每年出版 6 期
ISSN 打印: 1940-2503
ISSN 在线: 1940-2554
Indexed in
THE UNIFIED INTEGRAL TRANSFORMS (UNIT) ALGORITHM WITH TOTAL AND PARTIAL TRANSFORMATION
摘要
The theory and algorithm behind the open-source mixed symbolic-numerical computational code named UNIT (unified integral transforms) are described. The UNIT code provides a computational environment for finding solutions of linear and nonlinear partial differential systems via integral transforms. The algorithm is based on the well-established analytical-numerical methodology known as the generalized integral transform technique (GITT), together with the mixed symbolic-numerical computational environment provided by the Mathematica system (version 7.0 and up). This paper is aimed at presenting a partial transformation scheme option in the solution of transient convective-diffusive problems, which allows the user to choose a space variable not to be integral transformed. This approach is shown to be useful in situations when one chooses to perform the integral transformation on those coordinates with predominant diffusion effects only, whereas the direction with predominant convection effects is handled numerically, together with the time variable, in the resulting transformed system of one-dimensional partial differential equations. Test cases are selected based on the nonlinear three-dimensional Burgers' equation, with the establishment of reference results for specific numerical values of the governing parameters. Then the algorithm is illustrated in the solution of conjugated heat transfer in microchannels.
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Cotta R.M., Naveira-Cotta C.P., Knupp D.C., Zotin J.L.Z., Pontes P.C., Eigenfunction Expansions for Coupled Nonlinear Convection-Diffusion Problems in Complex Physical Domains, Journal of Physics: Conference Series, 745, 2016. Crossref
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Antonini Alves T., Ramos R.A.V., Maia C.R.M., Aplicação da transformada integral generalizada e da transformação conforme na solução de um problema de convecção forçada laminar em dutos de setor de anel circular, Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 32, 4, 2016. Crossref
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Knupp Diego C., Cotta Renato M., Naveira-Cotta Carolina P., Fluid flow and conjugated heat transfer in arbitrarily shaped channels via single domain formulation and integral transforms, International Journal of Heat and Mass Transfer, 82, 2015. Crossref
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Cotta Renato M, Naveira-Cotta Carolina Palma, Knupp Diego C., Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions, International Journal of Numerical Methods for Heat & Fluid Flow, 26, 3/4, 2016. Crossref
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de Souza J. R. B., Lisboa K. M., Allahyarzadeh A. B., de Andrade G. J. A., Loureiro J. B. R., Naveira-Cotta C. P., Freire A. P. Silva, Orlande H. R. B., Silva G. A. L., Cotta R. M., Thermal analysis of anti-icing systems in aeronautical velocity sensors and structures, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38, 5, 2016. Crossref
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Cotta Renato M., Naveira-Cotta Carolina P., Knupp Diego C., Enhanced convergence of eigenfunction expansions in convection-diffusion with multiscale space variable coefficients, Numerical Heat Transfer, Part A: Applications, 70, 5, 2016. Crossref
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Zanon Zotin Jose Luiz, Campos Knupp Diego, Cotta Renato Machado, Conjugated heat transfer in complex channel-substrate configurations: Hybrid solution with total integral transformation and single domain formulation, 2017 16th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm), 2017. Crossref
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Cotta R. M., Naveira-Cotta C. P., Knupp D. C., Zotin J. L. Z., Pontes P. C., Almeida A. P., Recent advances in computational-analytical integral transforms for convection-diffusion problems, Heat and Mass Transfer, 54, 8, 2018. Crossref
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Cotta Renato M., Knupp Diego C., Quaresma João N. N., Analytical Methods in Heat Transfer, in Handbook of Thermal Science and Engineering, 2017. Crossref
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Cotta Renato Machado, Knupp Diego C., Quaresma João N. N., Analytical Methods in Heat Transfer, in Handbook of Thermal Science and Engineering, 2018. Crossref
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Knupp Diego C., Mascouto Fabricio S., Abreu Luiz A.S., Naveira-Cotta Carolina P., Cotta Renato M., Conjugated heat transfer in circular microchannels with slip flow and axial diffusion effects, International Communications in Heat and Mass Transfer, 91, 2018. Crossref
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Pinheiro I. F., Sphaier L. A., de B. Alves L. S., Integral transform solution of integro-differential equations in conduction-radiation problems, Numerical Heat Transfer, Part A: Applications, 73, 2, 2018. Crossref
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Lisboa Kleber Marques, Su Jian, Cotta Renato M., Vector eigenfunction expansion in the integral transform solution of transient natural convection, International Journal of Numerical Methods for Heat & Fluid Flow, 29, 8, 2019. Crossref
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Cotta Renato M., Lisboa Kleber M., Curi Marcos F., Balabani Stavroula, Quaresma João N. N., Perez-Guerrero Jesus S., Macêdo Emanuel N., Amorim Nelson S., A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier–Stokes equations formulation, Numerical Heat Transfer, Part B: Fundamentals, 76, 2, 2019. Crossref
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Cotta Renato M., Naveira-Cotta Carolina P., Knupp Diego C., Convective Eigenvalue Problems for Convergence Enhancement of Eigenfunction Expansions in Convection–Diffusion Problems, Journal of Thermal Science and Engineering Applications, 10, 2, 2018. Crossref
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Costa J. M., Pontes P. C., Naveira-Cotta C. P., Tiwari M. K., Balabani S., Cotta R. M., Hybrid Approach in Microscale Transport Phenomena: Application to Biodiesel Synthesis in Micro-reactors, in Innovations in Sustainable Energy and Cleaner Environment, 2020. Crossref
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Cotta Renato M., Knupp Diego C., Quaresma João N. N., Lisboa Kleber M., Naveira-Cotta Carolina P., Zotin José Luiz Z., Miyagawa Helder K., Integral Transform Benchmarks of Diffusion, Convection–Diffusion, and Conjugated Problems in Complex Domains, in 50 Years of CFD in Engineering Sciences, 2020. Crossref
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Carvalho Igor S., Cotta Renato M., Naveira-Cotta Carolina P., Tiwari Manish K., Hybrid integral transform analysis of supercooled droplets solidification, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477, 2248, 2021. Crossref
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Pelisoli Leonardo O., Cotta Renato M., Naveira-Cotta Carolina P., Couto Paulo, Three-dimensional transient flow in heterogeneous reservoirs: Integral transform solution of a generalized point-source problem, Journal of Petroleum Science and Engineering, 211, 2022. Crossref
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Akel Mohamed, Elshehabey Hillal M., Ahmed Ragaa, Persson Lars E., Generalized Laplace-Type Transform Method for Solving Multilayer Diffusion Problems, Journal of Function Spaces, 2022, 2022. Crossref
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Silva Elizeu Melo da, Quaresma João N. N., Macêdo Emanuel N., Cotta Renato M., Integral transforms for three-dimensional pumping in confined, leaky, and unconfined aquifers, Journal of Hydrology and Hydromechanics, 69, 3, 2021. Crossref
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Pinheiro Isabela F., Sphaier Leandro A., SEMI-ANALYTICAL METHOD FOR INTEGRAL TRANSFORM SOLUTION OF TRANSIENT DIFFUSION WITH VARIABLE COEFFICIENTS , Computational Thermal Sciences: An International Journal, 14, 4, 2022. Crossref
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Cotta Renato M., Lisboa Kleber M., Naveira-Cotta Carolina Palma, Zotin José Luiz Z., ANALYTICAL-COMPUTATIONAL METHODS IN ENERGY EFFICIENCY AND SUSTAINABLE ENERGIES , Proceeding of Proceedings of CONV-22: Int. Symp. on Convective Heat and Mass Transfer June 5 – 10, 2022, Turkey, 2022. Crossref