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Application of Finite Elements in the Prediction of a Two-Dimensional Temperature Profile for Study of Advection-Conduction Phenomena


Affiliations
1 Mechanical Engineering Department, DIMER Research Group, Universidad del Atlantico, Barranquilla,, Colombia
2 Mechanical Engineering Department, KAI Research Group, Universidad del Atlántico, Barranquilla, Colombia
3 Chemical Engineering Department, Sustainable Chemical and Biochemical Processes Research Group, Universidad del Atlántico, Barranquilla, Colombia
 

Background/Objectives: Thermodynamic study of advection phenomena relies on the analytical methods to solve a series of Partial Differential Equations (PDE) that generates from multi-dimensional problems, which becomes more and more complex, especially when a 2D or 3D temperature profile is required. Methods: For the solution of heat transfer problems with simultaneous advection-conduction phenomena, finite differences of 2nd, 4th and 6th order were used to approximate the solution of a two-dimensional PDE. Findings: The results show that a low discretization of the system, originated substantial errors in the application of the high order finite, but, when is correctly used, the numeric approximation shows with great precision the temperature profile for the simultaneous advection and conduction heat transfer. Application: To develop a method to accurately predict the temperature profile for complex heat transfer applications where simultaneous advection and conduction are takeninto account.
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  • Molina-Giraldo N, Blum P, Zhu K, Bayer P, Fang Z. A moving finite line source model to simulate borehole heat exchangers with groundwater advection. International Journal of Thermal Sciences. 2011; 50(12):2506–13. Crossref

  • Li H, Nagano K, Lai Y. Heat transfer of a horizontal spiral heat exchanger under groundwater advection. International Journal of Heat and Mass Transfer. 2012; 55(23-24):6819– 31. Crossref

  • Caissie D, Luce CH. Quantifying streambed advection and conduction heat fluxes. Water Resources Research. 2017; 53(2):1595–624. Crossref

  • Asgari M, Akhlaghi M. Transient thermal stresses in twodimensional functionally graded thick hollow cylinder with finite length. Archive of Applied Mechanics. 2010; 80(4):353–76. Crossref

  • Sawyer AH, Cardenas MB, Buttles J. Hyporheic temperature dynamics and heat exchange near channel-spanning logs. Water Resources Research. 2012; 48(1):1–11. Crossref

  • Kreyszig H. Advanced engineering mathematics. 19th ed. USA: John Wiley and Sons, Inc. 2011. p. 1-1244.

  • Incropera FP, Dewitt DP, Bergman TL, Lavine AS. Fundamentals of heat and mass transfer. 12 ed. Hoboken NJ: John Wiley and Sons, Inc. 2007. p. 1–9997.

  • Cogne C, Labouret S, Peczalski R, Louisnard O, Baillon F, Espitalier F. Theoretical model of ice nucleation induced by acoustic cavitation. Part 1: Pressure and temperature profiles around a single bubble. Ultrasonics Sonochemistry. 2016; 29:447–54. Crossref PMid:26044460

  • Rana P, Bhargava R. Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study. Communications in Nonlinear Science and Numerical Simulation. 2012; 17(1):212–26. Crossref

  • Raymond J, Therrien R, Gosselin L, Lefebvre R. Numerical analysis of thermal response tests with a groundwater flow and heat transfer model. Renewable Energy. 2011; 36(1):315–24. Crossref

  • Soleimani S, Sheikholeslami M, Ganji DD, Gorji-Bandpay M. Natural convection heat transfer in a nanofluid filled semi-annulus enclosure. International Communications in Heat and Mass Transfer. 2012; 39(4):565–74. Crossref

  • Zhao J. Compact finite difference methods for high order integro-differential equations. Applied Mathematics and Computation. 2013; 221:66–78. Crossref

  • Lele SK. Compact finite difference schemes with spectrallike resolution. Journal of Computational Physics. 1992; 103(1):16–42. Crossref

  • Camargo C, Garcia C, Forero JED, Rincon A. Modelo estadístico para la caracterizacion y optimizacion en bombas perifericas. Ingenieria y Desarrollo. 2017; 36(1):18–39. Crossref


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  • Application of Finite Elements in the Prediction of a Two-Dimensional Temperature Profile for Study of Advection-Conduction Phenomena

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Authors

Jorge Duarte Forero
Mechanical Engineering Department, DIMER Research Group, Universidad del Atlantico, Barranquilla,, Colombia
Guillermo E. Valencia
Mechanical Engineering Department, KAI Research Group, Universidad del Atlántico, Barranquilla, Colombia
Luis G. Obregon
Chemical Engineering Department, Sustainable Chemical and Biochemical Processes Research Group, Universidad del Atlántico, Barranquilla, Colombia

Abstract


Background/Objectives: Thermodynamic study of advection phenomena relies on the analytical methods to solve a series of Partial Differential Equations (PDE) that generates from multi-dimensional problems, which becomes more and more complex, especially when a 2D or 3D temperature profile is required. Methods: For the solution of heat transfer problems with simultaneous advection-conduction phenomena, finite differences of 2nd, 4th and 6th order were used to approximate the solution of a two-dimensional PDE. Findings: The results show that a low discretization of the system, originated substantial errors in the application of the high order finite, but, when is correctly used, the numeric approximation shows with great precision the temperature profile for the simultaneous advection and conduction heat transfer. Application: To develop a method to accurately predict the temperature profile for complex heat transfer applications where simultaneous advection and conduction are takeninto account.

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DOI: https://doi.org/10.17485/ijst%2F2018%2Fv11i25%2F128762