Search results for: two dimensional

Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

Abstract:

In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: explicit group method, finite difference, helmholtz equation, rotated grid, standard grid

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Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis

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Authors: Hee Sun (Sunny) Choi, Gerhard Bruyns, Wang Zhang, Sky Cheng, Saijal Sharma

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The main focus of this paper is to propose a comprehensive framework for the cognitive measurement and modelling of the built environment. This will involve exploring and measuring neural mechanisms. The aim is to create a foundation for further studies in this field that are consistent and rigorous. Additionally, this framework will facilitate collaboration with cognitive neuroscientists by establishing a shared conceptual basis. The goal of this research is to develop a human-centric approach for urban design that is scientific and measurable, producing a set of urban design guidelines that incorporate cognitive measurement and modelling. By doing so, the broader intention is to design urban spaces that prioritize human needs and well-being, making them more liveable.

Keywords: vertical urbanism, human centric design, spatial cognition and psychology, vertical urban design guidelines

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Authors: S. Belhour, A. K. Ferouani, C. Azizi

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In recent years, a considerable effort (experience, numerical simulation, and theoretical prediction models) has characterised by high efficiency and low cost. Then an improved physics analytical model for simulating is proposed. The performance of GaAs MESFETs has been developed for use in device design for high frequency. This model is based on mathematical analysis, and a new approach for the standard model is proposed, this approach allowed to conceive applicable model for MESFET’s operating in the turn-one or pinch-off region and valid for the short-channel and the long channel MESFET’s in which the two dimensional potential distribution contributed by the depletion layer under the gate is obtained by conventional approximation. More ever, comparisons between the analytical models with different values of mobility are proposed, and a good agreement is obtained.

Keywords: analytical, gallium arsenide, MESFET, mobility, models

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Authors: Suleiman Bashir Adamu, Lawan Sani Taura

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We study the role of boundary conditions via -symmetric quantum mechanics, where denotes parity operator and denotes time reversal operator. Using the one-dimensional Schrödinger Hamiltonian for a free particle in an infinite square well, we introduce symmetric boundary conditions. We find solutions of the 1D Klein-Gordon equation for a free particle in an infinite square well with Hermitian boundary and symmetry boundary conditions, where in both cases the energy eigenvalues and eigenfunction, respectively, are obtained.

Keywords: Eigenvalues, Eigenfunction, Hamiltonian, Klein- Gordon equation, PT-symmetric quantum mechanics

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Authors: Ibrahim Ajani Tijani, C. W. Lim

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Limited studies have examined the effect of size on the mechanical behavior of confined concrete subjected to 3-dimensional (3D) test. With the novel 3D testing system to produce passive confinement, concrete cubes were tested to examine the effect of size on stress-strain behavior of the specimens. The effect of size on 3D stress-strain relationship was scrutinized and compared to the stress-strain relationship available in the literature. It was observed that the ultimate stress and the corresponding strain was related to the confining rigidity and size. The size shows a significant effect on the intersection stress and a new model was proposed for the intersection stress based on the conceptual design of the confining plates.

Keywords: concrete, aggregate size, size effect, 3D compression, passive confinement

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Authors: A. R. Manu, V. K. Agrawal, K. N. Balasubramanya Murthy

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Authentication is required in stored database systems so that only authorized users can access the data and related cloud infrastructures. This paper proposes an authentication technique using multi-factor and multi-dimensional authentication system with multi-level security. The proposed technique is likely to be more robust as the probability of breaking the password is extremely low. This framework uses a multi-modal biometric approach and SMS to enforce additional security measures with the conventional Login/password system. The robustness of the technique is demonstrated mathematically using a statistical analysis. This work presents the authentication system along with the user authentication architecture diagram, activity diagrams, data flow diagrams, sequence diagrams, and algorithms.

Keywords: design, implementation algorithms, performance, biometric approach

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Authors: Yakup Ulusu, Numan Eczacıoğlu, İsa Gökçe, Helen Waller, Jeremy H. Lakey

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Besides having the appropriate amino acid sequence to perform the function of proteins, it is important to have correct conformation after this sequence to process. To consist of this conformation depends on the amino acid sequence at the primary structure, hydrophobic interaction, chaperones and enzymes in charge of folding etc. Misfolded proteins are not functional and tend to be aggregated. Cysteine originating disulfide cross-links make stable this conformation of functional proteins. When two of the cysteine amino acids come side by side, disulfide bond is established that forms a cystine bridge. Due to this feature cysteine plays an important role on the formation of three-dimensional structure of many proteins. There are two cysteine amino acids (C44, C69) in the Tol-A-III protein. Unlike protein disulfide bonds from within his own, any non-specific cystine bridge causes a change in the three dimensional structure of the protein. Proteins can be expressed in various host cells as directly or fusion (chimeric). As a result of overproduction of the recombinant proteins, aggregation of insoluble proteins in the host cell can occur by forming a crystal structure called inclusion body. In general fusion proteins are produced for provide affinity tags to make proteins more soluble and production of some toxic proteins via fusion protein expression system like pTolT. Proteins can be modified by using a site-directed mutagenesis. By this way, creation of non-specific disulfide crosslinks can be prevented at fusion protein expression system via the present cysteine replaced by another amino acid such as serine, glycine or etc. To do this, we need; a DNA molecule that contains the gene that encodes for the target protein, required primers for mutation to be designed according to site directed mutagenesis reaction. This study was aimed to be replaced cysteine encoding codon TGT with serine encoding codon AGT. For this sense and reverse primers designed (given below) and used site-directed mutagenesis reaction. Several new copy of the template plasmid DNA has been formed with above mentioned mutagenic primers via polymerase chain reaction (PCR). PCR product consists of both the master template DNA (wild type) and the new DNA sequences containing mutations. Dpn-l endonuclease restriction enzyme which is specific for methylated DNA and cuts them to the elimination of the master template DNA. E. coli cells obtained after transformation were incubated LB medium with antibiotic. After purification of plasmid DNA from E. coli, the presence of the mutation was determined by DNA sequence analysis. Developed this new plasmid is called PtolT-δ.

Keywords: site directed mutagenesis, Escherichia coli, pTolT, protein expression

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Authors: Sina Saadati, Mohammadreza Razzazi

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Since Java is an object-oriented language, It can be used to solve a wide range of problems. One of the considerable usages of this language can be found in Agent-based modeling and simulation. Despite the significant power of Java, There is not an easy method to render a 3-dimensional human model. In this article, we are about to develop a library which helps modelers present a 3D human model and control it with Java. The library runs two server programs. The first one is a web page server that can connect to any browser and present an HTML code. The second server connects to the browser and controls the movement of the model. So, the modeler will be able to develop a simulation and display a good-looking human model without any knowledge of any graphical tools.

Keywords: agent-based modeling and simulation, human model, graphics, Java, distributed systems

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Authors: A. Amiri Delouei

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In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

Keywords: functionally graded materials, unsteady heat conduction, cylinder, temperature distribution

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, decomposition method, generalized thermoelasticity, algorithm

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Authors: M. Maier, I. Dedigama, J. Majasan, Y. Wu, Q. Meyer, L. Castanheira, G. Hinds, P. R. Shearing, D. J. L. Brett

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Increasing the efficiency of electrolyser technology is commonly seen as one of the main challenges on the way to the Hydrogen Economy. There is a significant lack of understanding of the different states of operation of polymer electrolyte membrane water electrolysers (PEMWE) and how these influence the overall efficiency. This in particular means the two-phase flow through the membrane, gas diffusion layers (GDL) and flow channels. In order to increase the efficiency of PEMWE and facilitate their spread as commercial hydrogen production technology, new analytic approaches have to be found. Acoustic emission (AE) offers the possibility to analyse the processes within a PEMWE in a non-destructive, fast and cheap in-situ way. This work describes the generation and analysis of AE data coming from a PEM water electrolyser, for, to the best of our knowledge, the first time in literature. Different experiments are carried out. Each experiment is designed so that only specific physical processes occur and AE solely related to one process can be measured. Therefore, a range of experimental conditions is used to induce different flow regimes within flow channels and GDL. The resulting AE data is first separated into different events, which are defined by exceeding the noise threshold. Each acoustic event consists of a number of consequent peaks and ends when the wave diminishes under the noise threshold. For all these acoustic events the following key attributes are extracted: maximum peak amplitude, duration, number of peaks, peaks before the maximum, average intensity of a peak and time till the maximum is reached. Each event is then expressed as a vector containing the normalized values for all criteria. Principal Component Analysis is performed on the resulting data, which orders the criteria by the eigenvalues of their covariance matrix. This can be used as an easy way of determining which criteria convey the most information on the acoustic data. In the following, the data is ordered in the two- or three-dimensional space formed by the most relevant criteria axes. By finding spaces in the two- or three-dimensional space only occupied by acoustic events originating from one of the three experiments it is possible to relate physical processes to certain acoustic patterns. Due to the complex nature of the AE data modern machine learning techniques are needed to recognize these patterns in-situ. Using the AE data produced before allows to train a self-learning algorithm and develop an analytical tool to diagnose different operational states in a PEMWE. Combining this technique with the measurement of polarization curves and electrochemical impedance spectroscopy allows for in-situ optimization and recognition of suboptimal states of operation.

Keywords: acoustic emission, gas diffusion layers, in-situ diagnosis, PEM water electrolyser

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Authors: A. Tavangari, N. Salehzadeh

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In the crack growth analysis, the Stress Intensity Factor (SIF) is a fundamental prerequisite. In the present study, the mode I stress intensity factor (SIF) of three-dimensional penny-Shaped crack is obtained in an isotropic elastic cylindrical medium with arbitrary dimensions under arbitrary loading at the top of the cylinder, by the semi-analytical method based on the Rayleigh-Ritz method. This method that is based on minimizing the potential energy amount of the whole of the system, gives a very close results to the previous studies. Defining the displacements (elastic fields) by hypothetical functions in a defined coordinate system is the base of this research. So for creating the singularity conditions at the tip of the crack the appropriate terms should be found.

Keywords: penny-shaped crack, stress intensity factor, fracture mechanics, Ritz method

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Authors: Adriana Radan Ungureanu

Abstract:

The industrial landscape is changing due to the financial crises, poor availability of raw materials, new discoveries and interdisciplinary collaborations. New ideas shape the change through technologies and bring responses for a better life. The process of change is leaded by big players like states and companies, but they cannot keep their places on the market without the help of the small ones. The main tool of change is technology and the entire developed world dedicated efforts for decades in this direction. Even the expectations are not yet met, the research for finding adequate solutions is far from to be stopped. A relevant example is nanotechnology where most of discoveries still remain into laboratory and could not succeed to find the right way to the market. In front of this situation the right question could be: ”Is it worth investing in nanotechnology in the name of an uncertain future but with very little impact on present?” This paper tries to find a positive answer from a three-dimensional approach using a descriptive analyse based on available database supplied by the European case studies, reports, and literature.

Keywords: Europe, KET’s, nanotechnology, technology

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Authors: N. K. Mohd Affendi, T. A. R. Tuan Abdullah, S. A. Syed Mustaffa

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In power industry transformer is an important component and most of us familiar by the functioning principle of a transformer electrically. There are many losses occur during the operation of a transformer that causes heat generation. This heat, if not dissipated properly will reduce the lifetime and effectiveness of the transformer. Transformer cooling helps in maintaining the temperature rise of various paths. This paper proposed to minimize the ambient temperature of the transformer room in order to lower down the temperature of the transformer. A simulation has been made using finite element methods programs called FEMM (Finite Elements Method Magnetics) to create a virtual model based on actual measurement of a transformer. The generalization of the two-dimensional (2D) FEMM results proves that by minimizing the ambient temperature, the heat of the transformer is decreased. The modeling process and of the transformer heat flow has been presented.

Keywords: heat generation, temperature rise, ambient temperature, FEMM

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Authors: Hassina Gheribi, Salim Boukebbab

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The measurement of the parts manufactured on CMM (coordinate measuring machine) is based on the association of a surface of perfect geometry to the group of dots palpated via a mathematical calculation of the distances between the palpated points and itself surfaces. Surfaces not being never perfect, they are measured by a number of points higher than the minimal number necessary to define them mathematically. However, the central problems of three-dimensional metrology are the estimate of, the orientation parameters, location and intrinsic of this surface. Including the numerical uncertainties attached to these parameters help the metrologist to make decisions to be able to declare the conformity of the part to specifications fixed on the design drawing. During this paper, we will present a data-processing model in Visual Basic-6 which makes it possible automatically to determine the whole of these parameters, and their uncertainties.

Keywords: coordinate measuring machines (CMM), associated surface, uncertainties of measurement, acquisition and modeling

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Authors: Mesias Alfeus, Kirsty Fitzhenry, Alessia Lederer

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The present paper provides empirical studies to estimate defaultable bonds in the South African financial market. The main goal is to estimate the unobservable factors affecting bond yields for South African major banks. The maximum likelihood approach is adopted for the estimation methodology. Extended Kalman filtering techniques are employed in order to tackle the situation that the factors cannot be observed directly. Multi-dimensional Cox-Ingersoll-Ross (CIR)-type factor models are considered. Results show that default risk increased sharply in the South African financial market during COVID-19 and the CIR model with jumps exhibits a better performance.

Keywords: default intensity, unobservable state variables, CIR, α-CIR, extended kalman filtering

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Authors: J. C. Cheng, Y. L. Tsay, Z. D. Chan, C. H. Yang

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In this study the physical system under consideration is a three-dimensional (3-D) cabinet with arrays of block heat sources mounted on one of the walls of the cabinet. The block heat sources dissipate heat to the cabinet surrounding through the conjugate conduction and natural convection. The results illustrate that the difference in hot spot temperatures of the system (θH) for the situations with and without consideration of thermal interaction is higher for smaller Rayleigh number (Ra), and can be up to 94.73% as Ra=10^5. In addition, the heat transfer characteristics depends strongly on the dimensionless heat conductivity of cabinet wall (Kwf), heat conductivity of block (Kpf) and length of cabinet (Ax). The maximum reduction in θH is 70.01% when Kwf varies from 10 to 1000, and it is 30.07% for Ax from 0.5 to 1. While the hot spot temperature of system is not sensitive to the cabinet angle (Φ).

Keywords: block heat sources, 3-D cabinet, thermal interaction, heat transfer

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Authors: S. Al Dandachli, F. Perales, Y. Monerie, F. Jamin, M. S. El Youssoufi, C. Pelissou

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The goal of this research is to study the fracture process and mechanical behavior of concrete under I–II mixed-mode stress, which is essential for ensuring the safety of concrete structures. For this purpose, two-dimensional simulations of three-point bending tests under variable load and geometry on notched cement paste samples of composite samples (cement paste/siliceous aggregate) are modeled by employing Cohesive Zone Models (CZMs). As a result of experimental validation of these tests, the CZM model demonstrates its capacity to predict fracture propagation at the local scale.

Keywords: cement paste, interface, cohesive zone model, fracture, three-point flexural test bending

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Authors: Mihika Shivkumar, Krishna Kumar, C. Perisamy

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3D printing is a method of manufacturing wherein materials, such as plastic or metal, are deposited in layers one on top of the other to produce a three dimensional object. 3D printing is most commonly associated with creating engineering prototypes. However, its applications in the field of human health care have been frequently disregarded. Medical applications for 3D printing are expanding rapidly and are envisaged to revolutionize health care. Medical applications for 3D printing, both present and its potential, can be categorized broadly, including: creation of customized prosthetics tissue and organ fabrication; creation of implants, and anatomical models and pharmaceutical research regarding drug dosage forms. This piece breaks down bioprinting in the healthcare sector. It focuses on the better subtle elements of every particular point, including how 3D printing functions in the present, its impediments, and future applications in the health care sector.

Keywords: bio-printing, prototype, drug delivery, organ regeneration

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Authors: Beghdadi Lotfi, Bouziane Abdelhafid

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A finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the Stokes theorem. To valid the accuracy of the method two numerical experiments s are used: conduction in a regular block (with known analytical solution) and conduction in a rotated block (case with curved boundaries).The numerical results show good agreement with analytical results. To demonstrate the accuracy of the method, the absolute and root-mean square errors versus the grid size are examined quantitatively.

Keywords: Stokes theorem, unstructured grid, heat transfer, complex geometry

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Authors: Samira Cherid, Samir Bentata, Feyza Zahira Meghoufel, Yamina Sefir, Sabria Terkhi, Fatima Bendahma, Bouabdellah Bouadjemi, Ali Zitouni

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Using the transfer-matrix technique and the Kronig Penney model, we numerically and analytically investigate the effect of short-range correlated disorder in random dimer model (RDM) on transmission properties of light in one dimension photonic crystals made of three different materials. Such systems consist of two different structures randomly distributed along the growth direction, with the additional constraint that one kind of these layers appears in pairs. It is shown that the one-dimensional random dimer photonic crystals support two types of extended modes. By shifting of the dimer resonance toward the host fundamental stationary resonance state, we demonstrate the existence of the ballistic response in these systems.

Keywords: photonic crystals, disorder, correlation, transmission

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Authors: Si Chen, Quanhong Jiang

Abstract:

In the increasingly mature posture recognition technology, human movement information is widely used in sports rehabilitation, human-computer interaction, medical health, human posture assessment, and other fields today; this project uses the most original ideas; it is proposed to use the collection equipment for the collection of myoelectric data, reflect the muscle posture change on a degree of freedom through data processing, carry out data-muscle three-dimensional model joint adjustment, and realize basic pose recognition. Based on this, bionic aids or medical rehabilitation equipment can be further developed with the help of robotic arms and cutting-edge technology, which has a bright future and unlimited development space.

Keywords: pose recognition, 3D animation, electromyography, machine learning, bionics

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Authors: Hamad Almohamadi, Nabeel H. Alharthi, Abdulrahman Aljabri

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In this study, two-dimensional CuFeOx is deposited on nickel foam for the fabrication of electrocatalyst for oxygen evolution reaction (OER). The in-situ hydrothermal synthesis of CuFeOx in presence of aloe vera extract was found to yield unique nano-rose-like morphology which aided to improve the electrochemical surface area of the electrode. The phytochemical assisted synthesis of CuFeOx using 75% aloe vera extract resulted in improved OER electrocatalytic performance by attaining the overpotential of 310 mV for 50 mA cm−2 and 410 mV for 100 mA cm−2. The electrode also sustained robust stability throughout the 50 h of chronopotentiometry studies under alkaline electrolyte conditions, thus proving to be prospective electrode material for efficient OER in electrochemical water splitting.

Keywords: water splitting, phytochemicals, oxygen evaluation reaction, Tafel's slope, stability

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Authors: M. Naji, A. R. Khalim, M. Naji

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Integral Abutment Bridges (IAB) are defined as simple or multiple span bridges in which the bridge deck is cast monolithically with the abutment walls. This kind of bridges are becoming very popular due to different aspects such as good response under seismic loading, low initial costs, elimination of bearings and less maintenance. However, the main issue related to the analysis of this type of structures is dealing with soil-structure interaction of the abutment walls and the supporting piles. A two-dimensional, non-linear finite element (FE) model of an integral abutment bridge has been developed to study the effect of lateral time history displacement loading on the soil system.

Keywords: integral abutment bridge, soil structure interaction, finite element modeling, soil-pile interaction

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Authors: Ujjal Chattaraj, M. Raviteja, Chaitanya Aemala

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Over the years vehicular traffic has been given priority over pedestrian traffic. With the increase of population in cities, pedestrian traffic is increasing day by day. Pedestrian safety has become a matter of concern for the Traffic Engineers. Pedestrian comfort is primary important for the Engineers who design different pedestrian facilities. Pedestrian comfort and safety can be measured in terms of different level of service (LOS) of the facilities. In this study video data on pedestrian movement have been collected from different railway foot over bridges (FOB) in India. The level of service of those facilities has been analyzed. A cellular automata based model has been formulated to mimic the route choice behaviour of the pedestrians on the foot over bridges.

Keywords: cellular automata model, foot over bridge, level of service, pedestrian

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Authors: G. Nitesh

Abstract:

Stone column or granular pile is a proven technique to mitigate settlement in soft soil. Granular pile increases both rate of consolidation and stiffness of the ground. In this paper, a method to analyze further reduction in settlement of granular column reinforced with lime pile is presented treating the system as a unit cell and considering one-dimensional compression approach. The core of the granular pile is stiffened with a steel rod or lime column. Influence of a wide range of parameters such as area ratio of granular pile-soft soil, area ratio of lime pile-granular pile, modular ratio of granular pile and modular ratio of lime pile with respect to granular pile on settlement reduction factor, etc. are obtained and presented.

Keywords: lime pile, granular pile, soft soil, settlement

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Authors: Mengqi Zhu, Chang Nyung Kim

Abstract:

This study numerically investigates three-dimensional liquid-metal (LM) magnetohydrodynamic (MHD) flows in a misaligned duct under a uniform magnetic field. The duct consists of two misaligned horizontal channels (one is inflow channel, the other is outflow channel) and one central vertical channel. Computational fluid dynamics simulations are performed to predict the behavior of the MHD flows, using commercial code CFX. In the current study, a case with Hartmann number 1000 is considered. The electromagnetic features of LM MHD flows are elucidated to examine the interdependency of the flow velocity, current density, electric potential, pressure drop and Lorentz force. The results show that pressure decreases linearly along the main flow direction.

Keywords: CFX, liquid-metal magnetohydrodynamic flows, misaligned duct, pressure drop

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Authors: Bilal Tebboub, AmelLabbani

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This article introduces a compact sensor based on high-transmission, high-sensitivity two-dimensional photonic crystals. The photonic crystal consists of a square network of silicon rods in the air. The sensor is composed of two waveguide couplers and a microcavity designed for monitoring the percentage of hydrogen in the air and identifying gas types. Through the Finite-Difference Time-Domain (FDTD) method, we demonstrate that the sensor's resonance wavelength is contingent upon changes in the gas refractive index. We analyze transmission spectra, quality factors, and sensor sensitivity. The sensor exhibits a notable quality factor and a sensitivity value of 1374 nm/RIU. Notably, the sensor's compact structure occupies an area of 74.5 μm2, rendering it suitable for integrated optical circuits.

Keywords: 2-D photonic crystal, sensitivity, F.D.T.D method, label-free biosensing

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Authors: M. O. Durojaye, J. T. Agee

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This paper is on the one-dimensional, positive temperature coefficient (PTC) thermistor model with a hyperbolic tangent function approximation for the electrical conductivity. The method of asymptotic expansion was adopted to obtain the steady state solution and the unsteady-state response was obtained using the method of lines (MOL) which is a well-established numerical technique. The approach is to reduce the partial differential equation to a vector system of ordinary differential equations and solve numerically. Our analysis shows that the hyperbolic tangent approximation introduced is well suitable for the electrical conductivity. Numerical solutions obtained also exhibit correct physical characteristics of the thermistor and are in good agreement with the exact steady state solutions.

Keywords: electrical conductivity, hyperbolic tangent function, PTC thermistor, method of lines

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