Laminar fluid flow and heat transfer in an internally corrugated tube by means of the method of fundamental solutions and radial basis functions

Grabski, Jakub Krzysztof; Kołodziej, Jan Adam

doi:10.1016/j.camwa.2017.11.011

Cited by 14 publications

(6 citation statements)

References 57 publications

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“…where n is the normal direction. The product of friction factor and Reynolds [10,42] number takes the form…”

Section: The Momentum Equationmentioning

confidence: 99%

“…Finally, the dimensionless governing equation for heat transfer problem in the fluid region Ω 1 after some mathematical operations [10,42] takes the form…”

Section: The Energy Equationmentioning

confidence: 99%

“…The paper presents quite new application of a meshless procedure for solving fluid flow and heat transfer in a internally finned square duct. In comparison to the previous paper on application of the MFS and RBFs for solving fluid flow and heat transfer in internally corrugated or finned ducts [27,[41][42][43], in this paper, the MMFS is applied in order to obtain stable solution because of boundary singularities. Furthermore, instead of the commonly used DRM, the GRBFCM is employed in the paper for obtaining the particular solution in the Picard iteration process, what is also not so typical for application of the MFS for nonlinear and inhomogeneous problems.…”

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confidence: 99%

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A meshless procedure for analysis of fluid flow and heat transfer in an internally finned square duct

Grabski

2019

Heat Mass Transfer

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Application of the method of fundamental solutions in combination with the global radial basis function collocation method for analysis of fluid flow and heat transfer in an internally finned square duct is presented in the paper. Fluid flow problem is solved using the modified method of fundamental solutions. After that, the average fluid velocity and product of friction factor and Reynolds number can be determined. Heat transfer problem in the fluid is governed by a nonlinear equation with linear boundary conditions. The Picard iteration method is employed in the paper in order to transform the nonlinear problem into a sequence of inhomogeneous problems. At each iteration step, the general solution is obtained using the modified method of fundamental solutions and the particular solution is obtained using the global radial basis function collocation method. When the iteration process is stopped, the Nusselt number can be determined. Nomenclature aHalf of internal width of channel [m] bThickness of wall [m]

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“…where n is the normal direction. The product of friction factor and Reynolds [10,42] number takes the form…”

Section: The Momentum Equationmentioning

confidence: 99%

“…Finally, the dimensionless governing equation for heat transfer problem in the fluid region Ω 1 after some mathematical operations [10,42] takes the form…”

Section: The Energy Equationmentioning

confidence: 99%

mentioning

confidence: 99%

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A meshless procedure for analysis of fluid flow and heat transfer in an internally finned square duct

Grabski

2019

Heat Mass Transfer

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“…Liehui Xiao [17] used a wind tunnel experiment to conduct a cooling enhancement heat transfer experiment on corrugated fin tube bundles, and measured the temperature distribution on the fin surface through a visual window. Jakub Krzysztof Grabski [18] analyzed the fluid in the corrugated pipe by the basic solution method and the Radial Basis Functions. They verified that the Nusselt number increased with the increase of amplitude and ripple number.…”

Section: Introductionmentioning

confidence: 99%

A Three-Dimensional Numerical and Multi-Objective Optimal Design of Wavy Plate-Fins Heat Exchangers

Xue

Shi

et al. 2020

Processes

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This paper presents a method for optimizing wavy plate-fin heat exchangers accurately and efficiently. It combines CFD simulation, Radical Basis Functions (RBF) with multi-objective optimization to improve the performance. The optimization of the Colburn factor j and the friction coefficient f is regarded as a multi-objective optimization problem, due to the existence of two contradictory goals. The approximation model was obtained by Radical Basis Functions, and the shape of the heat exchanger was optimized by multi-objective genetic algorithm (MOGA). The optimization results showed that j increased by 17.62% and f decreased by 20.76%, indicating that the heat exchange efficiency was significantly enhanced and the fluid structure resistance reduced. Then, from the aspects of field synergy and tubulence energy, the performance advantage of the optimized structure was further confirmed.

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“…Subsequently, the Kansa method [17,18] that directly adopts the MQ RBF has been indicated to be an effective numerical tool for approximating PDE solutions. Numerous engineering problems, including Burgers' equation [19,20], heat transfer [21][22][23], and groundwater contaminant transport [24], have been solved using the Kansa method.…”

Section: Introductionmentioning

confidence: 99%

Space–Time Radial Basis Function–Based Meshless Approach for Solving Convection–Diffusion Equations

Xiao

Liu

2020

Mathematics

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This article proposes a space–time meshless approach based on the transient radial polynomial series function (TRPSF) for solving convection–diffusion equations. We adopted the TRPSF as the basis function for the spatial and temporal discretization of the convection–diffusion equation. The TRPSF is constructed in the space–time domain, which is a combination of n–dimensional Euclidean space and time into an n + 1–dimensional manifold. Because the initial and boundary conditions were applied on the space–time domain boundaries, we converted the transient problem into an inverse boundary value problem. Additionally, all partial derivatives of the proposed TRPSF are a series of continuous functions, which are nonsingular and smooth. Solutions were approximated by solving the system of simultaneous equations formulated from the boundary, source, and internal collocation points. Numerical examples including stationary and nonstationary convection–diffusion problems were employed. The numerical solutions revealed that the proposed space–time meshless approach may achieve more accurate numerical solutions than those obtained by using the conventional radial basis function (RBF) with the time-marching scheme. Furthermore, the numerical examples indicated that the TRPSF is more stable and accurate than other RBFs for solving the convection–diffusion equation.

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Laminar fluid flow and heat transfer in an internally corrugated tube by means of the method of fundamental solutions and radial basis functions

Cited by 14 publications

References 57 publications

A meshless procedure for analysis of fluid flow and heat transfer in an internally finned square duct

A meshless procedure for analysis of fluid flow and heat transfer in an internally finned square duct

A Three-Dimensional Numerical and Multi-Objective Optimal Design of Wavy Plate-Fins Heat Exchangers

Space–Time Radial Basis Function–Based Meshless Approach for Solving Convection–Diffusion Equations

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