Numerical Computation and Analysis of the Numerical Scheme Order of the Two-Dimensional Temperature Field of Thermoelectric Coolers Cold Substrate

被引：0

作者：

Guzella M.S. ^{[1
]}

Cabezas-Gómez L. ^{[2
]}

Guimarães L.G.M. ^{[3
]}

机构：

[1] Institute of Science and Technology, Federal University of the Jequitinhonha and Mucurí Valleys, Diamantina, Minas Gerais

[2] Heat Transfer Research Group, Department of Mechanical Engineering, Engineering School of São Carlos, University of São Paulo, São Carlos, São Paulo

[3] Department of Mechanical Engineering, Pontifical Catholic University of Minas Gerais, Belo Horizonte, Minas Gerais

来源：

International Journal of Applied and Computational Mathematics | 2017年 / 3卷 / 1期

关键词：

Finite difference method; Numerical simulation; Temperature field; Thermoelectric coolers;

D O I：

10.1007/s40819-015-0091-1

中图分类号：

学科分类号：

摘要：

This paper presents a numerical computation and analysis of the numerical scheme order of the two-dimensional temperature distribution in cold substrate of thermoelectric coolers with the presence of a discrete heat source. The finite difference method is applied to obtain the linear system of equations and the temperature at each node of the domain. The numerical code is implemented in the free software package GNU Octave. In the first part, a mesh independency study is carried on in order to establish a relation between accuracy and computational cost, comparing the simulated results with results from an approximate analytical solution available in the literature. It is observed excellent agreement between numerical and the analytical results. In the second part, an analysis of the overall order of the numerical scheme is carried on by considering numerical solutions for three different meshes and different formulations of the boundary conditions. Results show that the overall order of the numerical scheme is first-order even if full second-order discretization scheme is applied for all grid points, due to the presence of the discrete heat source. Those results are observed for the considered discretization schemes and are confirmed after using a continuous formulation for the heat source term. © 2015, Springer India Pvt. Ltd.

引用

页码：91 / 106

页数：15

共 21 条

[1]

Drabkin I.A., Yershova L.B., Kondratiev D.A., Gromov G.G., The effect of the substrates two-dimensional temperatura distribution on the TEC performance, Proceedings of 8Th European Workshop on Thermoelectrics, (2004)

[2]

Dresselhaus M.S., Chen G., Tang M.Y., Yang R., Lee H., Wang D., Ren Z., Fleurial J., Gogna P., New directions for low-dimensional thermoelectric materials, Adv. Mater., 19, pp. 1043-1053, (2007)

[3]

Dulnev G.N., Semyashkin E.M., (1968)

[4]

Dulnev G.N., Polschikov B.V., Temperature field of a plate with a discrete energy source, Eng. Phys. J., 29, 4, pp. 722-727, (1976)

[5]

Enescu D., Virjoghe E.O., A review on thermoeletric cooling parameters and performance, Renew. Sustain. Energy Rev., 38, pp. 903-916, (2014)

[6]

Ferziger J.H., Peric M., Computational Methods for Fluid Dynamics, (2002)

[7]

Gao X., Chen M., Andreasen S.J., Kaer S.K., Potential usage of thermoelectric in a high-temperature polymer electrolyte membrane (PEM) fuel cell system: two case studies, J. Electron. Mater., 41, 6, pp. 1838-1844, (2012)

[8]

Jovanovic B.S., Suli E., Analysis of Finite Difference Schemes, (2014)

[9]

Lapidus L., Pinder G.F., Numerical Solution of Partial Differential Equations in Science and Engineering, (1982)

[10]

Morton K.W., Mayers D.F., Numerical Solution of Partial Differential Equations, (1994)

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