Search results for: conduction

Authors: Bongsu Choi, Tae-Ho Song

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Vacuum insulation panel (VIP) is a promising thermal insulator for buildings, refrigerator, LNG carrier and so on. In general, it has the thermal conductivity of 2~4 mW/m•K. However, this thermal conductivity is that measured at the center of VIP. The total effective thermal conductivity of VIP is larger than this value due to the edge conduction through the envelope. In this paper, the edge conduction of VIP is examined theoretically, numerically and experimentally. To confirm the existence of the edge conduction, numerical analysis is performed for simple two-dimensional VIP model and a theoretical model is proposed to calculate the edge conductivity. Also, the edge conductivity is measured using the vacuum guarded hot plate and the experiment is validated against numerical analysis. The results show that the edge conductivity is dependent on the width of panel and thickness of Al-foil. To reduce the edge conduction, it is recommended that the VIP should be made as big as possible or made of thin Al film envelope.

Keywords: envelope, edge conduction, thermal conductivity, vacuum insulation panel

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Authors: A. Zanj, F. He

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In the current paper, a domain independent conduction model compatible for multi-physical system dynamic investigations is suggested. By means of a port-based approach, a classical nonlinear conduction model containing physical states is first represented. A compatible discrete configuration of the thermal domain in line with the elastic domain is then generated through the enhancement of the configuration of the conventional thermal element. The presented simulation results of a sample structure indicate that the suggested conductive model can cover a wide range of dynamic behavior of the thermal domain.

Keywords: multi-physical domain, conduction model, port based modeling, dynamic interaction, physical modeling

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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: 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: Usman Nasir, Minxiao Han, S. M. R. Kazmi

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Three phase inverters being used today are based on field orientation control (FOC) and sine wave PWM (SPWM) techniques because 120 degree or 180 degree conduction methods produce high value of THD (total harmonic distortion) in the power system. The indirect field orientation control (IFOC) method is difficult to implement in real systems due to speed sensor accuracy issue. This paper discusses the problem with IFOC and a PWM based 180 degree conduction mode for the three phase inverter. The modified control method improves THD and this paper also compares the results obtained using modified control method with the conventional 180 degree conduction mode.

Keywords: three phase inverters, IFOC, THD, sine wave PWM (SPWM)

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Authors: Dawit Burusie Abdi, Mamidala Jagadesh Kumar

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In this paper, using 2D TCAD simulations, the application of a dual material gate (DMG) for suppressing ambipolar conduction in a tunnel field effect transistor (TFET) is demonstrated. Using the proposed DMG concept, the ambipolar conduction can be effectively suppressed even if the drain doping is as high as that of the source doping. Achieving this symmetrical doping, without the ambipolar conduction in TFETs, gives the advantage of realizing both n-type and p-type devices with the same doping sequences. Furthermore, the output characteristics of the DMG TFET exhibit a good saturation when compared to that of the gate-drain underlap approach. This improved behavior of the DMG TFET makes it a good candidate for inverter based logic circuits.

Keywords: dual material gate, suppressing ambipolar current, symmetrically doped TFET, tunnel FETs, PNPN TFET

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Authors: Ihab Elaff

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Simulating the heart’s electrical stimulation is essential in modeling and evaluating the electrophysiology behavior of the heart. For achieving that, there are two structures in concern: the ventricles’ Myocardium, and the ventricles’ Conduction Network. Ventricles’ Myocardium has been modeled as anisotropic material from Diffusion Tensor Imaging (DTI) scan, and the Conduction Network has been extracted from DTI as a case-based structure based on the biological properties of the heart tissues and the working methodology of the Magnetic Resonance Imaging (MRI) scanner. Results of the produced activation were much similar to real measurements of the reference model that was presented in the literature.

Keywords: diffusion tensor, DTI, heart, conduction network, excitation propagation

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Authors: Ruxandra Barbulescu, Daniel Ioan, Gabriela Ciuprina

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The saltatory conduction is the way the action potential is transmitted along a myelinated axon. The potential diffuses along the myelinated compartments and it is regenerated in the Ranvier nodes due to the ion channels allowing the flow across the membrane. For an efficient simulation of populations of neurons, it is important to use reduced order models both for myelinated compartments and for Ranvier nodes and to have control over their accuracy and inner parameters. The paper presents a reduced order model of this neural system which allows an efficient simulation method for the saltatory conduction in myelinated axons. This model is obtained by concatenating reduced order linear models of 1D myelinated compartments and nonlinear 0D models of Ranvier nodes. The models for the myelinated compartments are selected from a series of spatially distributed models developed and hierarchized according to their modeling errors. The extracted model described by a nonlinear PDE of hyperbolic type is able to reproduce the saltatory conduction with acceptable accuracy and takes into account the finite propagation speed of potential. Finally, this model is again reduced in order to make it suitable for the inclusion in large-scale neural circuits.

Keywords: action potential, myelinated segments, nonlinear models, Ranvier nodes, reduced order models, saltatory conduction

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

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Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter Nrc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method are found to be good.

Keywords: convective and radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate

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Authors: Bashar Albaalbaki, Roger E. Khayat

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This work is a comparative study on the effect of Delaunay triangulation algorithms on discretization error for conduction-convection conservation problems. A structured triangulation and many unstructured Delaunay triangulations using three popular algorithms for node placement strategies are used. The numerical method employed is the vertex-centered finite volume method. It is found that when the computational domain can be meshed using a structured triangulation, the discretization error is lower for structured triangulations compared to unstructured ones for only low Peclet number values, i.e. when conduction is dominant. However, as the Peclet number is increased and convection becomes more significant, the unstructured triangulations reduce the discretization error. Also, no statistical correlation between triangulation angle extremums and the discretization error is found using 200 samples of randomly generated Delaunay and non-Delaunay triangulations. Thus, the angle extremums cannot be an indicator of the discretization error on their own and need to be combined with other triangulation quality measures, which is the subject of further studies.

Keywords: conduction-convection problems, Delaunay triangulation, discretization error, finite volume method

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Authors: Shirin Sarejloo

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Background: Electrophysiological-related manifestation of COVID-19 is a matter of debate in the literature nowadays. A wide spectrum of arrhythmias was observed among patients who have been infected with COVID-19. Objectives: This study discussed the prevalence of arrhythmias and conduction system disease in patients with COVID-19. Method: In this retrospective study, demographic and electrocardiographic data of 432 expired COVID-19 patients who had been admitted to Faghihi Hospital of Shiraz University of Medical Sciences from August2020 until December 2020 were reviewed. Results: Atrioventricular nodal block (AVB) was found in 40(9.3%) patients. Furthermore, 28(6.5%) of them suffered from the first degree of AVB, and 12(2.8%) suffered from complete heart block (CHB). Among 189 cases (59.0%), ST-T changes agreed with myocardial infarction or localized myocarditis. Findings of myocardial injury, including fragmented QRS and prolonged QTc were observed among 91 (21.1%) and 28 (6.5%), respectively. In victims of COVID-19, conduction disease was not related to any comorbidities. Fragmented QRS, axis deviation, presence of S1Q3T3, and poor R wave progression were significantly related to conduction system abnormalities in victims of COVID-19 (P-value > 0.05). Conclusion: Our findings can serve in future studies that aim to develop a risk stratification method for susceptible COVID-19 patients. The myocardial injury appears to role significantly in COVID-19 morbidity and mortality. Consequently, we recommend health policymakers consider separate catheterization laboratories that provide service only to COVID-19 patients.

Keywords: COVID-19, conduction system, ECG, atrioventricular block

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

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A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction

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Authors: Zue Chin Chang, Shih-Chang Liang

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RF magnetron sputtering is used on the ceramic targets, each of which contains zinc oxide (ZnO), zinc oxide doped with aluminum (AZO) and zinc oxide doped with gallium (GZO). The electric conduction mechanism of the AZO and GZO films came mainly from the Al and Ga, the oxygen vacancies, Zn interstitial atoms, and Al and/or Ga interstitial atoms. AZO and GZO films achieved higher conduction than did ZnO film, it being ion vacant and nonstoichiometric. The XRD analysis showed a preferred orientation along the (002) plane for ZnO, AZO, and GZO films.

Keywords: ZnO, AZO, GZO, doped, sputtering

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Authors: Jogbinder Singh Soodan, Ashok Kumar, Gobind Singh

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Background: This study aims to describe the motor nerve conduction velocity of selected nerves of both the upper and lower extremities in athletes. Thirty high-level sprinters (100 mts and 200 mts) and thirty high level distance runners (3000 mts) were volunteered to participate in the study. Method: Motor nerve conduction velocities (MNCV) of radial and sural nerves were recorded with the help of computerized equipment, NEUROPERFECT (MEDICAID SYSTEMS, India), with standard techniques of supramaximal percutaneus stimulation. The anthropometric measurements taken were body height (cms), age (yrs) and body weight (kgs). The neurophysiological parameters taken were MNCV of radial nerve (upper extremity) and sural nerve (lower extremity) of both sides (i.e. dominant and non-dominant) of the body. The room temperature was maintained at 37 degree Celsius. Results: Significant differences in motor nerve conduction velocities were found between dominant and non-dominant limbs in each group. The MNCV of radial nerve was obtained was significantly higher in the sprinters than long distance runners. The MNCV of sural nerve recorded was significantly higher in sprinters as compared to distance runners. Conclusion: The motor nerve conduction velocity of radial nerve was found to be higher in sprinters as compared to the distance runners and also, the MNCV for sural nerve was found to be higher in sprinters as compared to distance runners. In case of sprinters, the MNCV of radial and sural nerves were higher in dominant limbs (i.e. arms and legs) of both sides of the body. But, in case of distance runners, the MNCV of radial and sural nerves is higher in non dominant limbs.

Keywords: motor nerve conduction velocity, radial nerve, sural nerve, sprinters

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Authors: A. Ashok, K.Satapathy, B. Prerana Nashine

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The objective of this research work is to investigate for one dimensional transient radiative transfer equations with conduction using finite volume method. Within the infrastructure of finite-volume, we obtain the conservative discretization of the terms in order to preserve the overall conservative property of finitevolume schemes. Coupling of conductive and radiative equation resulting in fluxes is governed by the magnitude of emissivity, extinction coefficient, and temperature of the medium as well as geometry of the problem. The problem under consideration has been solved, for a slab dominating radiation coupled with transient conduction based on finite volume method. The boundary conditions are also chosen so as to give a good model of the discretized form of radiation transfer equation. The important feature of the present method is flexibility in specifying the control angles in the FVM, while keeping the simplicity in the solution procedure. Effects of various model parameters are examined on the distributions of temperature, radiative and conductive heat fluxes and incident radiation energy etc. The finite volume method is considered to effectively evaluate the propagation of radiation intensity through a participating medium.

Keywords: participating media, finite volume method, radiation coupled with conduction, transient radiative heat transfer

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Authors: Yu-Ching Yang, Haw-Long Lee, Win-Jin Chang

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The present work numerically analyzes the transient heat transfer in the absorber plates of a flat-plate solar collector based on the dual-phase-lag (DPL) heat conduction model. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods is used to solve the linear hyperbolic heat conduction equation. This work also examines the effect of different medium parameters on the behavior of heat transfer. Results show that, while the heat-flux phase lag induces thermal waves in the medium, the temperature-gradient phase lag smoothens the thermal waves by promoting non-Fourier diffusion-like conduction into the medium.

Keywords: absorber plates, dual-phase-lag, non-Fourier, solar collector

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Authors: Kunj Parikh, S. Bhattacharya, V. Natarajan

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TCAD numerical simulation is one of the most tried and tested powerful tools for designing devices in semiconductor foundries worldwide. It has also been used to explain conduction in organic thin films where the processing temperature is often enough to make homogeneous samples (often imperfect, but homogeneously imperfect). In this report, we have presented the results of TCAD simulation in multi-grain thin films. The work has addressed the inhomogeneity in one dimension, but can easily be extended to two and three dimensions. The effect of grain boundaries has mainly been approximated as barriers located at the junction between two adjacent grains. The effect of the value of grain boundary barrier, the bulk traps, and the measurement temperature have been investigated.

Keywords: polycrystalline thin films, space charge limited conduction, Technology Computer-Aided Design (TCAD) simulation, traps

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Authors: Po-Jen Su, Huann-Ming Chou

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In this article we uses the residual correction method to deal with transient thermoelastic problems with a hollow spherical region when the continuum medium possesses spherically isotropic thermoelastic properties. Based on linear thermoelastic theory, the equations of hyperbolic heat conduction and thermoelastic motion were combined to establish the thermoelastic dynamic model with consideration of the deformation acceleration effect and non-Fourier effect under the condition of transient thermal shock. The approximate solutions of temperature and displacement distributions are obtained using the residual correction method based on the maximum principle in combination with the finite difference method, making it easier and faster to obtain upper and lower approximations of exact solutions. The proposed method is found to be an effective numerical method with satisfactory accuracy. Moreover, the result shows that the effect of transient thermal shock induced by deformation acceleration is enhanced by non-Fourier heat conduction with increased peak stress. The influence on the stress increases with the thermal relaxation time.

Keywords: maximum principle, non-Fourier heat conduction, residual correction method, thermo-elastic response

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Authors: Razieh Teimouri

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Electrical modelling of Cu (In,Ga)Se₂ thin film solar cells is carried out with compositionally graded absorber and CdS buffer layer. Simulation results are compared with experimental data. Surface defect layers (SDL) are located in CdS/CIGS interface for improving open circuit voltage simulated structure through the analysis of the interface is investigated with or without this layer. When SDL removed, by optimizing the conduction band offset (CBO) position of the buffer/absorber layers with its recombination mechanisms and also shallow donor density in the CdS, the open circuit voltage increased significantly. As a result of simulation, excellent performance can be obtained when the conduction band of window layer positions higher by 0.2 eV than that of CIGS and shallow donor density in the CdS was found about 1×10¹⁸ (cm⁻³).

Keywords: CIGS solar cells, thin film, SCAPS, buffer layer, conduction band offset

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Authors: Ashok K. Satapathy, Prerana Nashine

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Radiative heat transfer in participating medium was anticipated using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient energy equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: participating media, finite volume method, radiation coupled with conduction, heat transfer

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Authors: Isao Tomita

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Electrical conduction in a quasi-one-dimensional polycrystalline metallic ring with a long electron phase coherence length realized at low temperature is investigated. In this situation, the wave nature of electrons is important in the ring, where the electrical current I can be induced by a vector potential that arises from a static magnetic field applied perpendicularly to the ring’s area. It is shown that if the average grain size of the polycrystalline ring becomes large (or comparable to the Fermi wavelength), the electrical current I increases to ~I0, where I0 is a current in a disorder-free ring. The cause of this increasing effect is examined, and this takes place if the electron localization length in the polycrystalline potential increases with increasing grain size, which gives rise to coherent connection of tails of a localized electron wave function in the ring and thus provides highly coherent electrical conduction.

Keywords: electrical conduction, electron phase coherence, polycrystalline metal, magnetic field

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Authors: Hong Yu, Dirk Heider, Suresh Advani

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Increasing demands for high strength and lightweight materials in aircraft industry prompted the wide use of carbon composites in recent decades. Carbon composite laminates used on aircraft structures are subject to lightning strikes. Unlike its metal/alloy counterparts, carbon fiber reinforced composites demonstrate smaller electrical conductivity, yielding more severe damages due to Joule heating. The anisotropic nature of composite laminates makes the electrical and thermal conduction within carbon composite laminates even more complicated. Good understanding of the electrical conduction behavior of carbon composites is the key to effective lightning protection design. The goal of this study is to numerically and experimentally investigate the impact of ultra-high temperature induced by simulated lightning strike on the electrical conduction of carbon composites. A lightning simulator is designed to apply standard lightning current waveform to composite laminates. Multiple carbon composite laminates made from IM7 and AS4 carbon fiber are tested and the transient resistance data is recorded. A microstructure based resistor network model is developed to describe the electrical and thermal conduction behavior, with consideration of temperature dependent material properties. Material degradations such as thermal and electrical breakdown are also modeled to include the effect of high current and high temperature induced by lightning strikes. Good match between the simulation results and experimental data indicates that the developed model captures the major conduction mechanisms. A parametric study is then conducted using the validated model to investigate the effect of system parameters such as fiber volume fraction, inter-ply interface quality, and lightning current waveforms.

Keywords: carbon composite, joule heating, lightning strike, resistor network

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Authors: Mostafa Sarabzadeh, Masoumeh Helalizadeh, Seyyed Mahmoud Hejazi

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Multiple Sclerosis is considered as diseases related to central nerve system, the chronic and progressive disease impress on sensory and motor function of people. Due to equilibrium problems in this patients that related to disorder of nerve conduction transmission from central nerve system to organs and the nature of elastic bands that can make changes in neuromuscular junctions and momentary actions, the aim of this research is evaluate elastic training effect by reactionary ropes on nerve conduction velocity (in lower and upper limb) and functional balance in female patients with Multiple Sclerosis. The study was a semi-experimental study that was performed based on pre and post-test method, The statistical community consisted of 16 women with MS in the age mean 25-40yrs, at low and intermediate levels of disease EDSS 1-4 (Expanded Disability Status Scale) that were divided randomly into elastic and control groups, so the training program of experimental group lasted six weeks, 3 sessions per week of elastic exercises with reactionary ropes. Electroneurography parameters (nerve conduction velocity- latency) of Upper and lower nerves (Median, Tibial, Sural, Peroneal) along with balance were investigated respectively by the Electroneurography system (ENG) and Timed up and go (TUG) functional test two times in before and after the training period. After that, To analyze the data were used of Dependent and Independent T-test (with sig level p<0.05). The results showed significant increase in nerve conduction velocity of Sural (p=0.001), Peroneal (p=0.01), Median (p=0.03) except Tibial and also development Latency Time of Tibial (p= 0), Peroneal (p=0), Median (p=0) except Sural. The TUG test showed significant decreases in execution time too (p=0.001). Generally, based on what the obtained data can indicate, modern training with elastic bands can contribute to enhanced nerve conduction velocity and balance in neurosis patients (MS) so lead to reduce problems, promotion of mobility and finally more life expectancy in these patients.

Keywords: balance, elastic bands, multiple sclerosis, nerve conduction, velocity

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Authors: Ana Rahma Yuniarti, Ki Moo Lim

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Slowed myocardial conduction velocity (CV) and shortened action potential duration (APD) due to some reason are associated with an increased risk of re-entrant excitation, predisposing to cardiac arrhythmia. That is because both of CV reduction and APD shortening induces shortening of wavelength. In this study, we investigated quantitatively the cardiac mechanical responses under various CV and APD using multi-scale computational model of the heart. The model consisted of electrical model coupled with the mechanical contraction model together with a lumped model of the circulatory system. The electrical model consisted of 149.344 numbers of nodes and 183.993 numbers of elements of tetrahedral mesh, whereas the mechanical model consisted of 356 numbers of nodes and 172 numbers of elements of hexahedral mesh with hermite basis. We performed the electrical simulation with two scenarios: 1) by varying the CV values with constant APD and 2) by varying the APD values with constant CV. Then, we compared the electrical and mechanical responses for both scenarios. Our simulation showed that faster CV and longer APD induced largest resultants wavelength and generated better cardiac pumping efficacy by increasing the cardiac output and consuming less energy. This is due to the long wave propagation and faster conduction generated more synchronous contraction of whole ventricle.

Keywords: conduction velocity, action potential duration, mechanical contraction model, circulatory model

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Authors: D Bhargavi, J. Sharath Kumar Reddy

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The present investigation has been undertaken to assess the effect of viscous dissipation and axial conduction on forced convection heat transfer in the entrance region of a parallel plate channel with the porous insert attached to both walls of the channel. The flow field is unidirectional. Flow in the porous region corresponds to Darcy-Brinkman model and the clear fluid region to that of plane Poiseuille flow. The effects of the parameters Darcy number, Da, Peclet number, Pe, Brinkman number, Br and a porous fraction γ_p on the local heat transfer coefficient are analyzed graphically. Effects of viscous dissipation employing the Darcy model and the clear fluid compatible model have been studied.

Keywords: porous material, channel partially filled with a porous material, axial conduction, viscous dissipation

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Authors: A. M. Tahsini, S. A. Hosseini

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In the present study, the surface temperature history of the adaptor part in a two-stage supersonic launch vehicle is accurately predicted. The full Navier-Stokes equations are used to estimate the aerodynamic heat flux. The one-dimensional heat conduction in solid phase is used to compute the temperature history. The instantaneous surface temperature is used to improve the applied heat flux, to improve the accuracy of the results.

Keywords: aerodynamic heating, heat conduction, numerical simulation, supersonic flight, launch vehicle

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Authors: E. Marušić-Paloka, I. Pažanin, M. Prša

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Subject of this study is the stationary heat conduction problem through a pipe filled with incompressible viscous fluid. In previous work, we observed the existence and uniqueness theorems for the corresponding boundary-value problem and within we have taken into account the effects of the pipe's dilatation due to the temperature of the fluid inside of the pipe. The main difficulty comes from the fact that flow domain changes depending on the solution of the observed heat equation leading to a non-standard coupled governing problem. The goal of this work is to find solution estimate since the exact solution of the studied problem is not possible to determine. We use an asymptotic expansion in order of a small parameter which is presented as a heat expansion coefficient of the pipe's material. Furthermore, an error estimate is provided for the mentioned asymptotic approximation of the solution for inner area of the pipe. Close to the boundary, problem becomes more complex so different approaches are observed, mainly Theory of Perturbations and Separations of Variables. In view of that, error estimate for the whole approximation will be provided with additional software simulations of gotten situation.

Keywords: asymptotic analysis, dilated pipe, error estimate, heat conduction

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Authors: Yuichi Anada

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Electrical properties of polymer solid is characterized by dielectric relaxation phenomenon. Complex permittivity shows a high dependence on frequency of external stimulation in the broad frequency range from 0.1mHz to 10GHz. The complex-permittivity dispersion gives us a lot of useful information about the molecular motion of polymers and the structure of polymer aggregates. However, the large dispersion of permittivity at low frequencies due to DC conduction of impurity ions often covers the dielectric relaxation in polymer solid. In experimental investigation, many researchers have tried to remove the DC conduction experimentally or analytically for a long time. On the other hand, our laboratory chose another way of research for this problem from the point of view of a reversal in thinking. The way of our research is to use the impurity ions in the DC conduction as a probe to detect the motion of polymer molecules and to investigate the structure of polymer aggregates. In addition to the complex permittivity, the electric modulus and the conductivity relaxation time are strong tools for investigating the ionic motion in DC conduction. In a non-crystalline part of melt-crystallized polymers, free spaces with inhomogeneous size exist between crystallites. As the impurity ions exist in the non-crystalline part and move through these inhomogeneous free spaces, the motion of ions reflects the microstructure of non-crystalline part. The ionic motion of impurity ions in poly(vinylidene fluoride) (PVDF) is investigated in this study. Frequency dependence of the loss permittivity of PVDF shows a characteristic of the direct current (DC) conduction below 1 kHz of frequency at 435 K. The electric modulus-frequency curve shows a characteristic of the dispersion with the single conductivity relaxation time. Namely, it is the Debye-type dispersion. The conductivity relaxation time analyzed from this curve is 0.00003 s at 435 K. From the plot of conductivity relaxation time of PVDF together with the other polymers against permittivity, it was found that there are two group of polymers; one of the group is characterized by small conductivity relaxation time and large permittivity, and another is characterized by large conductivity relaxation time and small permittivity.

Keywords: conductivity relaxation time, electric modulus, ionic motion, permittivity, poly(vinylidene fluoride), DC conduction

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Authors: Hamdy M. Youssef

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In this work, the usual Euler–Bernoulli nanobeam has been modeled in the context of Lord-Shulman thermoelastic theorem, which contains non-Fourier heat conduction law. The nanobeam has been subjected to a constant magnetic field and ramp-type thermal loading. The Laplace transform definition has been applied to the governing equations, and the solutions have been obtained by using a direct approach. The inversions of the Laplace transform have been calculated numerically by using Tzou approximation method. The solutions have been applied to a nanobeam made of silicon nitride. The distributions of the temperature increment, lateral deflection, strain, stress, and strain-energy density have been represented in figures with different values of the magnetic field intensity and ramp-time heat parameter. The value of the magnetic field intensity and ramp-time heat parameter have significant effects on all the studied functions, and they could be used as tuners to control the energy which has been generated through the nanobeam.

Keywords: nanobeam, vibration, constant magnetic field, ramp-type thermal loading, non-Fourier heat conduction law

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Authors: Jianhua Zhou, Yuwen Zhang

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A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.

Keywords: conduction, inverse problems, conjugated gradient method, laser

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