Article
Engineering, Multidisciplinary
W. B. da Silva, J. C. S. Dutra, C. E. P. Kopperschimidt, D. Lesnic, R. G. Aykroyd
Summary: The paper successfully estimates the time-dependent HTC in two-dimensional transient inverse heat conduction problems by combining MFS and PF-SIR methods, confirming the synergy between the two approaches.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Computer Science, Interdisciplinary Applications
F. Mostajeran, R. Mokhtari
Summary: This paper extends a semi-supervised deep neural network method to solve ill-posed backward heat conduction problems, which have long been a computational challenge. The methodology's effectiveness and robustness are demonstrated through various tests, including different boundary conditions, thermal diffusivity factors, and domains. Unlike traditional methods, no regularization technique is required. Simulation results show that this revolutionary strategy can efficiently and accurately extract solution patterns even with up to ten percent noise corruption in the input data. Additionally, as the final time is increased, the method remains efficient in recovering the initial time data, demonstrating its robustness. A comparison with the localized radial basis functions finite difference (RBF-FD) method supports the superiority of the semi-supervised neural network approach.
COMPUTER PHYSICS COMMUNICATIONS
(2022)
Article
Mathematics
Ke Sun, Shuang Ding, Junli Zhang, Yan-Cheng Liu
Summary: The localized method of fundamental solutions (LMFS) is a meshless numerical method that improves computational efficiency and avoids complex numerical integration processes. This article uses LMFS to solve eigenfrequency problems in electromagnetic waves and determines the resonant frequencies by introducing an external source.
Article
Thermodynamics
Xiaoli Ma, Yufeng Zhang, Zhonghe Han, Ningbo Zang, Zhijian Liu
Summary: The paper presents a performance modelling of a thermoelectric air conditioning system that utilizes high power heat sinks to effectively remove waste heat and increase COPs. The system provides heating, cooling, and heat recovery ventilation, and the waste heat can be used for domestic drying services. The results showed that using high power heat sinks and an air mixture of room ventilation air and outdoor air can significantly improve the cooling and heating COPs.
Article
Multidisciplinary Sciences
Agata Chmielowska, Damian Slota
Summary: The paper aims to adapt the alternating phase truncation (APT) method for solving the two-phase time-fractional Stefan problem. The adaptation allows for the determination of the approximate temperature distribution in a domain with a moving boundary between solid and liquid phases. The APT method reduces the entire domain to liquid phase by adding sufficient heat at each solid point and then solves the heat equation transformed to the enthalpy form in the obtained region. Subsequently, the heat added is subtracted, and the domain is reduced to solid phase by subtracting sufficient heat from each liquid point. The heat equation is then solved in this region, and the previously subtracted heat is added at the appropriate points.
Article
Mathematics, Applied
Jakub Krzysztof Grabski
Summary: This paper investigates the placement of source points for transient heat conduction problems using the method of fundamental solutions. The results show that placing the source points in a space much larger than the considered region, with negative time coordinate, can lead to very good accuracy.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Thermodynamics
Songkran Wiriyasart, Sommas Kaewluan
Summary: This study investigated the thermal performance of water heaters recovering waste heat from air conditioners. The results showed that water heaters have high thermal efficiency at low water mass flow rates. The integration of heat recovery system can significantly reduce the energy consumption of air conditioners and contribute to reducing global warming.
THERMAL SCIENCE AND ENGINEERING PROGRESS
(2024)
Article
Computer Science, Interdisciplinary Applications
Yan Wang, Zhi Qian
Summary: In this paper, a two-dimensional time-fractional inverse heat conduction problem is studied. The problem is severely ill-posed. A quasi-reversibility method is proposed to solve this problem with disturbed boundary value. The effectiveness of the proposed method is verified through numerical results.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Thermodynamics
Chenjiyu Liang, Yuan Wang, Xianting Li
Summary: This study proposes an air conditioning system that can control the temperature and humidity of the air simultaneously. By adjusting the air volume ratio and cooling water flow rate through a three-fluid heat exchanger, the supply air temperature can be regulated, and free cooling can be achieved by supplying low-temperature cooling water. Numerical models and experimental results confirm that this system can effectively regulate the supply air temperature over a wide range and achieve significant energy savings.
ENERGY CONVERSION AND MANAGEMENT
(2022)
Article
Mathematics, Applied
Pedro R. S. Antunes
Summary: The method of fundamental solutions (MFS) is a numerical method for solving linear partial differential equations. However, the ill-conditioning of the matrices in the original method limits its accuracy. This study proposes a new algorithm to overcome the ill-conditioning of classical MFS by expanding the basis functions in terms of harmonic polynomials.
NUMERICAL ALGORITHMS
(2022)
Article
Mathematics, Applied
Dinh-Nho Hao, Thuy T. Le, Loc H. Nguyen
Summary: This article introduces a new technique for computing numerical solutions to the nonlinear inverse heat conduction problem. By truncating the Fourier series and employing the Runge-Kutta method, the high-dimensional problem is converted into a 1D problem, addressing the nonlinearity and lack of partial derivative data.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Business
Joakim Bjorkdahl, Sara Fallahi, Magnus Holmen
Summary: This study explores the process of business model innovation in industrial firms through three case studies. It introduces the concept of problems to explain how formulation and solving of problems guide the search for a viable business model. The study shows that firms shift between backward-looking and forward-looking searches based on the perception of failure and high alternative costs.
INDUSTRIAL MARKETING MANAGEMENT
(2022)
Article
Mathematics, Interdisciplinary Applications
Andreea-Paula Voinea-Marinescu, Liviu Marin
Summary: The Cauchy problem in 2D and 3D steady-state anisotropic heat conduction was investigated with exact and perturbed data, utilizing a fading regularization method to solve the inverse problem and providing appropriate stopping criteria for different types of Cauchy data. Numerical implementation was realized for homogeneous solids in 2D and 3D using the meshless method of fundamental solutions.
COMPUTATIONAL MECHANICS
(2021)
Article
Engineering, Marine
Kue-Hong Chen, Yi-Hui Hsu, Jeng-Hong Kao
Summary: This article solves the problem of oblique incident wave with multiple cylinders using the method of fundamental solutions (MFS) combined with a proposed error estimation technique. The advantages of the proposed technique are reliable approximation of the analytical solution, determination of optimal number of points, and development of a scheme for adaptive distribution of source points. The theory of single-layer and double-layer potential formulas in the MFS method is considered, and numerical examples are provided to demonstrate the results.
Article
Construction & Building Technology
Tatsuhiro Yamamoto, Akihito Ozaki, Myongyang Lee, Keigo Aratsu, Ryo Fukui
Summary: Advanced thermal environment simulation technology has been rapidly developing in recent years, with the combination of energy simulations and computational fluid dynamics programs allowing for high-accuracy prediction of non-stationary thermal environments. The proposed method for predicting the thermal environment of air conditioners and radiant panels showed promising accuracy by calculating the maximum mean absolute error to be 0.674[-], even though minor errors were induced due to computational fluid dynamics being a steady-state analysis. The results indicate that the proposed method can be effectively applied in various scenarios, including office spaces.
BUILDING AND ENVIRONMENT
(2022)
Article
Mathematics, Applied
Chein-Shan Liu, Jiang-Ren Chang
APPLIED MATHEMATICS LETTERS
(2020)
Article
Mathematics, Applied
Zhuo-Jia Fu, Li-Wen Yang, Qiang Xi, Chein-Shan Liu
Summary: This paper presents a method to solve anomalous heat conduction problems under functionally graded materials using SBM, DRM, and Laplace transformation technique. It achieves high accuracy by combining these methods and avoiding the impact of time step on computational efficiency. The transient heat conduction equation with Caputo time fractional derivative is used to describe the phenomena, demonstrating the effectiveness of the proposed method through numerical examples and comparisons with analytical solutions and COMSOL simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Chein-Shan Liu, Jiang-Ren Chang
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2020)
Article
Thermodynamics
Chein-Shan Liu, Han-Taw Chen, Jiang-Ren Chang
NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
(2020)
Article
Mathematics
Chein-Shan Liu, Tsung-Lin Lee
Summary: The paper proves that two-step fourth-order optimal iterative schemes of the same class share a common feature and develops a new family of fourth-order optimal iterative schemes.
JOURNAL OF MATHEMATICS
(2021)
Article
Thermodynamics
Chein-Shan Liu, Jiang-Ren Chang
Summary: This paper presents a method for dealing with the nonlocal boundary conditions problem of nonlinear heat equations, using nonlocal boundary shape functions and novel techniques to quickly and accurately solve the problem.
NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
(2021)
Article
Mathematics
Chein-Shan Liu, Yung-Wei Chen
Summary: A new analytic method has been developed to improve the Lindstedt-Poincare method for strongly nonlinear oscillators by introducing a linearization technique in the nonlinear differential equation. This method provides accurate higher order solutions and is significant for solving strongly nonlinear oscillators with large amplitudes.
Article
Thermodynamics
Chein-Shan Liu, Chih-Wen Chang
Summary: In this article, a solution is provided for a nonlinear parabolic type partial differential equation (PDE) with non-separated and nonlocal conditions. The use of a nonlocal boundary shape function (NLBSF) and a novel splitting-linearizing technique allows for fast and accurate solutions to the nonlocal and nonlinear parabolic equation.
NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS
(2022)
Article
Multidisciplinary Sciences
Chein-Shan Liu, Chih-Wen Chang, Yung-Wei Chen, Yen-Shen Chang
Summary: In this paper, we determine the period of an n-dimensional nonlinear dynamical system using a derived formula in an (n + 1)-dimensional augmented space. We propose a boundary shape function method (BSFM) and iterative algorithms to solve periodic problems with given or unknown boundary values. The numerical examples demonstrate the advantages of the BSFM in terms of convergence speed, accuracy, and stability compared to the shooting method.
Article
Mathematics
Chein-Shan Liu, Essam R. El-Zahar, Chih-Wen Chang
Summary: In this paper, a mth-order asymptotic-numerical method is developed to solve a second-order singularly perturbed problem with variable coefficients. The method decomposes the solutions into two independent sub-problems and couples them through a left-end boundary condition. Unlike traditional asymptotic solutions, this method performs asymptotic series solution in the original coordinates, leading to better results.
Article
Mathematics
Chein-Shan Liu, Chih-Wen Chang, Yung-Wei Chen, Jian-Hung Shen
Summary: This paper presents a numerical method for solving non-homogeneous wave problems with nonlocal boundary conditions, and validates the effectiveness and stability of the method through numerical tests.
Article
Mathematics
Chein-Shan Liu, Jiang-Ren Chang, Jian-Hung Shen, Yung-Wei Chen
Summary: In this paper, the general Sturm-Liouville problem is transformed into two canonical forms with different boundary conditions. A boundary shape function method is proposed to solve these problems. By using normalization conditions for eigenfunctions and solving the eigenvalue curve, eigenvalues and eigenfunctions with desired accuracy can be obtained.
Article
Mathematics
Chein-Shan Liu, Chung-Lun Kuo, Chih-Wen Chang
Summary: Researchers have developed a simple method for solving linear and nonlinear eigenvalue problems. By solving a nonhomogeneous system and using a normalization condition on the eigen-equation, the method ensures the uniqueness of the eigenvector. By introducing a merit function, the method can obtain precise eigenvalues.
Article
Mathematics
Chein-Shan Liu, Essam R. El-Zahar, Chih-Wen Chang
Summary: This paper proposes a dynamical approach to determine the optimal values of parameters in iterative methods for solving linear equation systems. The new methods provide an alternative and proper choice of parameter values for accelerating convergence speed without knowing the theoretical optimal values. Numerical testings were used to assess the performance of the dynamic optimal methods.
Article
Engineering, Mechanical
Chein-Shan Liu, Chung-Lun Kuo, Chih-Wen Chang
Summary: This article introduces methods for solving the free vibration problem of multi-degree mechanical structures by linearizing it to a generalized eigenvalue problem or using iterative detection methods for quadratic eigenvalue problem. The study uses nonhomogeneous linear systems and projected eigen-equation to obtain response curves and eigenvectors, thereby saving computational cost.
