Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse

Dickson Kande; Titus Rotich; Fredrick Nyamwala

doi:doi:10.11648/j.ijssam.20230803.11

| Peer-Reviewed

Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse

Dickson Kande, Titus Rotich, Fredrick Nyamwala

Published in International Journal of Systems Science and Applied Mathematics (Volume 8, Issue 3)

Received: 20 May 2023 Accepted: 12 June 2023 Published: 9 October 2023

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In the last three decades, sub-division of farming land for settlement coupled with climatic variability and changes has presented a threat to food security by affecting the annual rainfall cycles, soil moisture and production. This called for responsive strategies in terms in order to deal with the threats posed where one of them is greenhouse farming where more favorable temperatures are obtained by applying the appropriate control methods. With this in mind, researchers of this paper aimed to improve the current and increase greenhouse farming in the Central Kenya region which has been one of the country’s food baskets and has been greatly affected. In a greenhouse, heat and mass transfer, is mainly through convection where convection is used to refer to the sum of advection and diffusion transfer. Ventilation is one of the most important components for the success of a greenhouse as it regulates the temperature, humidity and vapor pressure deficit to the required levels. To achieve this, controlled ventilation was adopted to provide right amount of dry air to sustain the evaporative cooling rate, without causing an unwanted rise in vapor pressure deficit and air temperature. The greenhouse is a dynamic controllable system implemented in either cold or hot regions to provide a specific climate conditions for the plants, where they will not grow optimally. The micro-climate parameters in a greenhouse are mainly the air temperature and the relative humidity which can be predicted by conducting experiments or by simulation. In relation to convection heat and mass transfer inside a greenhouse, this is required for two reasons: to regulate the greenhouse temperature and to remove water vapor transpired by the plants. A mathematical model which is a mathematical description of properties and interactions in the system is developed for the greenhouse under study. This paper implemented an RKM4 model of convective heat and mass transfer for ventilation and cooling systems inside a greenhouse based on the governing equations of fluid dynamics.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 8, Issue 3)
DOI	10.11648/j.ijssam.20230803.11
Page(s)	31-44
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

Greenhouse, Model, Ventilation, Systems, Runge-Kutta Methods, Heat Transfer, Mass Transfer

References

[1]	Kabubo-Mariara, J. and M. Kabara, Environment for Development.
[2]	Defraeye, T., et al., Convective heat and mass transfer modelling at air–porous material interfaces: Overview of existing methods and relevance. Chemical Engineering Science, 2012. 74: p. 49-58.
[3]	Dickson, K. K., A CFD Analysis of Heat and Mass Transfer in greenhouses: An Introduction. Mathematical Modeling and Application. Vol. 2, No. 2, 2017, pp. 17-20.
[4]	Rodríguez, F., et al., Modeling and control of greenhouse crop growth. 2015: Springer.
[5]	Roy, J., et al., PA—Precision Agriculture: convective and ventilation transfers in greenhouses, Part 1: the greenhouse considered as a perfectly stirred tank. Biosystems Engineering, 2002. 83 (1): p. 1-20.
[6]	Boulard, T. and B. Draoui, Natural ventilation of a greenhouse with continuous roof vents: measurements and data analysis. Journal of Agricultural engineering research, 1995. 61 (1): p. 27-35.
[7]	Raczek, A. and E. Wachowicz, Heat and mass exchange model in the air inside a greenhouse. Agricultural Engineering, 2014. 149: p. 185-195.
[8]	Radojević, N., et al., Microclimate control in greenhouses. FME Transactions, 2014. 42 (2): p. 167-171.
[9]	Velten, K., Mathematical modeling and simulation: introduction for scientists and engineers. 2009: John Wiley & Sons.
[10]	Leite, E. P., Matlab: modelling, programming and simulations. 2010: Sciyo.
[11]	Bergman, T. L. and F. P. Incropera, Fundamentals of heat and mass transfer. 2011: John Wiley & Sons. Kooli, S., et al. Modeling and Experimental Studies for Thermal Performance of a Ground Heat Storage System Integrated with a Greenhouse. in Ichmt Digital Library Online. 2009. Begel House Inc.
[12]	Ali, R. B., E. Aridhi, and A. Mami. Dynamic model of an agricultural greenhouse using Matlab-Simulink environment. in Sciences and Techniques of Automatic Control and Computer Engineering (STA), 2015 16th International Conference on. 2015. IEEE.
[13]	Castilla, N., Greenhouse technology and management. 2013: Cabi.
[14]	Alghannam, A. R. O., Using proportional integral derivative and Fuzzy logic with optimization for greenhouse. International Journal of Latest Trends in Agriculture and Food Sciences, 2012. 2 (2).
[15]	Potdar, S. R., C. B. Patil, and R. R. Mudholkar, Greenhouse Air-Temperature Modelling and Fuzzy Logic Control.
[16]	Dwyer, D., Defining ventilation boundary conditions for a greenhouse climate model. 2014.
[17]	Bartzanas, T. and C. Kittas. Heat and mass transfer in a large evaporative cooled greenhouse equipped with a progressive shading. in International Conference on Sustainable Greenhouse Systems-Greensys2004 691. 2004.
[18]	Zanino, R., S. Giors, and L. S. Richard, CFD model of ITER CICC. Part VI: Heat and mass transfer between cable region and central channel. Cryogenics, 2010. 50 (3): p. 158-166.
[19]	Sharma, P., G. Tiwari, and V. Sorayan, Temperature distribution in different zones of the micro-climate of a greenhouse: a dynamic model. Energy conversion and management, 1999. 40 (3): p. 335-348.
[20]	Rodríguez, F., et al. Modelling and simulation of greenhouse climate using Dymola. in IFAC 15th Triennial World Congress. Barcelona. Pp. 2002.
[21]	Chao, J., et al., Simple Model of Temperature in the Pomona College Organic Farm Greenhouse. 2014.
[22]	Baptista, F., et al., Greenhouses climate modelling. Tests, adaptation and validation of a dynamic climate model. Spanish Journal of Agricultural Research, 2010. 8 (2): p. 285-298.
[23]	Druma, A. M., Dynamic climate model of a greenhouse. 1998: United Nations University.

Cite This Article

Plain Text BibTeX RIS

APA Style

Dickson Kande, Titus Rotich, Fredrick Nyamwala. (2023). Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse. International Journal of Systems Science and Applied Mathematics, 8(3), 31-44. https://doi.org/10.11648/j.ijssam.20230803.11

Copy | Download

ACS Style

Dickson Kande; Titus Rotich; Fredrick Nyamwala. Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse. Int. J. Syst. Sci. Appl. Math. 2023, 8(3), 31-44. doi: 10.11648/j.ijssam.20230803.11

Copy | Download

AMA Style

Dickson Kande, Titus Rotich, Fredrick Nyamwala. Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse. Int J Syst Sci Appl Math. 2023;8(3):31-44. doi: 10.11648/j.ijssam.20230803.11

Copy | Download

@article{10.11648/j.ijssam.20230803.11,
  author = {Dickson Kande and Titus Rotich and Fredrick Nyamwala},
  title = {Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {8},
  number = {3},
  pages = {31-44},
  doi = {10.11648/j.ijssam.20230803.11},
  url = {https://doi.org/10.11648/j.ijssam.20230803.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20230803.11},
  abstract = {In the last three decades, sub-division of farming land for settlement coupled with climatic variability and changes has presented a threat to food security by affecting the annual rainfall cycles, soil moisture and production. This called for responsive strategies in terms in order to deal with the threats posed where one of them is greenhouse farming where more favorable temperatures are obtained by applying the appropriate control methods. With this in mind, researchers of this paper aimed to improve the current and increase greenhouse farming in the Central Kenya region which has been one of the country’s food baskets and has been greatly affected. In a greenhouse, heat and mass transfer, is mainly through convection where convection is used to refer to the sum of advection and diffusion transfer. Ventilation is one of the most important components for the success of a greenhouse as it regulates the temperature, humidity and vapor pressure deficit to the required levels. To achieve this, controlled ventilation was adopted to provide right amount of dry air to sustain the evaporative cooling rate, without causing an unwanted rise in vapor pressure deficit and air temperature. The greenhouse is a dynamic controllable system implemented in either cold or hot regions to provide a specific climate conditions for the plants, where they will not grow optimally. The micro-climate parameters in a greenhouse are mainly the air temperature and the relative humidity which can be predicted by conducting experiments or by simulation. In relation to convection heat and mass transfer inside a greenhouse, this is required for two reasons: to regulate the greenhouse temperature and to remove water vapor transpired by the plants. A mathematical model which is a mathematical description of properties and interactions in the system is developed for the greenhouse under study. This paper implemented an RKM4 model of convective heat and mass transfer for ventilation and cooling systems inside a greenhouse based on the governing equations of fluid dynamics.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse
AU  - Dickson Kande
AU  - Titus Rotich
AU  - Fredrick Nyamwala
Y1  - 2023/10/09
PY  - 2023
N1  - https://doi.org/10.11648/j.ijssam.20230803.11
DO  - 10.11648/j.ijssam.20230803.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 31
EP  - 44
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20230803.11
AB  - In the last three decades, sub-division of farming land for settlement coupled with climatic variability and changes has presented a threat to food security by affecting the annual rainfall cycles, soil moisture and production. This called for responsive strategies in terms in order to deal with the threats posed where one of them is greenhouse farming where more favorable temperatures are obtained by applying the appropriate control methods. With this in mind, researchers of this paper aimed to improve the current and increase greenhouse farming in the Central Kenya region which has been one of the country’s food baskets and has been greatly affected. In a greenhouse, heat and mass transfer, is mainly through convection where convection is used to refer to the sum of advection and diffusion transfer. Ventilation is one of the most important components for the success of a greenhouse as it regulates the temperature, humidity and vapor pressure deficit to the required levels. To achieve this, controlled ventilation was adopted to provide right amount of dry air to sustain the evaporative cooling rate, without causing an unwanted rise in vapor pressure deficit and air temperature. The greenhouse is a dynamic controllable system implemented in either cold or hot regions to provide a specific climate conditions for the plants, where they will not grow optimally. The micro-climate parameters in a greenhouse are mainly the air temperature and the relative humidity which can be predicted by conducting experiments or by simulation. In relation to convection heat and mass transfer inside a greenhouse, this is required for two reasons: to regulate the greenhouse temperature and to remove water vapor transpired by the plants. A mathematical model which is a mathematical description of properties and interactions in the system is developed for the greenhouse under study. This paper implemented an RKM4 model of convective heat and mass transfer for ventilation and cooling systems inside a greenhouse based on the governing equations of fluid dynamics.
VL  - 8
IS  - 3
ER  -

Copy | Download

Author Information

Dickson Kande

Department of Mathematics, Physics and Computing, Moi University, Eldoret, Kenya
Titus Rotich

Department of Mathematics, Physics and Computing, Moi University, Eldoret, Kenya
Fredrick Nyamwala

Department of Mathematics, Physics and Computing, Moi University, Eldoret, Kenya

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Dickson Kande, Titus Rotich, Fredrick Nyamwala. (2023). Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse. International Journal of Systems Science and Applied Mathematics, 8(3), 31-44. https://doi.org/10.11648/j.ijssam.20230803.11

Copy | Download

ACS Style

Dickson Kande; Titus Rotich; Fredrick Nyamwala. Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse. Int. J. Syst. Sci. Appl. Math. 2023, 8(3), 31-44. doi: 10.11648/j.ijssam.20230803.11

Copy | Download

AMA Style

Dickson Kande, Titus Rotich, Fredrick Nyamwala. Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse. Int J Syst Sci Appl Math. 2023;8(3):31-44. doi: 10.11648/j.ijssam.20230803.11

Copy | Download

@article{10.11648/j.ijssam.20230803.11,
  author = {Dickson Kande and Titus Rotich and Fredrick Nyamwala},
  title = {Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {8},
  number = {3},
  pages = {31-44},
  doi = {10.11648/j.ijssam.20230803.11},
  url = {https://doi.org/10.11648/j.ijssam.20230803.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20230803.11},
  abstract = {In the last three decades, sub-division of farming land for settlement coupled with climatic variability and changes has presented a threat to food security by affecting the annual rainfall cycles, soil moisture and production. This called for responsive strategies in terms in order to deal with the threats posed where one of them is greenhouse farming where more favorable temperatures are obtained by applying the appropriate control methods. With this in mind, researchers of this paper aimed to improve the current and increase greenhouse farming in the Central Kenya region which has been one of the country’s food baskets and has been greatly affected. In a greenhouse, heat and mass transfer, is mainly through convection where convection is used to refer to the sum of advection and diffusion transfer. Ventilation is one of the most important components for the success of a greenhouse as it regulates the temperature, humidity and vapor pressure deficit to the required levels. To achieve this, controlled ventilation was adopted to provide right amount of dry air to sustain the evaporative cooling rate, without causing an unwanted rise in vapor pressure deficit and air temperature. The greenhouse is a dynamic controllable system implemented in either cold or hot regions to provide a specific climate conditions for the plants, where they will not grow optimally. The micro-climate parameters in a greenhouse are mainly the air temperature and the relative humidity which can be predicted by conducting experiments or by simulation. In relation to convection heat and mass transfer inside a greenhouse, this is required for two reasons: to regulate the greenhouse temperature and to remove water vapor transpired by the plants. A mathematical model which is a mathematical description of properties and interactions in the system is developed for the greenhouse under study. This paper implemented an RKM4 model of convective heat and mass transfer for ventilation and cooling systems inside a greenhouse based on the governing equations of fluid dynamics.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Numerical Model for the Convective Heat and Mass Flow for the Internal Climate of Greenhouse
AU  - Dickson Kande
AU  - Titus Rotich
AU  - Fredrick Nyamwala
Y1  - 2023/10/09
PY  - 2023
N1  - https://doi.org/10.11648/j.ijssam.20230803.11
DO  - 10.11648/j.ijssam.20230803.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 31
EP  - 44
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20230803.11
AB  - In the last three decades, sub-division of farming land for settlement coupled with climatic variability and changes has presented a threat to food security by affecting the annual rainfall cycles, soil moisture and production. This called for responsive strategies in terms in order to deal with the threats posed where one of them is greenhouse farming where more favorable temperatures are obtained by applying the appropriate control methods. With this in mind, researchers of this paper aimed to improve the current and increase greenhouse farming in the Central Kenya region which has been one of the country’s food baskets and has been greatly affected. In a greenhouse, heat and mass transfer, is mainly through convection where convection is used to refer to the sum of advection and diffusion transfer. Ventilation is one of the most important components for the success of a greenhouse as it regulates the temperature, humidity and vapor pressure deficit to the required levels. To achieve this, controlled ventilation was adopted to provide right amount of dry air to sustain the evaporative cooling rate, without causing an unwanted rise in vapor pressure deficit and air temperature. The greenhouse is a dynamic controllable system implemented in either cold or hot regions to provide a specific climate conditions for the plants, where they will not grow optimally. The micro-climate parameters in a greenhouse are mainly the air temperature and the relative humidity which can be predicted by conducting experiments or by simulation. In relation to convection heat and mass transfer inside a greenhouse, this is required for two reasons: to regulate the greenhouse temperature and to remove water vapor transpired by the plants. A mathematical model which is a mathematical description of properties and interactions in the system is developed for the greenhouse under study. This paper implemented an RKM4 model of convective heat and mass transfer for ventilation and cooling systems inside a greenhouse based on the governing equations of fluid dynamics.
VL  - 8
IS  - 3
ER  -

Copy | Download