Heat Distribution Within a Raw Cotton Seed

Mamatov Alisher Zununovich; Pardaev Xanimkul Normamatovich; Bomurotov Sherbek Najmidinovich

doi:doi:10.11648/j.ajma.20261303.11

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Heat Distribution Within a Raw Cotton Seed

Mamatov Alisher Zununovich^*

, Pardaev Xanimkul Normamatovich

, Bomurotov Sherbek Najmidinovich

Published in American Journal of Mechanics and Applications (Volume 13, Issue 3)

Received: 25 August 2026 Accepted: 4 September 2026 Published: 20 September 2026

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Abstract

The drying and active ventilation of raw cotton are important technological processes that directly affect the quality, storage stability, and further processing of cotton. During drying, heat and moisture transfer within individual cotton seeds plays a significant role in determining the efficiency of the overall process. Therefore, mathematical modeling of heat distribution inside a cotton seed is essential for improving and optimizing drying conditions. The purpose of this study is to develop and validate a mathematical model describing the heat distribution process inside a raw cotton seed during active ventilation and drying. For this purpose, an individual cotton seed is represented as a spherical object, and the heat conduction process inside the seed is described by a system of differential equations considering moisture evaporation and convective heat transfer between the seed surface and the surrounding drying medium. The boundary value problem is solved using the method of separation of variables (Fourier method). The unknown coefficients of the mathematical model are determined by applying the least squares method to experimental data. The proposed mathematical model was evaluated by comparing theoretical calculations with experimental results obtained at drying-agent temperatures of 100°C and 150°C. The comparison demonstrated good agreement between the calculated and experimental temperature distributions, with a deviation of less than 5%. This confirms the adequacy and reliability of the developed model for describing the heat transfer process inside raw cotton seeds under active drying conditions. The results of the study provide a theoretical basis for determining rational drying parameters and optimizing technological operating modes of industrial installations used for the drying and storage of raw cotton. The developed approach can also be applied to further investigations of coupled heat and moisture transfer processes in cotton seeds.

Published in	American Journal of Mechanics and Applications (Volume 13, Issue 3)
DOI	10.11648/j.ajma.20261303.11
Page(s)	35-40
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), 2026. Published by Science Publishing Group

Keywords

Raw Cotton, Seed, Heat Conduction, Mathematical Model, Active Ventilation, Drying Kinetics, Differential Equation, Method of Least Squares

References

[1]	Parpiev, A. P. (1977). Research on ways to intensify the process of drying raw cotton [Candidate dissertation, Technical Sciences]. Tashkent.
[2]	Mamatov, A. Z., & Parpiev, A. P. (1993). An approximate method for calculating the drying process of raw cotton. Izvestiya Vuzov. Tekhnologiya Tekstil'noi Promyshlennosti, (1), 99–101.
[3]	Mamatov, A. Z., & Parpiev, A. P. (1992). On the generalized mass transfer equation for calculating the drying kinetics of raw cotton. Reports of the Academy of Sciences of the Republic of Uzbekistan (DAN RUz), (6–7), 21–23.
[4]	Mamatov, A. Z., Parpiev, A. P., & Usmankulov, A. (2006). Solution to a problem of mass and heat transfer in a raw cotton seed. Journal of Textile Problems, (4).
[5]	Mamatov, A., Parpiev, A., & Shorakhmedova, M. (2021). Mathematical model for calculating the temperature field of a direct-flow drying drum. Journal of Physics: Conference Series, 2131(5), 052067.
[6]	Mamatov, A. Z., Usmankulov, A. K., Abbazov, I. Z., Norboyev, U. A., & Mukhametshina, E. T. (2021). Determination of temperature of components of cotton-raw material in a drum dryer with a constant. IOP Conference Series: Earth and Environmental Science, 939(1), 012052.
[7]	Mamatov, A. Z., Pardaev, Kh. N., Mardonov, J. Sh., & Plekhanov, A. F. (2021). Determining of the heat-moisture state of raw cotton in a drum dryer. Izvestiya Vysshikh Uchebnykh Zavedenii, Seriya Tekhnologiya Tekstil'noi Promyshlennosti, 391(1), 46–49.
[8]	Lykov, A. V. (1978). Heat and mass transfer. Energiya.
[9]	Ladyzhenskaya, O. A., Solonnikov, V. A., & Ural'tseva, N. N. (1967). Linear and quasilinear equations of parabolic type. Nauka.
[10]	Ladyzhenskaya, O. A., & Ural'tseva, N. N. (1973). Linear and quasilinear equations of elliptic type. Nauka.
[11]	Mikhlin, S. G. (1966). Numerical realization of variational methods. Nauka.
[12]	Mamatov, A., Bakhramov, S., & Narmamatov, A. (2021). An approximate solution by the Galerkin method of a quasilinear equation with a boundary condition containing the time derivative of the unknown function. AIP Conference Proceedings, 2365(1), 020036.
[13]	Wheeler, M. F. (1973). A priori error estimates for Galerkin approximations to parabolic partial differential equations. SIAM Journal on Numerical Analysis, 10(4), 723–759.
[14]	Douglas, J., Jr., & Dupont, T. (1973). Galerkin methods for parabolic equations with nonlinear boundary conditions. Numerische Mathematik, 20(3), 213–237.
[15]	Dendy, J. E., Jr. (1977). Galerkin methods for some highly nonlinear problems. SIAM Journal on Numerical Analysis, 14(2), 327–347.
[16]	Mitchell, A. R. (1979). A Galerkin method for nonlinear parabolic equations with nonlinear boundary conditions. SIAM Journal on Numerical Analysis, 16(2), 254–299.
[17]	Mamatov, A. Z., Raxmanov, J. T., & Sulaymanova, N. O. (2023). On the stability of the Galerkin method for solving the problem of determining the warm-moisture state of raw cotton. International Bulletin of Engineering and Technology, 3(6), 101–107.

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APA Style

Zununovich, M. A., Normamatovich, P. X., Najmidinovich, B. S. (2026). Heat Distribution Within a Raw Cotton Seed. American Journal of Mechanics and Applications, 13(3), 35-40. https://doi.org/10.11648/j.ajma.20261303.11

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ACS Style

Zununovich, M. A.; Normamatovich, P. X.; Najmidinovich, B. S. Heat Distribution Within a Raw Cotton Seed. Am. J. Mech. Appl. 2026, 13(3), 35-40. doi: 10.11648/j.ajma.20261303.11

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AMA Style

Zununovich MA, Normamatovich PX, Najmidinovich BS. Heat Distribution Within a Raw Cotton Seed. Am J Mech Appl. 2026;13(3):35-40. doi: 10.11648/j.ajma.20261303.11

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@article{10.11648/j.ajma.20261303.11,
  author = {Mamatov Alisher Zununovich and Pardaev Xanimkul Normamatovich and Bomurotov Sherbek Najmidinovich},
  title = {Heat Distribution Within a Raw Cotton Seed},
  journal = {American Journal of Mechanics and Applications},
  volume = {13},
  number = {3},
  pages = {35-40},
  doi = {10.11648/j.ajma.20261303.11},
  url = {https://doi.org/10.11648/j.ajma.20261303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20261303.11},
  abstract = {The drying and active ventilation of raw cotton are important technological processes that directly affect the quality, storage stability, and further processing of cotton. During drying, heat and moisture transfer within individual cotton seeds plays a significant role in determining the efficiency of the overall process. Therefore, mathematical modeling of heat distribution inside a cotton seed is essential for improving and optimizing drying conditions. The purpose of this study is to develop and validate a mathematical model describing the heat distribution process inside a raw cotton seed during active ventilation and drying. For this purpose, an individual cotton seed is represented as a spherical object, and the heat conduction process inside the seed is described by a system of differential equations considering moisture evaporation and convective heat transfer between the seed surface and the surrounding drying medium. The boundary value problem is solved using the method of separation of variables (Fourier method). The unknown coefficients of the mathematical model are determined by applying the least squares method to experimental data. The proposed mathematical model was evaluated by comparing theoretical calculations with experimental results obtained at drying-agent temperatures of 100°C and 150°C. The comparison demonstrated good agreement between the calculated and experimental temperature distributions, with a deviation of less than 5%. This confirms the adequacy and reliability of the developed model for describing the heat transfer process inside raw cotton seeds under active drying conditions. The results of the study provide a theoretical basis for determining rational drying parameters and optimizing technological operating modes of industrial installations used for the drying and storage of raw cotton. The developed approach can also be applied to further investigations of coupled heat and moisture transfer processes in cotton seeds.},
 year = {2026}
}

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TY  - JOUR
T1  - Heat Distribution Within a Raw Cotton Seed
AU  - Mamatov Alisher Zununovich
AU  - Pardaev Xanimkul Normamatovich
AU  - Bomurotov Sherbek Najmidinovich
Y1  - 2026/09/20
PY  - 2026
N1  - https://doi.org/10.11648/j.ajma.20261303.11
DO  - 10.11648/j.ajma.20261303.11
T2  - American Journal of Mechanics and Applications
JF  - American Journal of Mechanics and Applications
JO  - American Journal of Mechanics and Applications
SP  - 35
EP  - 40
PB  - Science Publishing Group
SN  - 2376-6131
UR  - https://doi.org/10.11648/j.ajma.20261303.11
AB  - The drying and active ventilation of raw cotton are important technological processes that directly affect the quality, storage stability, and further processing of cotton. During drying, heat and moisture transfer within individual cotton seeds plays a significant role in determining the efficiency of the overall process. Therefore, mathematical modeling of heat distribution inside a cotton seed is essential for improving and optimizing drying conditions. The purpose of this study is to develop and validate a mathematical model describing the heat distribution process inside a raw cotton seed during active ventilation and drying. For this purpose, an individual cotton seed is represented as a spherical object, and the heat conduction process inside the seed is described by a system of differential equations considering moisture evaporation and convective heat transfer between the seed surface and the surrounding drying medium. The boundary value problem is solved using the method of separation of variables (Fourier method). The unknown coefficients of the mathematical model are determined by applying the least squares method to experimental data. The proposed mathematical model was evaluated by comparing theoretical calculations with experimental results obtained at drying-agent temperatures of 100°C and 150°C. The comparison demonstrated good agreement between the calculated and experimental temperature distributions, with a deviation of less than 5%. This confirms the adequacy and reliability of the developed model for describing the heat transfer process inside raw cotton seeds under active drying conditions. The results of the study provide a theoretical basis for determining rational drying parameters and optimizing technological operating modes of industrial installations used for the drying and storage of raw cotton. The developed approach can also be applied to further investigations of coupled heat and moisture transfer processes in cotton seeds.
VL  - 13
IS  - 3
ER  -

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Author Information

Mamatov Alisher Zununovich

Department of Textile Machinery Engineering, Tashkent Institute of Textile and Light Industry, Tashkent, Uzbekistan

Contact Email

http://orcid.org/0009-0006-2458-7047
Pardaev Xanimkul Normamatovich

Department of Textile Machinery Engineering, Tashkent Institute of Textile and Light Industry, Tashkent, Uzbekistan

Contact Email

http://orcid.org/0009-0002-9930-177X
Bomurotov Sherbek Najmidinovich

Department of Mathematics, Gulistan State University, Gulistan, Uzbekistan

Contact Email

http://orcid.org/0009-0006-2601-9131

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APA Style

Zununovich, M. A., Normamatovich, P. X., Najmidinovich, B. S. (2026). Heat Distribution Within a Raw Cotton Seed. American Journal of Mechanics and Applications, 13(3), 35-40. https://doi.org/10.11648/j.ajma.20261303.11

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ACS Style

Zununovich, M. A.; Normamatovich, P. X.; Najmidinovich, B. S. Heat Distribution Within a Raw Cotton Seed. Am. J. Mech. Appl. 2026, 13(3), 35-40. doi: 10.11648/j.ajma.20261303.11

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AMA Style

Zununovich MA, Normamatovich PX, Najmidinovich BS. Heat Distribution Within a Raw Cotton Seed. Am J Mech Appl. 2026;13(3):35-40. doi: 10.11648/j.ajma.20261303.11

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@article{10.11648/j.ajma.20261303.11,
  author = {Mamatov Alisher Zununovich and Pardaev Xanimkul Normamatovich and Bomurotov Sherbek Najmidinovich},
  title = {Heat Distribution Within a Raw Cotton Seed},
  journal = {American Journal of Mechanics and Applications},
  volume = {13},
  number = {3},
  pages = {35-40},
  doi = {10.11648/j.ajma.20261303.11},
  url = {https://doi.org/10.11648/j.ajma.20261303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajma.20261303.11},
  abstract = {The drying and active ventilation of raw cotton are important technological processes that directly affect the quality, storage stability, and further processing of cotton. During drying, heat and moisture transfer within individual cotton seeds plays a significant role in determining the efficiency of the overall process. Therefore, mathematical modeling of heat distribution inside a cotton seed is essential for improving and optimizing drying conditions. The purpose of this study is to develop and validate a mathematical model describing the heat distribution process inside a raw cotton seed during active ventilation and drying. For this purpose, an individual cotton seed is represented as a spherical object, and the heat conduction process inside the seed is described by a system of differential equations considering moisture evaporation and convective heat transfer between the seed surface and the surrounding drying medium. The boundary value problem is solved using the method of separation of variables (Fourier method). The unknown coefficients of the mathematical model are determined by applying the least squares method to experimental data. The proposed mathematical model was evaluated by comparing theoretical calculations with experimental results obtained at drying-agent temperatures of 100°C and 150°C. The comparison demonstrated good agreement between the calculated and experimental temperature distributions, with a deviation of less than 5%. This confirms the adequacy and reliability of the developed model for describing the heat transfer process inside raw cotton seeds under active drying conditions. The results of the study provide a theoretical basis for determining rational drying parameters and optimizing technological operating modes of industrial installations used for the drying and storage of raw cotton. The developed approach can also be applied to further investigations of coupled heat and moisture transfer processes in cotton seeds.},
 year = {2026}
}

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TY  - JOUR
T1  - Heat Distribution Within a Raw Cotton Seed
AU  - Mamatov Alisher Zununovich
AU  - Pardaev Xanimkul Normamatovich
AU  - Bomurotov Sherbek Najmidinovich
Y1  - 2026/09/20
PY  - 2026
N1  - https://doi.org/10.11648/j.ajma.20261303.11
DO  - 10.11648/j.ajma.20261303.11
T2  - American Journal of Mechanics and Applications
JF  - American Journal of Mechanics and Applications
JO  - American Journal of Mechanics and Applications
SP  - 35
EP  - 40
PB  - Science Publishing Group
SN  - 2376-6131
UR  - https://doi.org/10.11648/j.ajma.20261303.11
AB  - The drying and active ventilation of raw cotton are important technological processes that directly affect the quality, storage stability, and further processing of cotton. During drying, heat and moisture transfer within individual cotton seeds plays a significant role in determining the efficiency of the overall process. Therefore, mathematical modeling of heat distribution inside a cotton seed is essential for improving and optimizing drying conditions. The purpose of this study is to develop and validate a mathematical model describing the heat distribution process inside a raw cotton seed during active ventilation and drying. For this purpose, an individual cotton seed is represented as a spherical object, and the heat conduction process inside the seed is described by a system of differential equations considering moisture evaporation and convective heat transfer between the seed surface and the surrounding drying medium. The boundary value problem is solved using the method of separation of variables (Fourier method). The unknown coefficients of the mathematical model are determined by applying the least squares method to experimental data. The proposed mathematical model was evaluated by comparing theoretical calculations with experimental results obtained at drying-agent temperatures of 100°C and 150°C. The comparison demonstrated good agreement between the calculated and experimental temperature distributions, with a deviation of less than 5%. This confirms the adequacy and reliability of the developed model for describing the heat transfer process inside raw cotton seeds under active drying conditions. The results of the study provide a theoretical basis for determining rational drying parameters and optimizing technological operating modes of industrial installations used for the drying and storage of raw cotton. The developed approach can also be applied to further investigations of coupled heat and moisture transfer processes in cotton seeds.
VL  - 13
IS  - 3
ER  -

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