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Tytuł artykułu

Homotopy perturbation method combined with Trefftz method in numerical identification of liquid temperature in flow boiling

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Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper is focused on numerical identification of 2D temperature fields in flow boiling of the liquid through a horizontal minichannel with a rectangular cross-section. The heat transfer process in the minichannel is described by a two-dimensional energy equation with the corresponding boundary conditions. Liquid temperature is determined using the homotopy perturbation method (HPM) with Trefftz functions for Laplace’a equation. The numerical solution to the energy equation found with the HPM is compared with the solution obtained for the simplified form of the energy equation. Considering that only the thermal sublayer is taken into account, both solutions give similar results.
Rocznik
Strony
969--980
Opis fizyczny
Bibliogr. 25 poz., rys.
Twórcy
  • Kielce University of Technology, Faculty of Management and Computer Modelling, Kielce, Poland
Bibliografia
  • 1. Al-Khatib M.J., Maciąg A., Pawińska A., 2014, The Trefftz functions in different methods of solving the direct and inverse problems for beam with variable stiffness, 8th International Conference on Inverse Problems in Engineering, 12-15 May, Cracow
  • 2. Biazar J., Ghazvini H., 2009, Convergence of the homotopy perturbation method for partial differential equations, Nonlinear Analysis: Real World Applications, 10, 2633-2640 3. Bohdal T., 2000, Modeling the process of bubble boiling on flows, Archives of Thermodynamics, 21, 34-75
  • 4. Ciałkowski M.J., Frąckowiak A., 2000, Heat Functions and Their Application to Solving Heat Conduction in Mechanical Problems (in Polish), Politechnika Poznańska
  • 5. Grysa K., Maciąg A., 2013, Homotopy perturbation method and Trefftz functions in the source function identification, APCOM&ISCM, 11-14 December, Singapore
  • 6. Grysa K., Maciąg A., Pawińska A., 2012, Solving nonlinear direct and inverse problems of stationary heat transfer by using Trefftz functions, International Journal of Heat and Mass Transfer, 55, 7336-7340
  • 7. He J.-H., 1999, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178, 3/4, 257-262
  • 8. He J.-H., 2000, A coupling method of homotopy technique and perturbation technique for nonlinear problems, International Journal of Non-Linear Mechanics, 35, 37-43
  • 9. He J.-H., 2006, Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B, 20, 10, 1141-1199
  • 10. Herrera I., 2000, Trefftz method: a general theory, Numerical Methods for Partial Differential Equations, 16, 561-580
  • 11. Hetmaniok E., Nowak I., Słota D., Wituła R., 2012, Application of the homotopy perturbation method for the solution of inverse heat conduction problem, International Communications in Heat and Mass Transfer, 39, 30-35
  • 12. Hożejowska S., Kaniowski R., Poniewski M.E., 2014, Application of adjustment calculus to the Trefftz method for calculating temperature field of the boiling liquid flowing in a minichannel, International Journal of Numerical Methods for Heat and Fluid Flow, 24, 811-824
  • 13. Hożejowska S., Piasecka M., 2014, Equalizing calculus in Trefftz method for solving two- -dimensional temperature field of FC-72 flowing along the minichannel, Heat and Mass Transfer, 50, 8, 1053-1063
  • 14. Hożejowska S., Piasecka M., Poniewski M.E., 2009, Boiling heat transfer in vertical minichannels. Liquid crystal experiments and numerical investigations, International Journal Thermal Sciences, 48, 1049-1059
  • 15. Jafari H., Seifi S., 2009, Solving a system of nonlinear fractional partial differential equations using homotopy analysis method, Communications in Nonlinear Science and Numerical Simulation, 14, 5, 1962-1969
  • 16. 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
  • 17. Momani S., Odibat Z., 2007, Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations, Computers and Mathematics with Applications, 54, 7/8, 910-919
  • 18. Piasecka M., 2013, Heat transfer mechanism, pressure drop and flow patterns during FC-72 flow boiling in horizontal and vertical minichannels with enhanced walls, International Journal of Heat and Mass Transfer, 66, 472-488
  • 19. Piasecka M., 2014, Flow Boiling on Enhanced Surfaces of Minichannels (in Polish), Politechnika Świętokrzyska
  • 20. Piasecka M., Poniewski M.E., Hożejowska S., 2004, Experimental evaluation of flow boiling incipience of subcooled fluid in a narrow channel, International Journal Heat and Fluid Flow, 25, 159-172
  • 21. Rajabi A., Ganji D.D., Taherian H., 2007, Application of homotopy perturbation method in nonlinear heat conduction and convection equations, Physics Letters A, 360, 570-573
  • 22. Słota D., 2011, Homotopy perturbation method for solving the two-phase inverse Stefan problem, Numerical Heat Transfer, Part A, 59, 755-768
  • 23. Trefftz E., 1926, Ein Gegenst¨uck zum Ritzschen Verfahren, 2 Int. Kongress f¨ur Technische Mechanik, 131-137
  • 24. Turkyilmazoglu M., 2011, Convergence of the homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 12, 9-14
  • 25. Zieliński A.P., 1995, On trial functions applied in the generalized Trefftz method, Advances in Engineering Software, 24, 147-155
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a096af46-3140-4755-8c13-04c69bd50774
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