Non-Fourier heat conduction/convection in moving medium

Han, Sang M.; Peddieson, John

doi:10.1016/j.ijthermalsci.2018.04.001

Cited by 5 publications

(5 citation statements)

References 18 publications

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“…Consequently, there has been a notable upsurge in scholarly attention towards the numerical resolution of such problems in recent years. Several numerical techniques, encompassing but not confined to the finite difference method (FDM) [2,3], the finite element method (FEM) [4][5][6], the finite difference method, finite volume method (FVM) [7], the boundary element method (BEM) [8,9], the meshless methods [1,[10][11][12], and the lattice Boltzmann method [13,14], have been put forth to address these concerns.…”

Section: Introductionmentioning

confidence: 99%

A Reduced-Order FEM Based on POD for Solving Non-Fourier Heat Conduction Problems under Laser Heating

Kou,

Zhang,

Zheng

et al. 2024

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The study presents a novel approach called FEM-POD, which aims to enhance the computational efficiency of the Finite Element Method (FEM) in solving problems related to non-Fourier heat conduction. The present method employs the Proper Orthogonal Decomposition (POD) technique. Firstly, spatial discretization of the second-order hyperbolic differential equation system is achieved through the Finite Element Method (FEM), followed by the application of the Newmark method to address the resultant ordinary differential equation system over time, with the resultant numerical solutions collected in snapshot form. Next, the Singular Value Decomposition (SVD) is employed to acquire the optimal proper orthogonal decomposition basis, which is subsequently combined with the FEM utilizing the Newmark scheme to construct a reduced-order model for non-Fourier heat conduction problems. To demonstrate the effectiveness of the suggested method, a range of numerical instances, including different laser heat sources and relaxation durations, are executed. The numerical results validate its enhanced computational accuracy and highlight significant time savings over addressing non-Fourier heat conduction problems using the full order FEM with the Newmark approach. Meanwhile, the numerical results show that when the number of elements or nodes is relatively large, the CPU running time of the FEM-POD method is even hundreds of times faster than that of classical FEM with the Newmark scheme.

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Section: Introductionmentioning

confidence: 99%

A Reduced-Order FEM Based on POD for Solving Non-Fourier Heat Conduction Problems under Laser Heating

Kou,

Zhang,

Zheng

et al. 2024

Coatings

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“…This is a parabolic model and neglects thermal relaxation effects which can be significant in polymer processing. To more accurately represent thermal behaviour therefore a non-Fourier model [11] is required. The Cattaneo-Christov model [12,13] provides an excellent approximation for computing thermal relaxation effects associated with hyperbolic heat conduction.…”

Section: Introductionmentioning

confidence: 99%

Mixed convection Casson polymeric flow from a nonlinear stretching surface with radiative flux and non‐Fourier thermal relaxation effects: Computation with CSNIS

et al. 2023

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Thermal non-Newtonian polymer coating flows is growing as a major area in materials processing. Inspired by new developments in this field which require more sophisticated mathematical models, the current investigation examines the laminar viscoplastic boundary layer flow and mixed convective heat transfer over a power-law nonlinear stretching surface. To simulate thermal relaxation effects the hyperbolic Cattaneo-Christov heat flux model is deployed. The non-Newtonian polymer characteristics are described by employing the Casson flow model. High temperature conditions invoke thermal radiation flux which is analyzed with an algebraic flux model. Via robust similarity transformations, the primitive partial differential conservation equations for momentum and energy equations are rendered into a system of coupled non-linear ordinary differential equations with associated wall and free stream boundary conditions. The emerging boundary value problem is solved numerically with an efficient Chebyshev Spectral Newton Iterative scheme (CSNIS), in the MATLAB platform. The resulting solutions are discussed for different emerging parameters using graphs and tables. Validation is included with special cases from the literature. With increasing power law stretching index increases, the flow is decelerated, and temperatures are reduced. Increment in mixed convection parameter boosts the velocity but suppresses temperature and thermal boundary layer thickness. Increasing non-Fourier Deborah number, temperatures are depleted whereas with increasing radiative flux parameter they are increased. With elevation in Casson non-Newtonian parameter, velocity is decreased whereas temperature is enhanced and Nusselt number is suppressed.

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“…Also, the effect of fin surface conditions was studied. Han and Peddieson [23] investigated the Non-Fourier one-dimensional unsteady equation in a body for medium speeds less than (sub-critical), equal to (critical), and greater than (super-critical) the thermal wave speed. Liu et al [24] studied a hyperbolic lattice Boltzmann method (HLBM) compare to the parabolic lattice Boltzmann method (PLBM) to survey the non-Fourier effects.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Heat Conduction in a Symmetrical Cylinder Using the Solution Structure Theorem and Superposition Technique

et al. 2019

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In this paper, non-Fourier heat conduction in a cylinder with non-homogeneous boundary conditions is analytically studied. A superposition approach combining with the solution structure theorems is used to get a solution for equation of hyperbolic heat conduction. In this solution, a complex origin problem is divided into, different, easier subproblems which can actually be integrated to take the solution of the first problem. The first problem is split into three sub-problems by setting the term of heat generation, the initial conditions, and the boundary condition with specified value in each sub-problem. This method provides a precise and convenient solution to the equation of non-Fourier heat conduction. The results show that at low times (t = 0.1) up to about r = 0.4, the contribution of T1 and T3 dominate compared to T2 contributing little to the overall temperature. But at r > 0.4, all three temperature components will have the same role and less impact on the overall temperature (T).

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Non-Fourier heat conduction/convection in moving medium

Cited by 5 publications

References 18 publications

A Reduced-Order FEM Based on POD for Solving Non-Fourier Heat Conduction Problems under Laser Heating

A Reduced-Order FEM Based on POD for Solving Non-Fourier Heat Conduction Problems under Laser Heating

Mixed convection Casson polymeric flow from a nonlinear stretching surface with radiative flux and non‐Fourier thermal relaxation effects: Computation with CSNIS

Analytical Solution of Heat Conduction in a Symmetrical Cylinder Using the Solution Structure Theorem and Superposition Technique

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