fractional diffusion equation (SFDE) problem. Note that the symmetry of an efficient approximation to the SFDE based on a numerical method is related to the compatibility of a discretization scheme and a linear system solver. The application of the one-dimensional, linear, unconditionally stable, and implicit finite difference approximation to SFDE was studied. The general differential equation of the SFDE was discretized using the space-fractional derivative of Caputo with a half-sweep finite difference scheme. The implicit approximation to the SFDE was formulated, and the formation of a linear system with a coefficient matrix, which was large and sparse, is shown. The construction of a general preconditioned system of equation is also presented. This study’s contribution is the introduction of a half-sweep preconditioned successive over relaxation (HSPSOR) method for the solution of the SFDE-based system of equation. This work extended the use of the HSPSOR as an efficient numerical method for the time-fractional diffusion equation, which has been presented in the 5th North American International Conference on industrial engineering and operations management in Detroit, Michigan, USA, 10–14 August 2020. The current work proposed several SFDE examples to validate the performance of the HSPSOR iterative method in solving the fractional diffusion equation. The outcome of the numerical investigation illustrated the competence of the HSPSOR to solve the SFDE and proved that the HSPSOR is superior to the standard approximation, which is the full-sweep preconditioned SOR (FSPSOR), in terms of computational complexity.

A numerical model to simulate the dynamic performance of Breathing Walls

A one-dimensional Finite Difference Model for Breathing Wall components under time dependent Dirichlet boundary conditions is presented. The algorithm undergoes a comprehensive validation against a dynamic analytical model, under either sinusoidal and generically periodic boundary conditions, adopting different airflow velocities and in relation to capacitive and resistive materials alternatively. It is found that the accurate prediction of the temperature profile inside the wall is influenced primarily by the timestep, whose optimal value can be identified through a preliminary frequency analysis of the boundary conditions. Moreover, for a better prediction of the surface heat flow density, and especially in insulating materials, refining the space grid below 1 mm is recommended, as well as the adoption of a 3-point numerical scheme. The numerical model is finally tested against experimental data on a porous concrete wall, showing that numerical errors may compare to other sources of uncertainties, regarding materials properties and boundary conditions.

Isomorphism between one-Dimensional and multidimensional finite difference operators

<p style='text-indent:20px;'>Finite difference operators are widely used for the approximation of continuous ones. It is well known that the analysis of continuous differential operators may strongly depend on their dimensions. We will show that the finite difference operators generate the same algebra, regardless of their dimension.

Thermal behavior of external-insulated cold-formed steel non-load-bearing walls exposed to different fire conditions

An external-insulated cold-formed steel (CFS) wall is a potential configuration that overcomes the disadvantage of cavity insulation in the fire performance of such walls and can meet the sound and thermal insulation requirements for building structures by increasing the thickness of insulation material. This paper conducted eight mid-scale non-load-bearing fire experiments on external-insulated wall specimens. Four different fire conditions were tested, including ISO 834 fire, external fire, hydrocarbon fire and a typical realistic design fire. A quasi-steady heat transfer state was identified at the final stage of external fire exposure. The effect of substituting the cavity insulation with external insulation on the fire performance is discussed by comparison with the previous fire experiments on cavity-insulated CFS walls. The results show that external insulation is a more reasonable configuration than cavity insulation for improving the fire resistance of CFS walls. In addition, two types of stud buckling, which include the local buckling of the whole stud section and local buckling of stud hot flange and adjacent web, were identified for non-load-bearing walls in fire, and the corresponding cause and conditions were described. In addition, to achieve high efficiency in the thermal performance modeling of CFS walls in fire, a quick and simplified calculation method was developed to get the temperature profile of steel frame based on a one-dimensional finite difference method. Moreover, an unexposed surface temperature of 900 °C was recommended as the criterion to predict the falling-off of the fire-side face-layer gypsum plasterboards of CFS walls in the heat transfer modeling.

Nonlinear solutions for laterally loaded piles

A nonlinear analysis framework for laterally loaded piles is presented that is as accurate as equivalent three-dimensional nonlinear finite element analysis, but computationally one order of magnitude faster. The nonlinear behavior of sands and clays are account for by using hyperbolic modulus–reduction relationships. These nonlinear–elastic constitutive models are used to calculate the reduced modulus at different points in the soil based on the soil strains induced by lateral pile displacement. The reduced modulus at different points in the soil domain are spatially integrated to calculate the reduced soil resistance parameters associated with the differential equation governing the lateral pile displacement. The differential equations governing the lateral displacements of pile and soil under equilibrium are obtained by applying the principle of virtual work to a continuum-based pile–soil system. These coupled differential equations are solved using the one-dimensional finite difference method following an iterative algorithm. The accuracy of the analysis is verified against equivalent three-dimensional nonlinear finite element analysis, and the validity of the analysis in predicting the field response is checked by comparisons with multiple pile load test results. Parametric studies are performed to gain insights into the lateral pile response.

Thermal Response of an Orthotropic Non-charring Ablative Material

In this paper, the thermal response of orthotropic carbon–carbon is studied. In the first step, non-charring materials ablation is implemented into a finite volume solver. Carbon–carbon ablative thermal behavior is studied under a time-dependent heat flux. The equilibrium surface thermochemistry model of carbon ablation in air including the diffusion and sublimation along with energy source term, heated wall recession and material properties are all applied in FLUENT 6.3 solver via user-defined functions. Stagnation point temperature, recession and net heat flux for the isotropic case are compared with the published one-dimensional finite difference results. Subsequently, the effects of orthotropic conductivity of the material on surface temperature, ablation mass flux, recession rate of the heated wall and the temperature distribution through the material are described. Results indicate that higher surface temperature and ablation mass flux as well as lower interior temperatures are achieved by the orthotropic material response, compared to the isotropic one. The same conclusion can be made by increasing the ratio of “in-plane” to “through-the-thickness” conductivities. In brief, this work presents a methodology for modeling two- and three-dimensional non-charring material ablation within FLUENT solver to study the thermal response of an anisotropic ablator, sharp geometries and metal–insulator interface where a classic one-dimensional approach is inaccurate.