Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.

Effect analysis of unilateral deaf adults wearing bone-conduction hearing aids:A case report

The prevalence of unilateral deafness(SSD)or asymmetric hearing loss(AHL)among patients with hearing impairments ranges from 7.2%to 15.0%,indicating a relatively significant proportion.However,these individuals often overlook their hearing loss,resulting in delayed or inadequate treatment.This oversight can lead to a lack of binaural summation and squelch effect,as well as the head shadow effect,which can significantly impact their speech recognition and sound localization abilities,especially in noisy environments.Recently,a groundbreaking Sound Bite™Pinyin®Bone Conduction Hearing Aid(HA)device has been has been introduced as a viable alternative to traditional percutaneous stimulation hearing assistance devices.This innovative device harnesses bone conduction technology to convey sound vibrations directly to the inner ear via the bones of the jaw and skull,effectively bypassing the air conduction pathway that is commonly compromised in individuals with hearing loss.This report details the evaluation and adjustment process of a HA device worn by a 31-year-old female patient who suffers from a congenital ossicular chain deformity in her right ear,while maintaining normal hearing in her left ear.The report comprehensively covers the hearing thresholds of the 31-year-old female patient on the day of fitting the hearing aid and one month later.It also presents assessments of the hearing aid’s performance through the Abbreviated Profile of Hearing Aid Benefit(APHAB)questionnaire,conducted three days after adjustment,one month later,and one year later.Furthermore,the report details the evaluation of the patient’s sound localization ability,comparing her performance before and after wearing the hearing aid device.Additionally,it includes measurements of her speech recognition ability for monosyllabic words and Yang Yang Ge words,which are specific tests in the Chinese language,conducted two years after the initial fitting of the hearing aid.The discovery that bone-anchored hearing devices can significantly enhance hearing thresholds in patients with unilateral conductive hearing loss represents a significant milestone.These devices not only improve speech recognition ability but also enhance sound localization in noisy environments.This improvement is accompanied by a high level of subjective satisfaction among patients,indicating a positive impact on their overall quality of life.

Effects of atrial septal defects on the cardiac conduction system

The case report presented in this edition by Mu et al.The report presents a case of atrial septal defect(ASD)associated with electrocardiographic changes,noting that the crochetage sign resolved after Selective His Bundle Pacing(S-HBP)without requiring surgical closure.The mechanisms behind the appearance and resolution of the crochetage sign remain unclear.The authors observed the dis-appearance of the crochetage sign post-S-HBP,suggesting a possible correlation between these specific R waves and the cardiac conduction system.This editorial aims to explore various types of ASD and their relationship with the cardiac con-duction system,highlighting the diagnostic significance of the crochetage sign in ASD.

Variational Approach to 2D and 3D Heat Conduction Modeling

The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.

Axonal Conduction Velocity: A Computer Study

This paper derives rigorous statements concerning the propagation velocity of action potentials in axons. The authors use the Green’s function approach to approximate the action potential and find a relation between conduction velocity and the impulse profile. Computer simulations are used to bolster the analysis.

Development and Optimization of Universal Bone Conduction Hearing Spectacles

Background: Non-implantable bone anchored hearing devices (BCHDs) are utilized for patients with conductive or mixed hearing loss who are unsuitable for conventional hearing aids or have unresolved middle ear issues. These devices can be surgically implanted or attached using adhesive plates, dental sticks, elastic headbands, or bone conduction spectacles. Optimal fitting of bone conduction spectacles requires appropriate frame selection and contact pressure in the temporal and mastoid areas. The ANSI S3.6 and DIN EN ISO 389-3 standards recommend a contact area of approximately 1.75 cm2 and a maximum force of 5.4 N for effective sound transmission and comfort. Methods: This study aimed to evaluate the technical fit and mechanical stability of universal bone conduction hearing spectacles compared to established systems. A Sen-Pressure 02 thin-film sensor connected to an Arduino Uno R3 board measured contact force in the temporal and mastoid areas. Several BCHDs were tested, including the Bruckhoff la belle BC D50/70, Radioear B71 headset, Radioear B71 elastic headband, Cochlear Baha SoundArc M, and Cochlear Baha elastic headband, on a PVC artificial head, with data analyzed using ANOVA and LSD post hoc tests. Results: The la belle BC D50/70 spectacles showed comparable contact force to established BCHDs, ensuring adequate sound transmission and comfort. Significant differences were observed between the systems, with the Radioear B71 headset exhibiting the highest forces. The la belle BC D50/70 had similar forces to the Radioear B71 elastic headband. Conclusion: The la belle BC D50/70 universal bone conduction hearing spectacles are a technically equivalent alternative to established BCHDs, maintaining pressure below 5.4 N. Future research should explore the impact of different contact forces on performance and comfort, and the integration of force control in modified spectacles. This study indicates that the la belle BC D50/70 is a viable alternative that meets audiological practice requirements.

Variational Approach to Heat Conduction Modeling

It is known that Fourier’s heat equation, which is parabolic, implies an infinite velocity propagation, or, in other words, that the mechanism of heat conduction is established instantaneously under all conditions. This is unacceptable on physical grounds in spite of the fact that Fourier’s law agrees well with experiment. However, discrepancies are likely to occur when extremely short distances or extremely short time intervals are considered, as they must in some modern problems of aero-thermodynamics. Cattaneo and independently Vernotte proved that such process can be described by Heaviside’s telegraph equation. This paper shows that this fact can be derived using calculus of variations, by application of the Euler-Lagrange equation. So, we proved that the equation of heat conduction with finite velocity propagation of the thermal disturbance can be obtained as a solution to one variational problem.

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

Sterilization Effect of Cooking Process for Guilin Rice Noodles Based on Heat Conduction Model

Guilin rice noodles, a unique cuisine from Guilin, Guangxi, is renowned both domestically and internationally as one of the top ten “Guilin Classics”. Utilizing a heat conduction model, this study explores the effectiveness of the cooking process in sterilizing Guilin rice noodles before consumption. The model assumes that a large pot is filled with boiling water which is maintained at a constant high temperature heat resource through continuous gentle heating. And the room temperature is set as the initial temperature for the preheating process and the final temperature for the cooling process. The objective is to assess whether the cooking process achieves satisfactory sterilization results. The temperature distribution function of rice noodle with time is analytically obtained using the separation of variables method in the three-dimensional cylindrical coordinate system. Meanwhile, the thermal diffusion coefficient of Guilin rice noodles is obtained in terms of Riedel’ theory. By analyzing the elimination characteristics of Pseudomonas cocovenenans subsp. farinofermentans, this study obtains the optimal time required for effective sterilization at the core of Guilin rice noodles. The results show that the potential Pseudomonas cocovenenans subsp. farinofermentans will be completely eliminated through continuously preheating more than 31 seconds during the cooking process before consumption. This study provides a valuable reference of food safety standards in the cooking process of Guilin rice noodles, particularly in ensuring the complete inactivation of potentially harmful strains such as Pseudomonas cocovenenans subsp. farinofermentans.

Decay rates and time lags of heat conduction in building construction under field conditions

The field measurements of decay rates and time lags of heat conduction in a building construction taken in Nanjing during the summer of 2001 are presented.The decay rates and time lags are calculated according to the frequency responses of the heat absorbed by the room＇s internal surfaces,inside surface temperature,indoor air temperature and outdoor synthetic temperature.The measured results match very well with the theoretical results of the zeroth and the first order values of the decay rates and time lags of heat conduction in the building construction,but the difference between the measured values and the theoretical values for the second order is too great to be accepted.It is therefore difficult to accurately test the second order value.However,it is still advisable to complete the analysis using the zeroth-and the first-orders values of the decay rates and time lags of heat conduction in building construction under field conditions,because in these cases the decay rates of heat conduction reach twenty which meets the requirements of engineering plans.

Ionic Conduction and Fuel Cell Performance of Ba0.98Ce0.8Tm0.2O3-α Ceramic

The perovskite-type oxide solid solution Ba0.98Ce0.8Tm0.2O3-α was prepared by high temperature solid-state reaction and its single phase character was confirmed by X-ray diffraction. The conduction property of the sample was investigated by alternating current impedance spectroscopy and gas concentration cell methods under different gases atmospheres in the temperature range of 500-900 ℃. The performance of the hydrogen-air fuel cell using the sample as solid electrolyte was measured. In wet hydrogen, the sample is a pure protonic conductor with the protonic transport number of 1 in the range of 500-600 ℃, a mixed conductor of proton and electron with the protonic transport number of 0.945-0.933 above 600 ℃. In wet air, the sample is a mixed conductor of proton, oxide ion, and electronic hole. The protonic transport numbers are 0.010-0.021, and the oxide ionic transport numbers are 0.471-0.382. In hydrogen-air fuel cell, the sample is a mixed conductor of proton, oxide ion and electron, the ionic transport numbers are 0.942 0.885. The fuel cell using Ba0.98Ce0.8Tm0.2O3-α as solid electrolyte can work stably. At 900 ℃, the maximum power output density is 110,2 mW/cm2, which is higher than that of our previous cell using Ba0.98Ce0.8Tm0.2O3-α （x〈≤1, RE=Y, Eu, Ho） as solid electrolyte.

Solution of an Inverse Problem of Heat Conduction of 45 Steel with Martensite Phase Transformation in High Pressure during Gas Quenching

In order to simulate thermal strains, thermal stresses, residual stresses and microstructure of the steel during gas quenching by means of the numerical method, it is necessary to obtain an accurate boundary condition of temperature field. The surface heat transfer coefficient is a key parameter. The explicit finite difference method, nonlinear estimation method and the experimental relation between temperature and time during gas quenching have been used to solve the inverse problem of heat conduction. The relationship between surface temperature and surface heat transfer coefficient of a cylinder has been given. The nonlinear surface heat transfer coefficients include the coupled effects between martensitic phase transformation and temperature.

HYBRID FEM WITH FUNDAMENTAL SOLUTIONS AS TRIAL FUNCTIONS FOR HEAT CONDUCTION SIMULATION

A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional finite element method （FEM） and boundary element method （BEM）, and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.

Fast precise integration method for hyperbolic heat conduction problems

A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.

Fuzzy finite difference method for heat conduction analysis with uncertain parameters

A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.

Normal thermal conduction in lattice models with asymmetric harmonic interparticle interactions

We study the thermal conduction behaviors of one-dimensional lattice models with asymmetric harmonic interparticle interactions. Normal thermal conductivity that is independent of system size is observed when the lattice chains are long enough. Because only the harmonic interactions are involved, the result confirms, without ambiguity, that asymmetry plays a key role in normal thermal conduction in one-dimensional momentum conserving lattices. Both equilibrium and nonequilibrium simulations are performed to support the conclusion.

Temperature waves in chemical reaction-diffusion-heat conduction systems with two ends respectively subject to Dirichlet and no-flux conditions

Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous two-variable system with one end subject to Dirichlet conditions, while the other end no-flux conditions. Furthermore, the conditions for the emergence of temperature waves are found out by the linear stability analysis and verified by a diagram for successive steps of evolution of spatial profile of temperature during a period that is plotted by numerical simulations on a computer. Without doubt, these results are in favor of the heat balance in chemical reactor designs.

Thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction

Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction areinvestigated analytically and numerically. The corresponding dispersion relation is a sixth-orderalgebraic equation, governed by six non-dimensional parameters: two thermoelastic couplingconstants, one chirality parameter, the ratio between extensional and torsional moduli, the Fouriernumber, and the dimensionless thermal relaxation. The behavior of the solutions is discussedfrom two perspectives with an asymptotic-numerical approach: (1) the effect of thermal relaxationon the elastic wave celerities, and (2) the effect of thermoelastic coupling on the thermal wavecelerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered.However, with large wavenumbers, the solutions behave differently depending on the thermalrelaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from theclassical result of the speed of second sound.

A phase-field study on the oxidation behavior of Ni considering heat conduction

Phase-field modeling approach has been used to study the oxidation behavior of pure Ni when considering heat conduction. In this calculation, the dependence of the coefficient of the Cahn–Hilliard equation Lc on the temperature T was considered. To this end, high-temperature oxidation experiments and phase-field modeling for pure Ni were performed in air under atmospheric pressure at 600,700, and 800？C. The oxidation rate was measured by thermogravimetry and Lc at these temperatures was determined via interactive algorithm. With the Lc-T relationship constructed, oxidation behavior of Ni when considering heat conduction was investigated. The influence of temperature boundaries on the oxidation degree, oxide film thickness, and specific weight gain were discussed. The phase-field modeling approach proposed in this study will give some highlights of the oxidation resistance analysis and cooling measures design of thermal protection materials.

Meshless analysis of three-dimensional steady-state heat conduction problems

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson＇s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method （RKPM）. A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.