Integral transform solution of eigenvalue problems within irregular geometries: Comparative analysis of different methodologies

References

• R. M. Cotta, Integral Transforms in Computational Heat and Fluid Flow. Boca Raton, FL, USA: CRC Press, 1993, pp. 41–55.
   Google Scholar
• D. C. Knupp, R. M. Cotta, and C. P. Naveira-Cotta, “Heat transfer in microchannels with upstream–downstream regions coupling and wall conjugation effects,” Numer. Heat Transfer Part B, vol. 64, no. 5, pp. 365–387, 2013. DOI: 10.1080/10407790.2013.810535.
   Web of Science ®Google Scholar
• D. C. Knupp, R. M. Cotta, C. P. Naveira-Cotta, and S. Kakaç, “Transient conjugated heat transfer in microchannels: integral transforms with single domain formulation,” Int. J. Therm. Sci., vol. 88, pp. 248–257, 2015. DOI: 10.1016/j.ijthermalsci.2014.04.017.
   Web of Science ®Google Scholar
• R. Zhang, Z. Chen, G. Xie, and B. Sunden, “Numerical analysis of constructal water-cooled microchannel heat sinks with multiple bifurcations in the entrance region,” Numer. Heat Transfer Part A, vol. 67, no. 6, pp. 632–650, 2015. DOI: 10.1080/10407782.2014.937286.
   Web of Science ®Google Scholar
• G. Xie, Y. Li, F. Zhang, and B. Sundén, “Analysis of micro-channel heat sinks with rectangular-shaped flow obstructions,” Numer. Heat Transfer Part A, vol. 69, no. 4, pp. 335–351, 2016. DOI: 10.1080/10407782.2015.1080580.
   Web of Science ®Google Scholar
• M. B. Turgay, and A. G. Yazıcıoğlu, “Numerical simulation of fluid flow and heat transfer in a trapezoidal microchannel with COMSOL multiphysics: a case study,” Numerical Heat Transfer, Part A, vol. 73, no. 5, pp. 332–346, 2018. DOI: 10.1080/10407782.2017.1420302.
   Web of Science ®Google Scholar
• L. A. Sphaier, R. M. Cotta, C. P. Naveira-Cotta, and J. N. N. Quaresma, “The UNIT algorithm for solving one-dimensional convection-diffusion problems via integral transforms,” Int. Commun. Heat Mass Transfer, vol. 38, no. 5, pp. 565–571, 2011. DOI: 10.1016/j.icheatmasstransfer.2010.12.036.
   Web of Science ®Google Scholar
• R. M. Cotta, D. C. Knupp, C. P. Naveira-Cotta, L. A. Sphaier, and J. N. N. Quaresma, “Unified integral transforms algorithm for solving multidimensional nonlinear convection-diffusion problems,” Numer. Heat Transfer Part A, vol. 63, no. 11, pp. 840–866, 2013. DOI: 10.1080/10407782.2013.756763.
   Web of Science ®Google Scholar
• J. Lima, and M. Rêgo, “On the integral transform solution of low-magnetic MHD flow and heat transfer in the entrance region of a channel,” Int. J. Non Linear Mech., vol. 50, pp. 25–39, 2013. DOI: 10.1016/j.ijnonlinmec.2012.10.014.
   Web of Science ®Google Scholar
• I. F. Pinheiro, L. A. Sphaier, and L. S. d. B. Alves, “Integral transform solution of integro-differential equations in conduction-radiation problems,” Numer. Heat Transfer A, vol. in press, vol. 73, no. 2, pp. 94–114, 2018.
   Web of Science ®Google Scholar
• D. C. Knupp, W. F. Sacco, and A. J. S. Neto, “Direct and inverse analysis of diffusive logistic population evolution with time delay and impulsive culling via integral transforms and hybrid optimization,” Appl. Math. Comput., vol. 250, pp. 105–120, 2015. DOI: 10.1016/j.amc.2014.10.060.
   Web of Science ®Google Scholar
• E. V. M. dos Reis, L. A. Sphaier, L. C. d. S. Nunes, and L. S. d. B. Alves, “Pipeline dynamic response via linear and nonlinear stability analyses,” Ocean Eng., vol. 163, pp. 533–543, 2018. Submitted for publication. DOI: 10.1016/j.oceaneng.2018.06.002.
   Web of Science ®Google Scholar
• D. J. N. M. Chalhub, L. A. Sphaier, and L. S. d. B. Alves, “Integral transform solution of convective heat transfer problems using upwind approximations,” Numer. Heat Transfer Part B, vol. 63, no. 2, pp. 167–187, 2013. DOI: 10.1080/10407790.2013.740398.
   Web of Science ®Google Scholar
• L. A. Sphaier, and A. Barletta, “Unstable mixed convection in a heated horizontal porous channel,” Int. J. Therm. Sci., vol. 78, pp. 77–89, 2014. DOI: 10.1016/j.ijthermalsci.2013.12.002.
   Web of Science ®Google Scholar
• L. A. Sphaier, A. Barletta, and M. Celli, “Unstable mixed convection in a heated inclined porous channel,” J. Fluid Mech., vol. 778, pp. 428–450, 2015. DOI: 10.1017/jfm.2015.394.
   Web of Science ®Google Scholar
• R. H. Deucher, P. Couto, and G. C. R. Bodstein, “Transient solution for the energy balance in porous media considering viscous dissipation and expansion/compression effects using integral transforms,” Transp. Porous Media, vol. 116, no. 2, pp. 753–775, 2017. DOI: 10.1007/s11242-016-0799-3.
   Web of Science ®Google Scholar
• I. F. Pinheiro, H. L. Serrano, L. A. Sphaier, F. C. Peixoto, and V. N. H. Silva, “Integral transform analysis of heat and mass diffusion in chemically reacting systems with Michaelis–Menten kinetics,” Int. Commun. Heat Mass Transfer, vol. 100, pp. 20–26, 2019. DOI: 10.1016/j.icheatmasstransfer.2018.10.003.
   Web of Science ®Google Scholar
• J. B. Aparecido, R. M. Cotta, and M. N. Özişik, “Analytical solutions to two-dimensional diffusion type problems in irregular geometries,” J. Franklin Inst., vol. 326, no. 3, pp. 421–434, 1989. DOI: 10.1016/0016-0032(89)90021-5.
   Web of Science ®Google Scholar
• F. A. A. Barbuto, and R. M. Cotta, “Integral transformation of elliptic problems within irregular domains: fully developed channel flow,” Int. J. Numer. Methods Heat Fluid Flow, vol. 7, no. 8, pp. 778–793, 1997. DOI: 10.1108/09615539710193065.
   Web of Science ®Google Scholar
• J. S. Pérez Guerrero, J. N. N. Quaresma, and R. M. Cotta, “Simulation of laminar flow inside ducts of irregular geometry using integral transforms,” Comput. Mech., vol. 25, no. 4, pp. 413–420, 2000. DOI: 10.1007/s004660050488.
   Web of Science ®Google Scholar
• D. C. Knupp, C. P. Naveira-Cotta, A. Renfer, M. K. Tiwari, R. M. Cotta, and D. Poulikakos, “Analysis of conjugated heat transfer in micro-heat exchangers via integral transforms and non-intrusive optical techniques,” Int. J. Numer. Methods Heat Fluid Flow, vol. 25, no. 6, pp. 1444–1462, 2015. DOI: 10.1108/HFF-08-2014-0259.
   Web of Science ®Google Scholar
• D. C. Knupp, R. M. Cotta, and C. P. Naveira-Cotta, “Fluid flow and conjugated heat transfer in arbitrarily shaped channels via single domain formulation and integral transforms,” Int. J. Heat Mass Transfer, vol. 82, pp. 479–489, 2015. DOI: 10.1016/j.ijheatmasstransfer.2014.11.007.
   Web of Science ®Google Scholar
• M. D. Mikhailov, and R. M. Cotta, “Integral transform solution of eigenvalue problems,” Commun. Numer. Methods Eng., vol. 10, no. 10, pp. 827–835, 1994. DOI: 10.1002/cnm.1640101009.
   Google Scholar
• R. M. Cotta, C. P. Naveira-Cotta, and D. C. Knupp, “Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions,” Int. J. Numer. Methods Heat Fluid Flow, vol. 26, no. 3/4, pp. 767–789, 2016. DOI: 10.1108/HFF-08-2015-0309.
   Web of Science ®Google Scholar
• R. M. Cotta, C. P. Naveira-Cotta, and D. C. Knupp, “Convective eigenvalue problems for convergence enhancement of eigenfunction expansions in convection–diffusion problems,” J. Therm. Sci. Eng. Appl., vol. 10, no. 2, pp. 021009, 2018. DOI: 10.1115/1.4037576.
   Web of Science ®Google Scholar
• R. M. Cotta, C. P. Naveira-Cotta, D. C. Knupp, J. L. Z. Zotin, P. C. Pontes, and A. P. Almeida, “Recent advances in computational-analytical integral transforms for convection-diffusion problems,” Heat Mass Transfer, vol. 54, no. 8, pp. 2475–2496, 2017. DOI: 10.1007/s00231-017-2186-1.
   Web of Science ®Google Scholar
• L. A. Sphaier, and R. M. Cotta, “Integral transform analysis of multidimensional eigenvalue problems within irregular domains,” Numer. Heat Transfer Part B, vol. 38, no. 2, pp. 157–175, 2000.
   Web of Science ®Google Scholar
• L. A. Sphaier, and R. M. Cotta, “Analytical and hybrid solutions of diffusion problems within arbitrarily shaped regions via integral transforms,” Comput. Mech., vol. 29, no. 3, pp. 265–276, 2002. DOI: 10.1007/s00466-002-0339-6.
   Web of Science ®Google Scholar
• L. A. Sphaier, “Integral transformation of diffusion problems within irregular domains: mixed symbolic-numerical computation,” Master’s thesis, Universidade Federal do Rio de Janeiro – COPPE, Rio de Janeiro, RJ, Brazil, 2000.
   Google Scholar
• R. M. Cotta, C. P. Naveira-Cotta, D. C. Knupp, J. L. Z. Zotin, and P. C. Pontes, “Eigenfunction expansions for coupled nonlinear convection-diffusion problems in complex physical domains,” J. Phys. Conf. Ser., vol. 745, pp. 022001, 2016. DOI: 10.1088/1742-6596/745/2/022001.
   Google Scholar
• M. D. Mikhailov, and R. M. Cotta, “Ordering rules for double and triple eigenseries in the solution of multidimensional heat and fluid flow problems,” Int. Commun. Heat Mass Transfer, vol. 23, no. 2, pp. 299–303, 1996. DOI: 10.1016/0735-1933(96)00015-2.
   Web of Science ®Google Scholar
• E. J. Corrêa, R. M. Cotta, and H. R. B. Orlande, “On the reduction of computational costs in eigenfunction expansions of multidimensional diffusion problems,” Int. J. Numer. Methods Heat Fluid Flow, vol. 7, pp. 675–695, 1997. DOI: 10.1108/09615539710185569.
   Web of Science ®Google Scholar
• S. Wolfram, The Mathematica Book, 5th ed. New York, NY, USA/Champaign, IL, USA: Wolfram Media/Cambridge University Press, 2003.
   Google Scholar