1,2M. Sandoval-Hernandez, 3N. Carrillo-Ramon, 1S. E. Torreblanca-Bouchan, 1A. de J. Mota-Hernandez, 4G. J. Morales-Alarcon, 3A. R. Escobar-Flores, 5J. Farias-Uscanga , 3J. E Perez-Jacome-Friscione, 3U. A. Filobello-Nino, 3H. Vazquez-Leal, 6S. Y. Campos-Dominguez, 6S. Ocaña-Pimentel
1Centro de Bachillerato Tecnológico industrial y de servicios No. 190, Av. 15 Col. Venustiano Carranza 2da Sección, Boca del Río, 94297, Veracruz, México.
2Escuela de Ingeniería, Universidad de Xalapa, Carretera Xalapa-Veracruz Km 2 No. 341,91190 Xalapa,Veracruz, México
3Facultad de Instrumentación Electrónica, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, Xalapa, 91090, Veracruz, México.
4Instituto de Psicología y Educación, Universidad Veracruzana, Agustín Melgar 2, col. 21 de Marzo, Xalapa, 91010 Veracruz, México.
5Centro de Bachillerato Tecnológico industrial y de servicios No. 268, Av. La Bamba, Geovillas del Puerto, 91777, Veracruz, Veracruz, México.
6Facultad de Arquitectura, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltrán S/N, Xalapa, 91090, Veracruz, México
DOI : https://doi.org/10.47191/ijmra/v7-i05-63Google Scholar Download Pdf
ABSTRACT:
The aim of this paper is to show the application of the method of weighted residuals through subdomains to offer a solution to the steady-state one-dimensional heat conduction problem in a slab with thermal conductivity linearly dependent on temperature. The proposed solution is a fourth-degree polynomial, derived using three subdomains. Despite its simplicity, the solution demonstrates good accuracy, as evidenced by an RMS error of 𝟎.𝟎𝟎𝟎𝟗𝟔𝟖𝟗𝟒𝟔𝟎𝟔𝟕𝟑𝟗𝟑𝟎. However, if greater accuracy is required, the Method of Weighted Residuals allows for the use of more subdomains with a higher-degree polynomial.
KEYWORDS:Nonlinear differential equations, boundary value problems, heat problems.
REFERENCES1) Çengel, Y. A. Boles, Michael A. 2019. Termodinámica. McGrawHill
2) Lewis, G. N., Randall, M., Pitzer, K. S., and Brewer, L., 2020, Thermodynamics. Courier Dover Publications.
3) Sandoval-Hernandez, M. A., Vazquez-Leal, H., Filobello-Nino, U., and Hernandez-Martinez, L., 2019. New handy and accurate approximation for the Gaussian integrals with applications to science and engineering. Open Mathematics, 17(1), 1774-1793. https://doi.org/10.1515/math-2019-0131
4) Vázquez-Leal, H., Filobello-Nino, U., Sarmiento-Reyes, A., Sandoval-Hernández, M., Pérez-Sesma, J. A. A., Pérez-Sesma, A., V. M. Jimenez-Fernandez, Huerta-Chua, J., Castro-Gonzalez, F. J., Sanchez-Orea, j., Hernández Machuca, S. F., Cuellar-Hernández, L., Pretelin Canela, J. E., Gasca-Herrera, A. E., Sampieri-Gonzalez, C. E., Palma-Graye, B. E., Contreras-Hernandez, A. D. , Alvarez-Gasca, O. and González-Martínez, F. J., 2017. Application of HPM to Solve Unsteady Squeezing Flow of a Second-Grade Fluid between Circular Plates. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS), 27(1), 161-178. https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/1421
5) Patel, T., M.N. Mehta and Pradhan V.H., 2012. The numerical solution of Burger’s equation arising into the irradiation of tumour tissue inbiological diffusing system by homotopy analysis method. Asian Journal of Applied Sciences, 5: 60-66. https://doi.org/10.3923/ajaps.2012.60.66
6) Adomian, G., and Rach, R. (1985). On the solution of algebraic equations by the decomposition method. Journal of mathematical analysis and applications, 105(1), 141-166. https://doi.org/10.1016/0022-247X(85)90102-7
7) Filobello-Nino, U., Sandoval-Hernandez, M. A., Alvarez-Gasca, O., Vazquez-Leal, H., Contreras-Hernandez, A. D., Hoyos-Reyes, C., Carrillo-Ramon, N., Bagatella-Flores, N., Sanchez-Orea, J., Cuellar-Hernandez, L., Mendez-Perez, J. M., Jimenez-Fernandez, V. M., Mota-Hernandez, A. J., Morales-Alarcon, G. J., S.F. Hernandez-Machuca, Martinez-Barrios, F. and Garcia-Lozano, M., 2022, Analytical Exact and Approximate Solutions for Certain Diffusion Reactions, INTERNATIONAL JOURNAL OF ENGINEERING RESEARCH & TECHNOLOGY (IJERT) Volume 11, Issue 11 (November 2022). https://www.ijert.org/analytical-exact-and-approximate-solutions-for-certain-diffusion-reactions
8) Sandoval-Hernandez, M. A., Filobello-Nino, U. A., Vazquez-Leal, H., Huerta-Chua, J., Castaneda-Sheissa, R., Diaz-Arango, G. U., Callejas-Molina R.A, Torreblanca-Bouchan, S.E, Chong-Duran, J., and Pablo-Lopez, B., 2021a, Taylor Series Method Coupled with Shooting Technique for Solving Boundary Value Problems, INTERNATIONAL JOURNAL OF ENGINEERING RESEARCH & TECHNOLOGY (IJERT) Volume 10, Issue 10 (October 2021). https://www.ijert.org/taylor-series-method-coupled-with-shooting-technique-for-solving-boundary-value-problems
9) Filobello-Nino, U., Alvarez-Gasca, O., Contreras-Hernandez, A. D., Palma-Grayeb, B. E., Cuellar-Hernandez, L., Hoyos-Reyes, C., J. M. Mendez-Perez, Jimenez-Fernandez, V. M., Sandoval-Hernandez, M. A., Callejas-Molina, R. A. Hernandez-Machuca, S. F., Pretelin-Canela, J. E., Cervantes-Perez, J., Vazquez-Aguirre, J. L., Varela-Lara, L. J., Bagatella-Flores, N., Vazquez-Leal, H., 2021, A Handy Analytical Approximate Solution for A Heat Transfer Problem by using A Version of Taylor Method with Boundary Conditions, INTERNATIONAL JOURNAL OF ENGINEERING RESEARCH & TECHNOLOGY (IJERT) Volume 10, Issue 02 (February 2021). https://www.ijert.org/a-handy-analytical-approximate-solution-for-a-heat-transfer-problem-by-using-a-version-of-taylor-method-with-boundary-conditions
10) Vazquez-Leal, H., Sandoval-Hernandez, M., Castaneda-Sheissa, R., Filobello-Nino, U., and Sarmiento-Reyes, A. 2015, Modified Taylor solution of equation of oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics. International Journal of Applied Mathematical Research, 4(2), 253-258. https://doi.org/10.14419/ijamr.v4i2.4273
11) Sandoval-Hernandez, M., Vazquez-Leal, H., Filobello-Nino, U., De-Leo-Baquero, E., Bielma-Perez, A. C., Vichi-Mendoza, J. C., Alvarez-Gasca, O., Contreras-Hernandez, A. D., Bagatella-Flores, N., Palma-Grayeb, B. E., Sanchez-Orea, J. Cuellar-Hernandez, L., 2021b. The Quadratic Equation and its Numerical Roots. International Journal of Engineering Research y Technology, 10(6), 301-305. https://www.ijert.org/the-quadratic-equation-and-its-numerical-roots
12) Villadsen, J., and Michelsen, M. L. 1978. Solution of differential equation models by polynomial approximation, Prentice-Hall
13) Finlayson, B. A. 1980. Nonlinear analysis in chemical engineering, McGraw-Hill
14) Vemuri, V. R., and Karplus, W. J., 1981. Digital computer treatment of partial differential equations. Prentice Hall Professional Technical Reference.
15) Faires, J. D., and Burden, R. L. 2012. Numerical methods, 4th. Cengage Learning.
16) Chapra, S. C., Canale, R. P., Ruiz, R. S. G., Mercado, V. H. I., Díaz, E. M., and Benites, G. E. 2011. Métodos numéricos para ingenieros New York, NY, USA: McGraw-Hill.
Volume 07 Issue 05 May 2024
There is an Open Access article, distributed under the term of the Creative Commons Attribution – Non Commercial 4.0 International (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/), which permits remixing, adapting and building upon the work for non-commercial use, provided the original work is properly cited.
Our Services and Policies
Authors should prepare their manuscripts according to the instructions given in the authors' guidelines. Manuscripts which do not conform to the format and style of the Journal may be returned to the authors for revision or rejected.
The Journal reserves the right to make any further formal changes and language corrections necessary in a manuscript accepted for publication so that it conforms to the formatting requirements of the Journal.
International Journal of Multidisciplinary Research and Analysis will publish 12 monthly online issues per year,IJMRA publishes articles as soon as the final copy-edited version is approved. IJMRA publishes articles and review papers of all subjects area.
Open access is a mechanism by which research outputs are distributed online, Hybrid open access journals, contain a mixture of open access articles and closed access articles.
International Journal of Multidisciplinary Research and Analysis initiate a call for research paper for Volume 07 Issue 11 (November 2024).
PUBLICATION DATES:
1) Last Date of Submission : 26 November 2024 .
2) Article published within a week.
3) Submit Article : editor@ijmra.in or Online
Why with us
1 : IJMRA only accepts original and high quality research and technical papers.
2 : Paper will publish immediately in current issue after registration.
3 : Authors can download their full papers at any time with digital certificate.
The Editors reserve the right to reject papers without sending them out for review.
Authors should prepare their manuscripts according to the instructions given in the authors' guidelines. Manuscripts which do not conform to the format and style of the Journal may be returned to the authors for revision or rejected. The Journal reserves the right to make any further formal changes and language corrections necessary in a manuscript accepted for publication so that it conforms to the formatting requirements of the Journal.