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Tytuł artykułu

The application of Beck’s method combined with FEM and Trefftz functions to determine the heat transfer coefficient in a minichannel

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this study is to determine the heat transfer coefficient between the heated surface and the boiling fluid flowing in a minichannel on the basis of experimental data. The calculation model is based on Beck’s method coupled with the FEM and Trefftz functions. The Trefftz functions used in the Hermite interpolation are employed to construct the shape functions in the FEM. The unknown local values of the heat transfer coefficient at the foil- -fluid contact surface are calculated from Newton’s law. The temperature of the heated foil and the heat flux on the foil surface are determined by solving a two-dimensional inverse heat conduction problem. The study is focused on the identification of the heat transfer coefficients in the subcooled boiling region and the saturated nucleate boiling region. The results are compared with the data obtained through the one-dimensional method. The investigations also reveal how the smoothing of measurement data affects calculation results.
Rocznik
Strony
103--116
Opis fizyczny
Bibliogr. 37 poz., rys., tab.
Twórcy
  • Kielce University of Technology, Department of Management and Computer Modelling, Kielce, Poland
Bibliografia
  • 1. Beck J.V., Blackwell B., Clair C.R.St., 1985, Inverse Heat Conduction. Ill-Posed Problems, Wiley-Interscience Publ., New York
  • 2. Beck J.V., 1970, Nonlinear estimation applied to the nonlinear inverse heat conduction problem, International Journal of Heat and Mass Transfer, 13, 703-716
  • 3. Ciałkowski M.J., 2002, New type of basic functions of FEM in application to solution of inverse heat conduction problem, Journal of Thermal Science, 11, 163-171
  • 4. Ciałkowski M.J., Grysa K., 2010, Trefftz method in solving the inverse problems, Journal Inverse Ill-Posed Problems, 18, 595-616
  • 5. Ciałkowski M.J., Frąckowiak A., 2002, Solution of the stationary 2D inverse heat conduction problem by Treffetz method, Journal of Thermal Science, 11, 148-162
  • 6. Duda P., Taler J., 2009, A new method for identification of thermal boundary conditions in water-wall tubes of boiler furnaces, International Journal of Heat and Mass Transfer, 52, 1517-1524
  • 7. Grysa K., Hożejowska S., Maciejewska B., 2012, Compensatory calculus and Trefftz functions applied to local heat transfer coefficient determination in a minichannel, Journal of Theoretical and Applied Mechanics, 50, 087-1096
  • 8. Grysa K., Maciejewska B., 2013, Trefftz functions for the non-stationary problems, Journal of Theoretical and Applied Mechanics, 51, 251-264
  • 9. Herrera I., 2000, Trefftz method: a general theory, Numerical Methods for Partial Differential Equations, 16, 561-580
  • 10. Hożejowska S., Maciejewska B., Poniewski M.E., 2015, Numerical analysis of boiling twophase flow in mini- and microchannels, [In:] Encyclopedia of Two-Phase Heat Transfer and Flow. I. Fundamentals and Method, Thome J.R. (Edit.), World Scientific Publishing Co Ltd., New Jersey
  • 11. Hożejowska S., Piasecka M., 2014, Equalizing calculus in Trefftz method for solving twodimensional temperature field of FC-72 flowing along the minichannel, Heat and Mass Transfer, 50, 1053-1063
  • 12. Hożejowska S., Piasecka M., Poniewski M.E., 2009, Boiling heat transfer in vertical minichannels. Liquid crystal experiments and numerical investigations, International Journal of Thermal Sciences, 48, 1049-1059
  • 13. Kincaid D., Cheney W., 2002, Numerical Analysis: Mathematics of Scientific Computing, 3rd ed., Brooks/Cole Publishing Company, Belmont, California
  • 14. Kompis V., Konkol F., Vasko M., 2001, Trefftz-polynomial reciprocity based FE formulations, Computer Assisted Mechanics and Engineering Sciences, 8, 385-395
  • 15. Kruk B., Sokała M., 1999, Sensitivity coefficients and heat polynomials in the inverse heat conduction problems, Journal of Applied Mathematics and Mechanics, ZAMM, 3, 693-694
  • 16. Kruk B., Sokała M., 2000, Sensitivity coefficients applied to two-dimensional transient inverse heat conduction problems, Journal of Applied Mathematics and Mechanics, ZAMM, 81, 945-946
  • 17. Kurpisz K., Nowak A.J., 1992, BEM approach to inverse heat conduction problem, Engineering Analysis with Boundary Elements, 10, 291-297
  • 18. Le Niliot C., Lefevre F., 2004, A parameter estimation approach to solve the inverse problem of point heat sources identification, International Journal of Heat and Mass Transfer, 47, 827-841
  • 19. Li Z.-C., Lu T.-T., Huang H.-T., Cheng A.H.-D., 2006, Trefftz, collocation, and other boundary methods – a comparison, Numerical Methods for Partial Differential Equations, 23, 1-52
  • 20. Lin D.T.W., Yan W.-M., Li H.-Y., 2008, Inverse problem of unsteady conjugated forced convection in parallel plate channels, International Journal of Heat and Mass Transfer, 51, 993-1002
  • 21. Maciejewska B., 2004, Application of the modified method of finite elements for identification of temperature of a body heated with a moving heat source, Journal of Theoretical and Applied Mechanics, 42, 771-787
  • 22. Maciąg A., 2011, The usage of wave polynomials in solving direct and inverse problems for two-dimensional wave equation, International Journal for Numerical Methods in Biomedical Engineering, 27, 1107-1125
  • 23. Ozer B.A., Oncel A.F., Hollingsworth D.H., Witte L.C., 2011, A method of concurrent thermographic-photographic visualization of flow boiling in a minichannel, Experimental Thermal and Fluid Science, 35, 1522-1529
  • 24. Piasecka M., 2013, Determination of the temperature field using liquid crystal thermography and analysis of two-phase flow structures in research on boiling heat transfer in a minichannel, Metrology and Measurement Systems, XX, 205-216
  • 25. Piasecka M., 2014a, Flow boiling heat transfer in a minichannel with enhanced heating surface, Heat Transfer Engineering, 35, 903-912
  • 26. Piasecka M., 2014b, Laser texturing, spark erosion and sanding of the surfaces and their practical applications in heat exchange devices, Advanced Material Research, 874, 95-100
  • 27. Piasecka M., 2014c, The use of enhanced surface in flow boiling heat transfer in a rectangular minichannels, Experimental Heat Transfer, 27, 231-255
  • 28. Piasecka M., 2015, Impact of selected parameters on boiling heat transfer and pressure drop in minichannels, International Journal of Refrigeration, 56, 198-212
  • 29. Piasecka M., Maciejewska B., 2012, The study of boiling heat transfer in vertically and horizontally oriented rectangular minichannels and the solution to the inverse heat transfer problem with the use of the Beck method and Trefftz functions, Experimental Thermal and Fluid Science, 38, 19-32
  • 30. Piasecka M., Maciejewska B., 2013, Enhanced heating surface application in a minichannel flow and the use of the FEM and Trefftz functions for the solution of inverse heat transfer problem, Experimental Thermal and Fluid Science, 44, 23-33
  • 31. Piasecka M., Maciejewska B., 2015, Heat transfer coefficient during flow boiling in a minichannel at variable spatial orientation, Experimental Thermal and Fluid Science, 68, 459-467
  • 32. Piasecka M., Strąk K., Maciejewska B., 2016, Calculations of flow boiling heat transfer in a minichannel using data from LCT and IRT, Heat Transfer Engineering, 38, 3, 332-346, http://dx.doi.org/10.1080/01457632.2016.1189272
  • 33. Shi J., Wang J., 2009, Inverse problem of transpiration cooling for estimating wall heat flux by LTNE model and CGM method, International Journal of Heat and Mass Transfer, 52, 2714-2720
  • 34. Tikhonov A.N., Arsenin V.Y., 1977, Solution of Ill-Posed Problems, Wiley, New York
  • 35. Trefftz E., 1926, Ein Gegenst¨uck zum Ritzschen Verfahren, 2 Int. Kongress f¨ur Technische Mechanik, Z¨urich, 1926, 131-137
  • 36. Tseng A.A., Chen T.C., Zhao F.Z., 1995, Direct sensitivity coefficient method for solving two-dimensional inverse heat conduction problems by finite-element scheme, Numerical Heat Transfer, Part B: Fundamentals, 27, 291-307
  • 37. Tseng A.A., Chen T.C., Zhao F.Z., 1996, Multidimensional inverse transient heat conduction problems by direct sensitivity coefficent method using a finite-element scheme, Numerical Heat Transfer, Part B: Fundamentals, 29, 365-38
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3f6f50bf-15f5-4a5c-b3e9-4c2845656f94
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