Thermal Conductivity Equations via the Improved Adomian Decomposition Methods

Ashenafi Gizaw Jije

doi:doi:10.11648/j.acm.20200903.11

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Thermal Conductivity Equations via the Improved Adomian Decomposition Methods

Ashenafi Gizaw Jije

Received: 1 April 2020 Accepted: 11 May 2020 Published: 27 May 2020

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Abstract

Several mathematical models that explain natural phenomena are mostly formulated in terms of nonlinear differential equations. Many problems in applied sciences such as nuclear physics, engineering, thermal management, gas dynamics, chemical reaction, studies of atomic structures and atomic calculations lead to singular boundary value problems and often only positive solutions are vital. However, most of the methods developed in mathematics are used in solving linear differential equations. For this reason, this research considered a model problem representing temperature distribution in heat dissipating fins with triangular profiles using MATLAB codes. MADM was used with a computer code in MATLAB to seek solution for the problem involving constant and a power law dependence of thermal conductivity on temperature governed by linear and nonlinear BVPs, respectively, for which considerable results were obtained. A problem formulated dealing with a triangular silicon fin and more examples were solved and analyzed using tables and figures for better elaborations where appreciable agreement between the approximate and exact solutions was observed. All the computations were performed using MATHEMATICA and MATLAB.

DOI	10.11648/j.acm.20200903.11
Published in	Applied and Computational Mathematics (Volume 9, Issue 3, June 2020)
Page(s)	30-55
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fins, Adomian Decomposition, Thermal Conductivity Equation, Nonnlinear

References

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[5]	Duan, J.-S, Rach, R., Baleanu, D. and Wazwaz, A.-M. 2012. A review of the Adomian decomposition method and its applications to fractional differential equations. Commun. Frac. Calc., 3 (2): 73-99.
[6]	Ebaid, A. 2010. Modification of Lesnic’s Approach and New Analytic Solutions for Some Nonlinear Second-Order Boundary Value Problems with Dirichlet Boundary Conditions. Zeitschrift f¨ ur Naturforschung, Tubingen, 65a: 692-296.
[7]	Hasan, Y. Q. and Zhu, L. M. 2008. Modified Adomian decomposition method for singular initial value problems in the second order ordinary differential equations. 3 (1): 183–193.
[8]	Hasan, Y. Q. and Zhu, L. M. 2009. A note on the use of modified Adomian decomposition method for solving singular boundary value problems of higher-order ordinary differential equations. Communications in Nonlinear Science and Numerical Simulation, 14 (8): 3261-3265.
[9]	Inc, M. and Evans, D. J. 2003. The decomposition method for solving a class of singular two- point boundary value problems. International Journal of Computational Mathematics. 80 (7): 869–882.
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Ashenafi Gizaw Jije. (2020). Thermal Conductivity Equations via the Improved Adomian Decomposition Methods. Applied and Computational Mathematics, 9(3), 30-55. https://doi.org/10.11648/j.acm.20200903.11

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Ashenafi Gizaw Jije. Thermal Conductivity Equations via the Improved Adomian Decomposition Methods. Appl. Comput. Math. 2020, 9(3), 30-55. doi: 10.11648/j.acm.20200903.11

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Ashenafi Gizaw Jije. Thermal Conductivity Equations via the Improved Adomian Decomposition Methods. Appl Comput Math. 2020;9(3):30-55. doi: 10.11648/j.acm.20200903.11

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@article{10.11648/j.acm.20200903.11,
  author = {Ashenafi Gizaw Jije},
  title = {Thermal Conductivity Equations via the Improved Adomian Decomposition Methods},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {3},
  pages = {30-55},
  doi = {10.11648/j.acm.20200903.11},
  url = {https://doi.org/10.11648/j.acm.20200903.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200903.11},
  abstract = {Several mathematical models that explain natural phenomena are mostly formulated in terms of nonlinear differential equations. Many problems in applied sciences such as nuclear physics, engineering, thermal management, gas dynamics, chemical reaction, studies of atomic structures and atomic calculations lead to singular boundary value problems and often only positive solutions are vital. However, most of the methods developed in mathematics are used in solving linear differential equations. For this reason, this research considered a model problem representing temperature distribution in heat dissipating fins with triangular profiles using MATLAB codes. MADM was used with a computer code in MATLAB to seek solution for the problem involving constant and a power law dependence of thermal conductivity on temperature governed by linear and nonlinear BVPs, respectively, for which considerable results were obtained. A problem formulated dealing with a triangular silicon fin and more examples were solved and analyzed using tables and figures for better elaborations where appreciable agreement between the approximate and exact solutions was observed. All the computations were performed using MATHEMATICA and MATLAB.},
 year = {2020}
}

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TY  - JOUR
T1  - Thermal Conductivity Equations via the Improved Adomian Decomposition Methods
AU  - Ashenafi Gizaw Jije
Y1  - 2020/05/27
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200903.11
DO  - 10.11648/j.acm.20200903.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 30
EP  - 55
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20200903.11
AB  - Several mathematical models that explain natural phenomena are mostly formulated in terms of nonlinear differential equations. Many problems in applied sciences such as nuclear physics, engineering, thermal management, gas dynamics, chemical reaction, studies of atomic structures and atomic calculations lead to singular boundary value problems and often only positive solutions are vital. However, most of the methods developed in mathematics are used in solving linear differential equations. For this reason, this research considered a model problem representing temperature distribution in heat dissipating fins with triangular profiles using MATLAB codes. MADM was used with a computer code in MATLAB to seek solution for the problem involving constant and a power law dependence of thermal conductivity on temperature governed by linear and nonlinear BVPs, respectively, for which considerable results were obtained. A problem formulated dealing with a triangular silicon fin and more examples were solved and analyzed using tables and figures for better elaborations where appreciable agreement between the approximate and exact solutions was observed. All the computations were performed using MATHEMATICA and MATLAB.
VL  - 9
IS  - 3
ER  -

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Author Information

Ashenafi Gizaw Jije

Department of Mathematics, Faculty of Natural and Computational Sciences, Gambella University, Gambella, Ethiopia

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Ashenafi Gizaw Jije. (2020). Thermal Conductivity Equations via the Improved Adomian Decomposition Methods. Applied and Computational Mathematics, 9(3), 30-55. https://doi.org/10.11648/j.acm.20200903.11

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ACS Style

Ashenafi Gizaw Jije. Thermal Conductivity Equations via the Improved Adomian Decomposition Methods. Appl. Comput. Math. 2020, 9(3), 30-55. doi: 10.11648/j.acm.20200903.11

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AMA Style

Ashenafi Gizaw Jije. Thermal Conductivity Equations via the Improved Adomian Decomposition Methods. Appl Comput Math. 2020;9(3):30-55. doi: 10.11648/j.acm.20200903.11

Copy | Download

@article{10.11648/j.acm.20200903.11,
  author = {Ashenafi Gizaw Jije},
  title = {Thermal Conductivity Equations via the Improved Adomian Decomposition Methods},
  journal = {Applied and Computational Mathematics},
  volume = {9},
  number = {3},
  pages = {30-55},
  doi = {10.11648/j.acm.20200903.11},
  url = {https://doi.org/10.11648/j.acm.20200903.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20200903.11},
  abstract = {Several mathematical models that explain natural phenomena are mostly formulated in terms of nonlinear differential equations. Many problems in applied sciences such as nuclear physics, engineering, thermal management, gas dynamics, chemical reaction, studies of atomic structures and atomic calculations lead to singular boundary value problems and often only positive solutions are vital. However, most of the methods developed in mathematics are used in solving linear differential equations. For this reason, this research considered a model problem representing temperature distribution in heat dissipating fins with triangular profiles using MATLAB codes. MADM was used with a computer code in MATLAB to seek solution for the problem involving constant and a power law dependence of thermal conductivity on temperature governed by linear and nonlinear BVPs, respectively, for which considerable results were obtained. A problem formulated dealing with a triangular silicon fin and more examples were solved and analyzed using tables and figures for better elaborations where appreciable agreement between the approximate and exact solutions was observed. All the computations were performed using MATHEMATICA and MATLAB.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Thermal Conductivity Equations via the Improved Adomian Decomposition Methods
AU  - Ashenafi Gizaw Jije
Y1  - 2020/05/27
PY  - 2020
N1  - https://doi.org/10.11648/j.acm.20200903.11
DO  - 10.11648/j.acm.20200903.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 30
EP  - 55
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20200903.11
AB  - Several mathematical models that explain natural phenomena are mostly formulated in terms of nonlinear differential equations. Many problems in applied sciences such as nuclear physics, engineering, thermal management, gas dynamics, chemical reaction, studies of atomic structures and atomic calculations lead to singular boundary value problems and often only positive solutions are vital. However, most of the methods developed in mathematics are used in solving linear differential equations. For this reason, this research considered a model problem representing temperature distribution in heat dissipating fins with triangular profiles using MATLAB codes. MADM was used with a computer code in MATLAB to seek solution for the problem involving constant and a power law dependence of thermal conductivity on temperature governed by linear and nonlinear BVPs, respectively, for which considerable results were obtained. A problem formulated dealing with a triangular silicon fin and more examples were solved and analyzed using tables and figures for better elaborations where appreciable agreement between the approximate and exact solutions was observed. All the computations were performed using MATHEMATICA and MATLAB.
VL  - 9
IS  - 3
ER  -

Copy | Download