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1

Feli, Saeed, and Maziar M Jalilian. "Theoretical model of low-velocity impact on foam-core sandwich panels using finite difference method." Journal of Sandwich Structures & Materials 19, no. 3 (2016): 261–90. http://dx.doi.org/10.1177/1099636216685316.

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In this article, a three-dimensional solution based on the Fourier’s series and finite difference method has been presented to study the low-velocity impact on sandwich panels with foam core and composite face sheets. The Navier’s equations are derived and displacements are substituted by their corresponding Fourier’s series and three partial differential equations with coefficients of Fourier’s series are obtained. The contact force has been considered as a Fourier’s series of impactor displacement and deflection of top face sheet. Also, the model is verified by experiments performed on sandw
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2

Suparti, Suparti, Alan Prahutama, Rukun Santoso, and Alvita Rachma Devi. "Spline-Fourier’s Method for Modelling Inflation in Indonesia." E3S Web of Conferences 73 (2018): 13003. http://dx.doi.org/10.1051/e3sconf/20187313003.

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Regression method is a statistical method for modelling dependent variable with independent variable. Nonparametric regression is an approach to regression analysis that is suitable for data that have an unknown curve shape. Modelling by using nonparametric regression method does not require any assumptions. Spline and Fourier methods are some of the estimators in nonparametric regression. The spline method requires optimal knots to obtain the best model. The most commonly used method to determine the optimal knots is Generalized Cross Validation (GCV). The Fourier method is a method based on
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3

Kanniappan, P., and K. Thangavel. "Modified Fourier’s Method of Solving Linear Programming Problems." OPSEARCH 35, no. 1 (1998): 45–56. http://dx.doi.org/10.1007/bf03398538.

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4

Khalaj-Amirhosseini, Mohammad. "Design of Nonuniformly Spaced Antenna Arrays Using Fourier’s Coefficients Equating Method." IEEE Transactions on Antennas and Propagation 66, no. 10 (2018): 5326–32. http://dx.doi.org/10.1109/tap.2018.2861981.

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5

Cao, Binzhao, and Fuyong Xu. "Analysis for New Types of Waveguide with Fourier’s Expansion-Differential Method." International Journal of Infrared and Millimeter Waves 29, no. 3 (2008): 240–48. http://dx.doi.org/10.1007/s10762-008-9326-0.

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6

Rakhymova, A. T., A. A. Ahmedov, and K. M. Shapen. "Determination of trigonometric Fourier’s series by the method of four-dimensional mathematics." Journal of Physics: Conference Series 1988, no. 1 (2021): 012027. http://dx.doi.org/10.1088/1742-6596/1988/1/012027.

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7

Lu, Dianchen, and Jie Liu. "Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation." Abstract and Applied Analysis 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/309420.

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The homotopy analysis method is applied to solve the variable coefficient KdV-Burgers equation. With the aid of generalized elliptic method and Fourier’s transform method, the approximate solutions of double periodic form are obtained. These solutions may be degenerated into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. The results indicate that this method is efficient for the nonlinear models with the dissipative terms and variable coefficients.
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8

Khan, Dolat, Musawa Yahya Almusawa, Waleed Hamali, and M. Ali Akbar. "Couple Stress Sodium Alginate-Based Casson Nanofluid Analysis through Fick’s and Fourier’s Laws with Inclined Microchannel." Journal of Function Spaces 2023 (April 19, 2023): 1–11. http://dx.doi.org/10.1155/2023/2824703.

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Casson nanofluid plays a vital role in food industries with sodium alginate nanoparticles. That is why many researchers used Casson nanofluid in their study. Due to this, the main objective of this study is to investigate the inclined microchannel flow of a Casson nanofluid based on sodium alginate (SA) under a few stresses. Because the plate at y = d is stationary and the plate at y = 0 is in motion, the fluid flows. Physically existent things utilize partial differential equations as a method of derivation. By using dimensionless variables, the underlying PDEs are dimensionless. Applying Fou
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9

Benmessaoud, Youcef, Frédéric Dubas, and Mickael Hilairet. "Combining the Magnetic Equivalent Circuit and Maxwell–Fourier Method for Eddy-Current Loss Calculation." Mathematical and Computational Applications 24, no. 2 (2019): 60. http://dx.doi.org/10.3390/mca24020060.

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In this paper, a hybrid model in Cartesian coordinates combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series) is developed. This model coupling has been applied to a U-cored static electromagnetic device. The main objective is to compute the magnetic field behavior in massive conductive parts (e.g., aluminum, magnets, copper, iron) considering the skin effect (i.e., with the eddy-current re
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10

Aouadi, Moncef, Taoufik Moulahi, and Najmeddine Attia. "Thermoelastic Extensible Timoshenko Beam with Symport Term: Singular Limits, Lack of Differentiability and Optimal Polynomial Decay." Mathematics 13, no. 5 (2025): 854. https://doi.org/10.3390/math13050854.

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In this article, we consider the equations of the nonlinear model of a thermoelastic extensible Timoshenko beam, recently derived by Aouadi in the context of Fourier’s law. The new aspect we propose here is to introduce a second sound model in the temperatures which turns into a Gurtin–Pipkin’s model. Thus, the derived equations are physically more realistic since they overcome the property of infinite propagation speed (Fourier’s law property). They are also characterized by the presence of a symport term. Moreover, it is possible to recover the Fourier, Cattaneo and Coleman–Gurtin laws from
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11

K, Gangadhar, Venkata Ramana, Dasaradha Ramaiah, and B. Rushi Kumar. "Slip Flow of a Nanofluid Over a Stretching Cylinder with Cattaneo-Christov Flux Model: Using SRM." International Journal of Engineering & Technology 7, no. 4.10 (2018): 225. http://dx.doi.org/10.14419/ijet.v7i4.10.20901.

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This article represents a numerical investigation of heat transfer and slip flow of a nanofluid over a stretching cylinder in magnetic field. In order to explore the heat transfer characteristics Cattaneo-Christov flux model is utilized in place of Fourier’s law. By using, suitable transformations, the governing partial differential equations are changed into non-linear ordinary differential equations. A numerical method, known as, spectral relaxation method is used to solve these equations. By using pictorial graphs, the relevant physical parameters that appear in temperature and velocity dis
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12

González-Domínguez, Monzón-Verona, and García-Alonso. "New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method." Applied Sciences 9, no. 21 (2019): 4521. http://dx.doi.org/10.3390/app9214521.

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In this paper, a new constitutive matrix Mτ for thermal conduction, for tetrahedral meshes, in a steady state thermal regime is developed through a new algebraic methodology, using the Cell Method as a computational method, which is included in the finite formulation. The constitutive matrix defines the behavior of solids when they are under a thermal potential. The results are compared with those obtained for the same problem by means of the constitutive matrix Mλ developed previously, taking in both cases with a 2D axisymmetric model as reference, calculated with the finite element method. T
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13

Domínguez, Pablo Ignacio González, José Miguel Monzón-Verona, Leopoldo Simón Rodríguez, and Adrián de Pablo Sánchez. "Thermal constitutive matrix applied to asynchronous electrical machine using the cell method." Open Physics 16, no. 1 (2018): 27–30. http://dx.doi.org/10.1515/phys-2018-0005.

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Abstract This work demonstrates the equivalence of two constitutive equations. One is used in Fourier’s law of the heat conduction equation, the other in electric conduction equation; both are based on the numerical Cell Method, using the Finite Formulation (FF-CM). A 3-D pure heat conduction model is proposed. The temperatures are in steady state and there are no internal heat sources. The obtained results are compared with an equivalent model developed using the Finite Elements Method (FEM). The particular case of 2-D was also studied. The errors produced are not significant at less than 0.2
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14

El Hamidi, Abdallah, Mokhtar Kirane, and Ali Tfayli. "An Inverse Problem for a Non-Homogeneous Time-Space Fractional Equation." Mathematics 10, no. 15 (2022): 2586. http://dx.doi.org/10.3390/math10152586.

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We consider the inverse problem of finding the solution of a generalized time-space fractional equation and the source term knowing the spatial mean of the solution at any times t∈(0,T], as well as the initial and the boundary conditions. The existence and the continuity with respect to the data of the solution for the direct and the inverse problem are proven by Fourier’s method and the Schauder fixed-point theorem in an adequate convex bounded subset. In the published articles on this topic, the incorrect use of the estimates in the generalized Mittag–Leffler functions is commonly performed.
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15

Djelloul Khedda, Zakarya, Kamel Boughrara, Frédéric Dubas, Baocheng Guo, and El Hadj Ailam. "Two-dimensional steady-state thermal analytical model of permanent-magnet synchronous machines operating in generator mode." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 41, no. 1 (2021): 125–54. http://dx.doi.org/10.1108/compel-07-2021-0226.

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Purpose Thermal analysis of electrical machines is usually performed by using numerical methods or lumped parameter thermal networks depending on the desired accuracy. The analytical prediction of temperature distribution based on the formal resolution of thermal partial differential equations (PDEs) by the harmonic modeling technique (or the Fourier method) is uncommon in electrical machines. Therefore, this paper aims to present a two-dimensional (2D) analytical model of steady-state temperature distribution for permanent-magnet (PM) synchronous machines (PMSM) operating in generator mode. D
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16

Gangadhar, K., K. V. Ramana, Oluwole Daniel Makinde, and B. Rushi Kumar. "MHD Flow of a Carreau Fluid Past a Stretching Cylinder with Cattaneo-Christov Heat Flux Using Spectral Relaxation Method." Defect and Diffusion Forum 387 (September 2018): 91–105. http://dx.doi.org/10.4028/www.scientific.net/ddf.387.91.

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A theoretical investigation of a hydromagnetic boundary layer flow of Carreau fluid over a stretching cylinder with surface slippage and temperature jump is presented in this paper. It is assumed that heat transfer characteristics of the flow follows Cattaneo-Christov heat flux model base on conventional Fourier’s law with thermal relaxation time. The spectral relaxation method (SRM) is being utilized to provide the solution of highly nonlinear system of coupled partial differential equations converted into dimensionless governing equations. The behaviour of flow parameters on velocity, temper
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17

Benmessaoud, Youcef, Daoud Ouamara, Frédéric Dubas, and Mickael Hilairet. "Investigation of Volumic Permanent-Magnet Eddy-Current Losses in Multi-Phase Synchronous Machines from Hybrid Multi-Layer Model." Mathematical and Computational Applications 25, no. 1 (2020): 14. http://dx.doi.org/10.3390/mca25010014.

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This paper investigates the permanent-magnet (PM) eddy-current losses in multi-phase PM synchronous machines (PMSM) with concentric winding and surface-mounted PMs. A hybrid multi-layer model, combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series), performs the eddy-current loss calculations. First, the magnetic flux density was obtained from the 2-D generic MEC and then subjected to the Fa
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18

Hu, Wenjing. "A new method to solve non-homogeneous wave equations of electromagnetic fields by fourier’s triple integral transform." IOP Conference Series: Earth and Environmental Science 81 (August 2017): 012210. http://dx.doi.org/10.1088/1755-1315/81/1/012210.

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19

Kovačič, Boštjan, Tomaž Motoh, and Samo Lubej. "Experimental analysis of the dynamic responses of bridging objects with alternative non-contact method." E3S Web of Conferences 110 (2019): 01028. http://dx.doi.org/10.1051/e3sconf/201911001028.

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Structure objects are exposed to different natural influences resulting in long-term and catastrophic outcomes. In order to avoid them, regular monitoring is needed. Various approaches to control condition of a structure can be considered, one of them is the measurement by means of monitoring which can be performed in different ways, depending on responses – static or dynamic, or both simultaneously. Specifically, technological development has enabled to monitor not only static but also dynamic responses by non-contact geodetic methods. Due to their simplicity and reliability of results, geode
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20

Gangadhar, K., Chintalapudi Suresh Kumar, S. Mohammed Ibrahim, and Giulio Lorenzini. "Effect of Viscous Dissipation on Upper - Convected Maxwell Fluid with Cattaneo-Christov Heat Flux Model Using Spectral Relaxation Method." Defect and Diffusion Forum 388 (October 2018): 146–57. http://dx.doi.org/10.4028/www.scientific.net/ddf.388.146.

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The study observes the flow and heat transfer in upper-convected Maxwell fluid over a rapidly stretching surface with viscous dissipation. Cattaneo-Christov heat flux model has been used in the preparation of the energy equation. The model is used in guessing the impacts of thermal relaxation time over boundary layer. Similarity method has been used to keep normal the supervising boundary layer equations. Local similarity solutions have been obtained through spectral relaxation method. The fluid temperature has a relation with thermal relaxation time inversely and our calculations have shown t
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21

Pang, Xiao Ping, and Jin Chen. "Study on 3D Shape Optimization for Hydrodynamic Journal Bearing Using Goal Attainment Multi-Objective Function." Applied Mechanics and Materials 319 (May 2013): 505–9. http://dx.doi.org/10.4028/www.scientific.net/amm.319.505.

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This paper is focused on multi-objective optimization to find the best performance related to the geometrical design of the hydrodynamic journal bearing in three dimensions 3D. The mathematical model for 3D film thickness profile was driven using Fourier’s series function and axial waviness value to represent in circumferential and axial direction respectively. A Goal attainment function was used as an optimization tool with goals to minimize the power loss and side leakage and to maximize the load capacity, while the amplitude (a), number of wave (m) and Fourier's series coefficients of the g
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22

Firdous, Hina, Syed Tauseef Saeed, Hijaz Ahmad, and Sameh Askar. "Using Non-Fourier’s Heat Flux and Non-Fick’s Mass Flux Theory in the Radiative and Chemically Reactive Flow of Powell–Eyring Fluid." Energies 14, no. 21 (2021): 6882. http://dx.doi.org/10.3390/en14216882.

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The behavior of convective boundary conditions is studied to delineate their role in heat and mass relegation in the presence of radiation, chemical reaction, and hydro-magnetic forces in three-dimensional Powell–Eyring nanofluids. Implications concerning non-Fourier’s heat flux and non-Fick’s mass flux with respect to temperature nanoparticle concentration were examined to discuss the graphical attributes of the principal parameters. An efficient optimal homotopy analysis method is used to solve the transformed partial differential equations. Tables and graphs are physically interpreted for s
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23

Liu, Guang Wei, Feng Ge Zhang, and Jin Xiang Gao. "Analytical Calculation Model of Air-Gap Magnetic Field for Claw Pole Machine with Outer PM Rotor." Advanced Materials Research 588-589 (November 2012): 463–66. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.463.

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In view of the time consuming and sensitive to finite element meshes, the finite element method is not suitable for claw pole machine with outer permanent magnet rotors with complicated and asymmetric 3D structure. A new analytical calculation model based on air-gap magnetic field analysis in polar coordinates is proposed. According to boundary conditions, the radial and tangential flux density is obtained by using the Fourier’s series, and then the cogging torque and no load EMF is calculated. In order to verify the accuracy of the analytical method, the finite element analysis is finished. M
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Kaczmarzyk, Marcin, Marcin Gawronski, and Grzegorz Piatkowski. "Application of Finite Difference Method for determining lunar regolith diurnal temperature distribution." E3S Web of Conferences 49 (2018): 00052. http://dx.doi.org/10.1051/e3sconf/20184900052.

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This study was performed in order to verify viability of using finite difference method and proposed simple astrometrical model for modelling heat transfer in lunar regolith. The concept was examined by developing FD model of heat flow for upper 0,9 m of lunar regolith, and comparing obtained results with in situ measurements provided by Apollo 15 and 17 heat flow experiments. The model was based on FDM approximation of Fourier’s law for one dimensional transient heat flow. Both constant and temperature-dependent thermophysical properties of lunar regolith were obtained from in situ measuremen
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Vaysfeld, N. D., Z. Yu Zhuravlova, O. P. Moyseenok, and V. V. Reut. "Investigation of the semi-strip’s stress state in the case of steady-state oscillations." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2019): 54–57. http://dx.doi.org/10.17721/1812-5409.2019/1.11.

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The elastic semi-strip under the dynamic load concentrated at the centre of the semi-strip’s short edge is considered. The lateral sides of the semi-strip are fixed. The case of steady-state oscillations is considered. The initial problem is reduced to the one-dimensional problem with the help of the semi-infinite sin-, cos-Fourier’s transform. The one-dimensional problem is formulated in the vector form. Its solution is constructed as a superposition of the general solution for the homogeneous equation and the partial solution for the inhomogeneous equation. The general solution for the homog
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Williams, Earl G. "Fourier acoustics: Uncovering the origins of sound." Journal of the Acoustical Society of America 153, no. 3_supplement (2023): A208. http://dx.doi.org/10.1121/10.0018675.

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No doubt, Jean-Baptiste Joseph Fourier has had a great impact in science. At the root of Fourier Acoustics, the Fourier series, when employed as a starting point and manipulated, allows us to uncover the origins of sound in a simple and elegant way, not only in acoustics but also in electromagnetics. A well-known stepping stone on the path is nearfield acoustical holography (NAH) and its theory can be recast almost completely, and simply, in terms of two-dimensional (2D) Fourier series and applied to any geometry. For separable coordinate systems, each of the components of the series can be pr
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Siarkowski, Marek, Tomasz Mrozek, Janusz Sylwester, Michalina Litwicka, and Magdalena Dąbek. "The non-Fourier image reconstruction method for the STIX instrument." Open Astronomy 29, no. 1 (2020): 220–30. http://dx.doi.org/10.1515/astro-2020-0022.

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AbstractIn this work we aimed to develop the image reconstruction algorithm without any analytical simplifications and restrictions. In our method we abandon Fourier’s approach to image reconstruction, and instead use the number of counts recorded in each detector pixel, and then reconstruct each image using a classical Richardson-Lucy algorithm. Among similar works performed in the past, our approach is based, for the first time, on the real geometry of STIX. We made a preliminary analysis of expected differences in STIX imaging which may occur due to usage of slightly different geometries. T
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Siarkowski, Marek, Tomasz Mrozek, Janusz Sylwester, Michalina Litwicka, and Magdalena Dąbek. "The non-Fourier image reconstruction method for the STIX instrument." Open Astronomy 29, no. 1 (2020): 220–30. http://dx.doi.org/10.1515/astro-2020-0022.

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AbstractIn this work we aimed to develop the image reconstruction algorithm without any analytical simplifications and restrictions. In our method we abandon Fourier’s approach to image reconstruction, and instead use the number of counts recorded in each detector pixel, and then reconstruct each image using a classical Richardson-Lucy algorithm. Among similar works performed in the past, our approach is based, for the first time, on the real geometry of STIX. We made a preliminary analysis of expected differences in STIX imaging which may occur due to usage of slightly different geometries. T
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29

Gadisa, Gosa, Tagay Takele, and Shibiru Jabessa. "Micropolar Couple Stress Nanofluid Flow by Non-Fourier’s-Law Heat Flux Model past a Stretching Sheet." Journal of Mathematics 2021 (January 15, 2021): 1–18. http://dx.doi.org/10.1155/2021/6683711.

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In this investigation, thermal radiation effect on MHD nonlinear convective micropolar couple stress nanofluid flow by non-Fourier’s-law heat flux model past a stretching sheet with the effects of diffusion-thermo, thermal-diffusion, and first-order chemical reaction rate is reported. The robust numerical method called the Galerkin finite element method is applied to solve the proposed fluid model. We applied grid-invariance test to approve the convergence of the series solution. The effect of the various pertinent variables on velocity, angular velocity, temperature, concentration, local skin
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Jiang, Peng, Jinkai Ni, and Lu Zhu. "Global Well-Posedness and Large-Time Behavior for the Equilibrium Diffusion Model in Radiation Hydrodynamics." Journal of Function Spaces 2023 (March 29, 2023): 1–9. http://dx.doi.org/10.1155/2023/2891000.

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In this paper, we investigate the global well-posedness of the equilibrium diffusion model in radiation hydrodynamics. The model consists of the compressible Navier-Stokes equations coupled with radiation effect terms described by the fourth power of temperature. The global existence of classical solutions to the Cauchy problem in the whole space is established when initial data is a small smooth perturbation of a constant equilibrium state: moreover, an algebraic rate of convergence of solutions toward equilibrium is obtained under additional conditions on initial data. The proof is based on
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Sheikh, Shahala, Lalsingh Khalsa, Nitin Chandel, and Vinod Varghese. "Hygrothermoelastic large deflection behaviour in a thin circular plate with non-Fourier and non-Fick law." Scientific Temper 15, no. 02 (2024): 2152–60. http://dx.doi.org/10.58414/scientifictemper.2024.15.2.27.

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The coupled fractional dual phase-lag hygrothermoelasticity theory, developed using fractional calculus principles, extends classical Fourier’s and Fick’s laws to a time-fractional differential equation. The concept is applied to a thin circular plate that is exposed to hygrothermal loadings. The finite integral transform method and decoupled technique are utilized to create closed-form expressions for various factors such as temperature, moisture, large deflection, and stresses. The study compares the results of the dual phase-lag model with those of classical and hyperbolic models. The phase
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Hu, Bing, Xiaoting Qu, Liang Fu, and Huadong Yan. "Engineering calculation and analysis of aerodynamic heating for hypersonic rocket sled." Journal of Physics: Conference Series 2478, no. 8 (2023): 082009. http://dx.doi.org/10.1088/1742-6596/2478/8/082009.

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Abstract Aerodynamic heating and temperature distribution are one of the problems that must be considered in the design of hypersonic rocket sled. In order to evaluate the aerodynamic heating environment of hypersonic rocket sled, the typical monorail rocket sled with cone cylinder combination is taken as the research object, the aerodynamic heating calculation methods such as Modified Newton Theory, Reynolds Analogy Theory, Reference Enthalpy Method and Fourier’s Law of Heat Conduction are used, and the temperature variation law of rocket sled conical surface under Mach 5 and Mach 7 ballistic
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Tulu, Ayele. "Analysis of Magnetohydrodynamic Micropolar Nanofluid Flow due to Radially Stretchable Rotating Disk Employing Spectral Method." Advances in Mathematical Physics 2023 (February 24, 2023): 1–16. http://dx.doi.org/10.1155/2023/5283475.

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The present analysis is aimed at examining MHD micropolar nanofluid flow past a radially stretchable rotating disk with the Cattaneo-Christov non-Fourier heat and non-Fick mass flux model. To begin with, the model is developed in the form of nonlinear partial differential equations (PDEs) for momentum, microrotation, thermal, and concentration with their boundary conditions. Employing suitable similarity transformation, the boundary layer micropolar nanofluid flows governing these PDEs are transformed into large systems of dimensionless coupled nonlinear ordinary differential equations (ODEs).
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Ashraf, Forsberg, Mattsson, and Thungström. "Thermoelectric Properties of n-Type Molybdenum Disulfide (MoS2) Thin Film by Using a Simple Measurement Method." Materials 12, no. 21 (2019): 3521. http://dx.doi.org/10.3390/ma12213521.

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In this paper, a micrometre thin film of molybdenum disulfide (MoS2) is characterized for thermoelectric properties. The sample was prepared through mechanical exfoliation of a molybdenite crystal. The Seebeck coefficient measurement was performed by generating a temperature gradient across the sample and recording the induced electrical voltage, and for this purpose a simple measurement setup was developed. In the measurement, platinum was utilized as reference material in the electrodes. The Seebeck value of MoS2 was estimated to be approximately −600 µV/K at a temperature difference of 40 °
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Ecsedi, István, and Ákos József Lengyel. "Analytical Solutions of Heat Conduction Problems for Anisotropic Solid Body." WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER 16 (August 25, 2021): 127–36. http://dx.doi.org/10.37394/232012.2021.16.15.

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Exact analytical solutions of heat conduction problems in anisotropic twodimensional solid bodies are presented in this study. Timedependent and steadystate problems are considered. A linear coordinate transformation is introduced which reduces the anisotropic heat conduction problem to an equivalent isotropic one. The solution of the anisotropic heat conduction problem is expressed in terms of solutions of the corresponding isotropic heat conduction problem. The connection of data of the applied linear coordinate transformation and the thermal material properties of anisotropic solid body is
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Akselsen, Andreas H., and Simen Å. Ellingsen. "Sheared free-surface flow over three-dimensional obstructions of finite amplitude." Journal of Fluid Mechanics 878 (September 18, 2019): 740–67. http://dx.doi.org/10.1017/jfm.2019.657.

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When shallow water flows over uneven bathymetry, the water surface is modulated. This type of problem has been revisited numerous times since it was first studied by Lord Kelvin in 1886. Our study analytically examines currents whose unperturbed velocity profile $U(z)$ follows a power law $z^{q}$, flowing over a three-dimensional uneven bed. This particular form of $U$, which can model a miscellany of realistic flows, allows explicit analytical solutions. Arbitrary bed shapes can readily be imposed via Fourier’s theorem provided their steepness is moderate. Three-dimensional vorticity–bathymet
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Khan, Zeeshan, Haroon Ur Rasheed, Sahib Noor, et al. "Analytical Solution of UCM Viscoelastic Liquid with Slip Condition and Heat Flux over Stretching Sheet: The Galerkin Approach." Mathematical Problems in Engineering 2020 (February 25, 2020): 1–7. http://dx.doi.org/10.1155/2020/7563693.

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This paper provides a substantial amount of study related to coupled fluid flow and heat conduction of an upper-convected-Maxwell viscoelastic liquid over a stretching plane with slip velocity. A new model, presented by Christov, for thermal convection is employed. The partial differential equations are converted to ordinary differential equations by using appropriate transformation variables. The transformed equations are solved analytically by using the Galerkin method. For the sake of soundness, a comparison is done with a numerical method, and good agreement is found. The impacts of variou
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Thangaratnam, Kari, Divya, and Evangeline Kumar. "Integrated Thermal Structural Analysis of Advanced Composite Plates and Shells." Applied Mechanics and Materials 877 (February 2018): 335–40. http://dx.doi.org/10.4028/www.scientific.net/amm.877.335.

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Thermo-structural analysis with advanced composite plates and shells has been performed using Finite element method in order to determine temperature response and associated thermal stress. On solving the Fourier’s heat conduction equation, temperature profile is arrived at, with the assumption of linear/uniform temperature distribution through the thickness. Finite element program is developed for steady-state heat transfer problems using Semiloof shell element. Validation for integrated thermo-structural analysis has been done and compared with the available results from literature. The new
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39

Dey, Paramita, and Bommana Sweety Dhar. "An overview on nanofibres: their whereabouts and applications in the pharmaceutical field." International Journal of Research in Pharmaceutical Sciences 16, no. 2 (2025): 21–30. https://doi.org/10.26452/ijrps.v16i2.4747.

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Nanofibers are generally solid, porous and high surface to volume ratio serving as an important approach towards various diseases in the medical field like wound healing, drug delivery, contraceptives, tissue engineering, bone regeneration etc. There are different types of nanofibers like polymeric, composite, inorganic and carbon. Electrospinning is a well known method of preparation that produces fibers ranging from micro meter to nanometer. Hence, nanofibers have an immense scope in therapeutic field. This paper deals with a vivid study about the emergence of nanofiber over the conventional
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Ahmad Shafique, Muhammad Ramzan, Zaib Un Nisa, Mudassar Nazar, and Hafeez Ahmad. "Unsteady Magnetohydrodynamic Flow of Second Grade Nanofluid (Ag-Cu) With CPC Fractional Derivative." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 97, no. 2 (2022): 103–14. http://dx.doi.org/10.37934/arfmts.97.2.103114.

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Unsteady magnetohydrodynamics (MHD) flow of fractionalized second grade nanofluid (Ag-Cu) over a vertical plate is obtained. The model is solved by using CPC fractional derivative. The novelty of present study is to generalized the model by using Fourier’s and Fick’s laws. The nanofluids are formed by dispersing two different nanoparticles, silver (Ag) and copper (Cu), into a based fluid. The governing dimensionless equations for velocity, concentration, and temperature profiles are solved using Laplace transform method and compared graphically. The effects of different parameters like fractio
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Duan, Xue Tao, Hao Luo, Bin Xu, and Jian Bin Luo. "Research on Numerical Simulation of Micro-Scale Couette Flow System." Advanced Materials Research 347-353 (October 2011): 2645–50. http://dx.doi.org/10.4028/www.scientific.net/amr.347-353.2645.

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In this paper, Couette flow which is a sort of flow system simplified in MEMS is explored mainly. The corresponding mathematical model has been built based on N- S Equation, Fourier’s Law and idea gas state equation. Applying the generalized differential quadrature method (GDQ) , the numerical simulation is made. The new model is verified using the direct simulation of Monte Carlo approach finally. The solutions of two different approaches are analyzed and compared. This model can been used to simulate the gas flow in the slip and transition region. The program of GDQ is simpler than DSMC’s an
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Al-Qahtani, H., and B. S. Yilbas. "Closed-form solution of Cattaneo equation including volumetric source in relation to laser short-pulse heating." Canadian Journal of Physics 89, no. 7 (2011): 761–67. http://dx.doi.org/10.1139/p11-053.

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The wave nature of the heating model is considered, incorporating the Cattaneo equation with the presence of a volumetric heat source. The volumetric heat generation resembles the step input laser short-pulse intensity. The governing of the heat equation is solved analytically using the Laplace transformation method. The stress field generated due to thermal contraction and expansion of the substrate material is formulated and the closed-form solution is presented. It is found that the wave nature of the heating is dominant during the period of the irradiated short-pulse; however, in the late
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43

Asjad, Muhammad Imran, Rizwan Karim, Abid Hussanan, Azhar Iqbal, and Sayed M. Eldin. "Applications of Fractional Partial Differential Equations for MHD Casson Fluid Flow with Innovative Ternary Nanoparticles." Processes 11, no. 1 (2023): 218. http://dx.doi.org/10.3390/pr11010218.

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This study deals with the modeling issues of the transport problem with a fractional operator. The fractional model with generalized Fourier’s law is discussed for Casson fluid flow over a flat surface. The dimensionless governing model is solved with the Laplace transform method, and the different comparisons are plotted from the obtained solutions. Other features of the problem have been analyzed instead of the symmetric behavior of the properties for different values of the fractional parameter. As a result, the ternary nanoparticles approach can be used to improve the fluid properties bett
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Algehyne, Ebrahem A., Essam R. El-Zahar, Muhammad Sohail, et al. "Thermal Improvement in Pseudo-Plastic Material Using Ternary Hybrid Nanoparticles via Non-Fourier’s Law over Porous Heated Surface." Energies 14, no. 23 (2021): 8115. http://dx.doi.org/10.3390/en14238115.

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The numerical, analytical, theoretical and experimental study of thermal transport is an active field of research due to its enormous applications and use in numerous systems. This report covers the impacts of thermal transport on pseudo-plastic material past over a horizontal, heated and stretched porous sheet. Modeling of energy conservation is based upon a generalized heat flux model along with a heat generation/absorption factor. The modeled phenomenon is derived in the Cartesian coordinate system under the usual boundary-layer approach proposed by Prandtl, which removes the complexity of
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Zeleke, Migbar Assefa, Lai Xin, and Li Sheng Liu. "Bond Based Peridynamic Formulation for Thermoelectric Materials." Materials Science Forum 883 (January 2017): 51–59. http://dx.doi.org/10.4028/www.scientific.net/msf.883.51.

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Modeling of heat and electrical current flow simultaneously in thermoelectric convertor using classical theories do not consider the influence of defects in the material. This is because traditional methods are developed based on partial differential equations (PDEs) and lead to infinite fluxes and stress fields at the crack tips. The usual way of solving such PDEs is by using numerical technique, like Finite Element Method (FEM). Although FEM is robust and versatile, it is not suitable to model evolving discontinuities since discontinuous fields are mathematically singular at the crack tip an
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Parveen, Nabeela, Muhammad Awais, Saeed Ehsan Awan, Wasim Ullah Khan, Yigang He, and Muhammad Yousaf Malik. "Entropy Generation Analysis and Radiated Heat Transfer in MHD (Al2O3-Cu/Water) Hybrid Nanofluid Flow." Micromachines 12, no. 8 (2021): 887. http://dx.doi.org/10.3390/mi12080887.

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This research concerns the heat transfer and entropy generation analysis in the MHD axisymmetric flow of Al2O3-Cu/H2O hybrid nanofluid. The magnetic induction effect is considered for large magnetic Reynolds number. The influences of thermal radiations, viscous dissipation and convective temperature conditions over flow are studied. The problem is modeled using boundary layer theory, Maxwell’s equations and Fourier’s conduction law along with defined physical factors. Similarity transformations are utilized for model simplification which is analytically solved with the homotopy analysis method
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Yu, Xueyong, Weiran Lin, Jinling Wei, Shuoping Wang, and Haifeng Ke. "Optimization Design of Oven Shape Based on Heat Distribution Model." Journal of Advanced Computational Intelligence and Intelligent Informatics 24, no. 4 (2020): 494–501. http://dx.doi.org/10.20965/jaciii.2020.p0494.

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We developed two models in this study: one to show the distribution of heat for pans of different shapes, and the other to select the best type of pan to maximize the number of pans that can fit in the oven and to maximize even heat distribution in the pans. We constructed a model of heat distribution. The uneven distribution of heat is mainly caused by heat conduction. We established a differential equation for heat conduction according to Fourier’s law. The finite-difference method and Gauss-Seidel iteration were used to solve the equation, and MATLAB was used to draw the corresponding heat-
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Zhang, Zhong, Ding Zhou, Xiuli Xu, and Xuehong Li. "Analysis of thick beams with temperature-dependent material properties under thermomechanical loads." Advances in Structural Engineering 23, no. 9 (2020): 1838–50. http://dx.doi.org/10.1177/1369433220901810.

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This study focuses on the thermoelastic behavior of simply supported thick beams with temperature-dependent material properties under thermomechanical loads. The heat conduction analysis is based on the one-dimensional Fourier’s law, and the displacement and stress analysis is based on the two-dimensional thermoelasticity theory. The solution of temperature field across the thickness is obtained. By dividing the beam into a series of thin slices, the temperature and the material properties in each slice are considered to be uniform. The state space method is used to give the displacements and
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Sana, Vladimír, and Michal Polak. "Human-Induced Vertical Vibration of the Footbridge across Opatovicka Street." Applied Mechanics and Materials 617 (August 2014): 7–12. http://dx.doi.org/10.4028/www.scientific.net/amm.617.7.

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The presented article is focused on a theoretical dynamic analysis of the footbridge across the Opatovicka street in Prague, which acts as a simply supported beam. The structure was loaded by an ordinary pedestrian traffic, synchronous runners and vandals. The ordinary traffic was simulated by the Monte Carlo method as a stream of moving periodic forces with stochastic parameters. The synchronous runners and vandals were modeled as a combination of biomechanical models of human body, which influenced the structure vibration only passively, and driving forces, which loaded the structure in the
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Koumekpo, Yao, Kossi Atchonouglo, Edo-Owodou Ayeleh, Arnaud Germaneau, Laettia Caillé, and Jean-Christophe Dupré. "Estimation of thermophysic properties of a bimaterial by temperature field measurement and finite element model updating." Mechanics & Industry 24 (2023): 4. http://dx.doi.org/10.1051/meca/2022030.

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The aim of this study is to identify simultaneously the thermal conductivity tensor and the heat capacity per unit volume of a bimaterial, whose heat conduction obeys Fourier’s law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution of the heat conduction equation solved numerically with the help of finite element method formulation. To identify the parameters, an inverse method is developed by using the finite element model updating (FEMU) based on the Levenberg-Marquardt algorithm. This inverse finite element method appr
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