Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio

Omariba Geofrey Ong'era; Johana Kibet Sigey; Jeconia Okelo Abonyo; Stephen Mbugua Karanja

doi:doi:10.11648/j.ajam.20251306.11

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Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio

Omariba Geofrey Ong'era^*

, Johana Kibet Sigey

, Jeconia Okelo Abonyo

, Stephen Mbugua Karanja

Published in American Journal of Applied Mathematics (Volume 13, Issue 6)

Received: 12 October 2025 Accepted: 21 October 2025 Published: 22 November 2025

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Abstract

This study involves analysis of turbulent natural convection of heat transfer with localized heating and cooling on opposite surfaces of a vertical cylinder. Numerical simulation of turbulent natural convection has been studied in the past using the k-epsilon (k-ε), k-omega (k-ω) and k-ω-SST turbulence models. Further research showed that the k-ω SST model performed better than the k-ε and k-ω models. The study of natural convections in an enclosure has several applications from natural space, warming of household rooms to sections of engineering and atomic installations. This study involves numerical simulation of natural convection flow in a cylindrical enclosure full of air using the k-ω-SST model with an objective of establishing the best position of the heater and the cooler for better distribution of heat in the enclosure. The transfer of heat due to natural convection inside a cylindrical closed cavity was modeled to include the effect of Rayleigh number. The non-linear terms in averaged momentum and energy equation respectively were modeled using k-ω-SST model to close the governing equations. The sidewalls were adiabatic, while the bottom and top surfaces are maintained at 320 K and 298 K, respectively, to induce natural convection. The governing equations, Reynolds-average Navier-Stokes (RANS), energy and turbulence transport, were discretized using the central finite difference method under the Boussinesq approximation. A low Reynolds number k-ω SST turbulence model was employed to accurately resolve turbulent effects. The study explored a range of aspect ratios (AR = 1, 2, 4, 8) while holding the Rayleigh number constant within the turbulent regime R_a =10¹⁰and assuming Prandtl number of 0.71. Simulations were conducted in ANSYS Fluent to obtain vector plot of velocity magnitude, contours of temperature distribution, streamline distributions, effective thermal conductivity, and intensity of turbulence. Results revealed that increasing AR leads to reduced turbulence, weaker convective strength, more stratified temperature fields, and diminished heat transfer efficiency. The findings highlight the critical role of the geometry of the enclosure in shaping the flow structure and thermal behavior in turbulent natural convection.

Published in	American Journal of Applied Mathematics (Volume 13, Issue 6)
DOI	10.11648/j.ajam.20251306.11
Page(s)	365-392
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), 2025. Published by Science Publishing Group

Keywords

Turbulent Natural Convection, k-ω SST Model, Vertical Cylinder, Effects of Aspect Ratio

References

[1]	Mahmood, M. A., Mustafa, M. A., Al-Azzawi, M. M., & Abdullah, A. R. (2024). Numerical investigation of natural convection heat transfer between two isothermal concentric vertical cylinders embedded with porous media. Journal of Fluid Mechanics and Thermal Sciences, 12(1), 45-63.
[2]	Saraç, B., Aksu, E., Demirtaş, C., & Ayhan, T. (2024). Free convection heat transfer and buoyancy-assisted flow over a heated plate inserted horizontally in a vertical channel with time-varying conditions. Journal of Thermal Analysis and Calorimetry, 149(5), 2255-2271.
[3]	Shah, M., Ali, M., & Khan, S. (2024). Heat transfer enhancement in a vertical cylindrical cavity using phase-change materials and nanofluids. International Journal of Thermal Sciences, 200(3), 108425.
[4]	Azzouz, R., & Ben Hamida, M. B. (2023). Unsteady natural convection heat transfer in a circular enclosure containing four heated cylinders under the influence of a magnetic field. Journal of Thermal Science and Engineering, 11(8), 2444.
[5]	Ibrahim, M. N. J., Hammoodi, K. A., Abdulsahib, A. D., & Flayyih, M. A. (2022). Natural convection in an inclined nanofluid-filled cavity with hot inner bodies. International Journal of Heat and Technology, 40(3), 306-317.
[6]	Gautam, S., Khan, M. J., Khan, A., Sharma, V., Farid, F., & Sharma, A. K. (2022). Enhancement of natural convection heat transfer in cylindrical enclosure with internal heat source. In Recent Advances in Manufacturing, Automation, Design and Energy Technologies: Proceedings from ICoFT 2020 (pp. 983-992). Springer Singapore.
[7]	Talukdar, D., & Tsubokura, M. (2021). Numerical study of natural-convection from horizontal cylinder at eccentric positions with change in aspect ratio of a cooled square enclosure. Heat and Mass Transfer, 57(1), 1-23.
[8]	Laidoudi, H., & Ameur, H. (2021). Investigation of the natural convection within an old circular enclosure containing three equal-sized cylinders of hot surface. Defect and Diffusion Forum, 409, 49-57.
[9]	Space, V. C. C. P. A. (2014). Numerical simulation of natural convection in a vertical conical cylinder partially annular space. American Journal of Energy Research, 2(2), 24-29.
[10]	Awuor, K. O. (2013). Turbulent natural convection in an enclosure: Numerical study of different models [PhD thesis, Kenyatta University].
[11]	Mobedi, M. (1994). A three-dimensional numerical study on natural convection heat transfer from rectangular fins on a horizontal surface Doctoral dissertation, Middle East Technical University.
[12]	Karanja, S., Sigey, J., Gatheri, F., & Kirima, E. (2017). Turbulent natural convection in an enclosure at varying aspect ratio. International Journal of Sciences: Basic and Applied Research (IJSBAR), 7(6), 79-109.
[13]	Daiz, Y., Alim, M. A., & Karim, M. M. (2019). Numerical investigation of natural convection in a vertical cylindrical annulus with different aspect ratios. International Communications in Heat and Mass Transfer, 108, 104316.
[14]	Zhou, X., Wang, Q., & Zhang, J. (2020). Numerical study of turbulent natural convection in vertical cylindrical cavities with localized heating. International Journal of Thermal Sciences, 151, 106288.

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Ong'era, O. G., Sigey, J. K., Abonyo, J. O., Karanja, S. M. (2025). Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio. American Journal of Applied Mathematics, 13(6), 365-392. https://doi.org/10.11648/j.ajam.20251306.11

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ACS Style

Ong'era, O. G.; Sigey, J. K.; Abonyo, J. O.; Karanja, S. M. Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio. Am. J. Appl. Math. 2025, 13(6), 365-392. doi: 10.11648/j.ajam.20251306.11

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AMA Style

Ong'era OG, Sigey JK, Abonyo JO, Karanja SM. Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio. Am J Appl Math. 2025;13(6):365-392. doi: 10.11648/j.ajam.20251306.11

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@article{10.11648/j.ajam.20251306.11,
  author = {Omariba Geofrey Ong'era and Johana Kibet Sigey and Jeconia Okelo Abonyo and Stephen Mbugua Karanja},
  title = {Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio
},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {6},
  pages = {365-392},
  doi = {10.11648/j.ajam.20251306.11},
  url = {https://doi.org/10.11648/j.ajam.20251306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251306.11},
  abstract = {This study involves analysis of turbulent natural convection of heat transfer with localized heating and cooling on opposite surfaces of a vertical cylinder. Numerical simulation of turbulent natural convection has been studied in the past using the k-epsilon (k-ε), k-omega (k-ω) and k-ω-SST turbulence models. Further research showed that the k-ω SST model performed better than the k-ε and k-ω models. The study of natural convections in an enclosure has several applications from natural space, warming of household rooms to sections of engineering and atomic installations. This study involves numerical simulation of natural convection flow in a cylindrical enclosure full of air using the k-ω-SST model with an objective of establishing the best position of the heater and the cooler for better distribution of heat in the enclosure. The transfer of heat due to natural convection inside a cylindrical closed cavity was modeled to include the effect of Rayleigh number. The non-linear terms in averaged momentum and energy equation respectively were modeled using k-ω-SST model to close the governing equations. The sidewalls were adiabatic, while the bottom and top surfaces are maintained at 320 K and 298 K, respectively, to induce natural convection. The governing equations, Reynolds-average Navier-Stokes (RANS), energy and turbulence transport, were discretized using the central finite difference method under the Boussinesq approximation. A low Reynolds number k-ω SST turbulence model was employed to accurately resolve turbulent effects. The study explored a range of aspect ratios (AR = 1, 2, 4, 8) while holding the Rayleigh number constant within the turbulent regime Ra =1010 and assuming Prandtl number of 0.71. Simulations were conducted in ANSYS Fluent to obtain vector plot of velocity magnitude, contours of temperature distribution, streamline distributions, effective thermal conductivity, and intensity of turbulence. Results revealed that increasing AR leads to reduced turbulence, weaker convective strength, more stratified temperature fields, and diminished heat transfer efficiency. The findings highlight the critical role of the geometry of the enclosure in shaping the flow structure and thermal behavior in turbulent natural convection.
},
 year = {2025}
}

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TY  - JOUR
T1  - Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio

AU  - Omariba Geofrey Ong'era
AU  - Johana Kibet Sigey
AU  - Jeconia Okelo Abonyo
AU  - Stephen Mbugua Karanja
Y1  - 2025/11/22
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251306.11
DO  - 10.11648/j.ajam.20251306.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 365
EP  - 392
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251306.11
AB  - This study involves analysis of turbulent natural convection of heat transfer with localized heating and cooling on opposite surfaces of a vertical cylinder. Numerical simulation of turbulent natural convection has been studied in the past using the k-epsilon (k-ε), k-omega (k-ω) and k-ω-SST turbulence models. Further research showed that the k-ω SST model performed better than the k-ε and k-ω models. The study of natural convections in an enclosure has several applications from natural space, warming of household rooms to sections of engineering and atomic installations. This study involves numerical simulation of natural convection flow in a cylindrical enclosure full of air using the k-ω-SST model with an objective of establishing the best position of the heater and the cooler for better distribution of heat in the enclosure. The transfer of heat due to natural convection inside a cylindrical closed cavity was modeled to include the effect of Rayleigh number. The non-linear terms in averaged momentum and energy equation respectively were modeled using k-ω-SST model to close the governing equations. The sidewalls were adiabatic, while the bottom and top surfaces are maintained at 320 K and 298 K, respectively, to induce natural convection. The governing equations, Reynolds-average Navier-Stokes (RANS), energy and turbulence transport, were discretized using the central finite difference method under the Boussinesq approximation. A low Reynolds number k-ω SST turbulence model was employed to accurately resolve turbulent effects. The study explored a range of aspect ratios (AR = 1, 2, 4, 8) while holding the Rayleigh number constant within the turbulent regime Ra =1010 and assuming Prandtl number of 0.71. Simulations were conducted in ANSYS Fluent to obtain vector plot of velocity magnitude, contours of temperature distribution, streamline distributions, effective thermal conductivity, and intensity of turbulence. Results revealed that increasing AR leads to reduced turbulence, weaker convective strength, more stratified temperature fields, and diminished heat transfer efficiency. The findings highlight the critical role of the geometry of the enclosure in shaping the flow structure and thermal behavior in turbulent natural convection.

VL  - 13
IS  - 6
ER  -

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Author Information

Omariba Geofrey Ong'era

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Juja, Kenya

Contact Email

http://orcid.org/0000-0001-6197-7120
Johana Kibet Sigey

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Juja, Kenya

http://orcid.org/0009-0004-1790-7351
Jeconia Okelo Abonyo

Department of Pure and Applied Mathematics, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Juja, Kenya

http://orcid.org/0009-0002-9439-4110
Stephen Mbugua Karanja

Department of Pure and Applied Mathematics, Meru University of Science and Technology, Meru city, Kenya

http://orcid.org/0000-0001-9972-2334

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APA Style

Ong'era, O. G., Sigey, J. K., Abonyo, J. O., Karanja, S. M. (2025). Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio. American Journal of Applied Mathematics, 13(6), 365-392. https://doi.org/10.11648/j.ajam.20251306.11

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ACS Style

Ong'era, O. G.; Sigey, J. K.; Abonyo, J. O.; Karanja, S. M. Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio. Am. J. Appl. Math. 2025, 13(6), 365-392. doi: 10.11648/j.ajam.20251306.11

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AMA Style

Ong'era OG, Sigey JK, Abonyo JO, Karanja SM. Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio. Am J Appl Math. 2025;13(6):365-392. doi: 10.11648/j.ajam.20251306.11

Copy | Download

@article{10.11648/j.ajam.20251306.11,
  author = {Omariba Geofrey Ong'era and Johana Kibet Sigey and Jeconia Okelo Abonyo and Stephen Mbugua Karanja},
  title = {Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio
},
  journal = {American Journal of Applied Mathematics},
  volume = {13},
  number = {6},
  pages = {365-392},
  doi = {10.11648/j.ajam.20251306.11},
  url = {https://doi.org/10.11648/j.ajam.20251306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251306.11},
  abstract = {This study involves analysis of turbulent natural convection of heat transfer with localized heating and cooling on opposite surfaces of a vertical cylinder. Numerical simulation of turbulent natural convection has been studied in the past using the k-epsilon (k-ε), k-omega (k-ω) and k-ω-SST turbulence models. Further research showed that the k-ω SST model performed better than the k-ε and k-ω models. The study of natural convections in an enclosure has several applications from natural space, warming of household rooms to sections of engineering and atomic installations. This study involves numerical simulation of natural convection flow in a cylindrical enclosure full of air using the k-ω-SST model with an objective of establishing the best position of the heater and the cooler for better distribution of heat in the enclosure. The transfer of heat due to natural convection inside a cylindrical closed cavity was modeled to include the effect of Rayleigh number. The non-linear terms in averaged momentum and energy equation respectively were modeled using k-ω-SST model to close the governing equations. The sidewalls were adiabatic, while the bottom and top surfaces are maintained at 320 K and 298 K, respectively, to induce natural convection. The governing equations, Reynolds-average Navier-Stokes (RANS), energy and turbulence transport, were discretized using the central finite difference method under the Boussinesq approximation. A low Reynolds number k-ω SST turbulence model was employed to accurately resolve turbulent effects. The study explored a range of aspect ratios (AR = 1, 2, 4, 8) while holding the Rayleigh number constant within the turbulent regime Ra =1010 and assuming Prandtl number of 0.71. Simulations were conducted in ANSYS Fluent to obtain vector plot of velocity magnitude, contours of temperature distribution, streamline distributions, effective thermal conductivity, and intensity of turbulence. Results revealed that increasing AR leads to reduced turbulence, weaker convective strength, more stratified temperature fields, and diminished heat transfer efficiency. The findings highlight the critical role of the geometry of the enclosure in shaping the flow structure and thermal behavior in turbulent natural convection.
},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Analysis of Turbulent Natural Convection of Heat Transfer with Localized Heating and Cooling on Opposite Surfaces of a Vertical Cylinder with Varying Aspect Ratio

AU  - Omariba Geofrey Ong'era
AU  - Johana Kibet Sigey
AU  - Jeconia Okelo Abonyo
AU  - Stephen Mbugua Karanja
Y1  - 2025/11/22
PY  - 2025
N1  - https://doi.org/10.11648/j.ajam.20251306.11
DO  - 10.11648/j.ajam.20251306.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 365
EP  - 392
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20251306.11
AB  - This study involves analysis of turbulent natural convection of heat transfer with localized heating and cooling on opposite surfaces of a vertical cylinder. Numerical simulation of turbulent natural convection has been studied in the past using the k-epsilon (k-ε), k-omega (k-ω) and k-ω-SST turbulence models. Further research showed that the k-ω SST model performed better than the k-ε and k-ω models. The study of natural convections in an enclosure has several applications from natural space, warming of household rooms to sections of engineering and atomic installations. This study involves numerical simulation of natural convection flow in a cylindrical enclosure full of air using the k-ω-SST model with an objective of establishing the best position of the heater and the cooler for better distribution of heat in the enclosure. The transfer of heat due to natural convection inside a cylindrical closed cavity was modeled to include the effect of Rayleigh number. The non-linear terms in averaged momentum and energy equation respectively were modeled using k-ω-SST model to close the governing equations. The sidewalls were adiabatic, while the bottom and top surfaces are maintained at 320 K and 298 K, respectively, to induce natural convection. The governing equations, Reynolds-average Navier-Stokes (RANS), energy and turbulence transport, were discretized using the central finite difference method under the Boussinesq approximation. A low Reynolds number k-ω SST turbulence model was employed to accurately resolve turbulent effects. The study explored a range of aspect ratios (AR = 1, 2, 4, 8) while holding the Rayleigh number constant within the turbulent regime Ra =1010 and assuming Prandtl number of 0.71. Simulations were conducted in ANSYS Fluent to obtain vector plot of velocity magnitude, contours of temperature distribution, streamline distributions, effective thermal conductivity, and intensity of turbulence. Results revealed that increasing AR leads to reduced turbulence, weaker convective strength, more stratified temperature fields, and diminished heat transfer efficiency. The findings highlight the critical role of the geometry of the enclosure in shaping the flow structure and thermal behavior in turbulent natural convection.

VL  - 13
IS  - 6
ER  -

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