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Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel

An analysis of the impact of internal heat generation and other heat parameters on the temperature, velocity and rate of heat transfer of the liquid moving upward in a channel is studied. A fully developed non-Darcy flow using boundary conditions of the third kind with internal heat generation in a...

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Main Authors: Nurul Asyiqin, Mat Yaman, Nur Asiah, Mohd Makhatar, Mohd Rijal, Ilias, Abdul Rahman, Mohd Kasim, Nurul Farahain, Mohammad
Format: Article
Language:English
Published: Semarak Ilmu Publishing 2023
Subjects:
Q Science (General)
QA Mathematics
Online Access:http://umpir.ump.edu.my/id/eprint/40944/1/Non-darcy%20newtonian%20liquid%20flow%20with%20internal%20heat%20generation.pdf
http://umpir.ump.edu.my/id/eprint/40944/
https://doi.org/10.37934/cfdl.15.10.5270
https://doi.org/10.37934/cfdl.15.10.5270
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spelling my.ump.umpir.409442024-05-28T08:09:25Z http://umpir.ump.edu.my/id/eprint/40944/ Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel Nurul Asyiqin, Mat Yaman Nur Asiah, Mohd Makhatar Mohd Rijal, Ilias Abdul Rahman, Mohd Kasim Nurul Farahain, Mohammad Q Science (General) QA Mathematics An analysis of the impact of internal heat generation and other heat parameters on the temperature, velocity and rate of heat transfer of the liquid moving upward in a channel is studied. A fully developed non-Darcy flow using boundary conditions of the third kind with internal heat generation in a vertical channel is selected as the mathematical model. By utilising the similarity transformation, the governing equations are reduced to non-linear ordinary differential equations (ODEs). The converted ODEs are numerically solved and analysed using the fourth-order Runge-Kutta (RK4) method, incorporating a shooting technique with Newton’s method. The generated numerical algorithms are programmed in MATLAB for velocity, temperature and the local Nusselt number analysis. The numerical results of the flow and temperature variables are presented graphically. The impact of the parameters on the Nusselt number is also graphed to determine which of the three types of boundary conditions is the best for allowing heat transmission. The severity of flow reversal is increased under the Robin and Dirichlet conditions by enhancing the Darcy and Forchheimer numbers while decreasing the Brinkman and internal heat generation values. The temperature profiles improved with the increase in Brinkman numbers. Both Nusselt numbers remained constant for the Neumann boundary condition for all parameters except internal heat generation and local heat exponent. The Robin boundary condition is found to be the best facilitates heat transmission, since it delivers more pleasing and realistic results than the Dirichlet and Neumann conditions. Semarak Ilmu Publishing 2023-08-29 Article PeerReviewed pdf en cc_by_nc_4 http://umpir.ump.edu.my/id/eprint/40944/1/Non-darcy%20newtonian%20liquid%20flow%20with%20internal%20heat%20generation.pdf Nurul Asyiqin, Mat Yaman and Nur Asiah, Mohd Makhatar and Mohd Rijal, Ilias and Abdul Rahman, Mohd Kasim and Nurul Farahain, Mohammad (2023) Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel. CFD Letters, 15 (10). pp. 52-70. ISSN 2180-1363. (Published) https://doi.org/10.37934/cfdl.15.10.5270 https://doi.org/10.37934/cfdl.15.10.5270
institution Universiti Malaysia Pahang Al-Sultan Abdullah
building UMPSA Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Pahang Al-Sultan Abdullah
content_source UMPSA Institutional Repository
url_provider http://umpir.ump.edu.my/
language English
topic Q Science (General)
QA Mathematics
spellingShingle Q Science (General)
QA Mathematics
Nurul Asyiqin, Mat Yaman
Nur Asiah, Mohd Makhatar
Mohd Rijal, Ilias
Abdul Rahman, Mohd Kasim
Nurul Farahain, Mohammad
Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel
description An analysis of the impact of internal heat generation and other heat parameters on the temperature, velocity and rate of heat transfer of the liquid moving upward in a channel is studied. A fully developed non-Darcy flow using boundary conditions of the third kind with internal heat generation in a vertical channel is selected as the mathematical model. By utilising the similarity transformation, the governing equations are reduced to non-linear ordinary differential equations (ODEs). The converted ODEs are numerically solved and analysed using the fourth-order Runge-Kutta (RK4) method, incorporating a shooting technique with Newton’s method. The generated numerical algorithms are programmed in MATLAB for velocity, temperature and the local Nusselt number analysis. The numerical results of the flow and temperature variables are presented graphically. The impact of the parameters on the Nusselt number is also graphed to determine which of the three types of boundary conditions is the best for allowing heat transmission. The severity of flow reversal is increased under the Robin and Dirichlet conditions by enhancing the Darcy and Forchheimer numbers while decreasing the Brinkman and internal heat generation values. The temperature profiles improved with the increase in Brinkman numbers. Both Nusselt numbers remained constant for the Neumann boundary condition for all parameters except internal heat generation and local heat exponent. The Robin boundary condition is found to be the best facilitates heat transmission, since it delivers more pleasing and realistic results than the Dirichlet and Neumann conditions.
format Article
author Nurul Asyiqin, Mat Yaman
Nur Asiah, Mohd Makhatar
Mohd Rijal, Ilias
Abdul Rahman, Mohd Kasim
Nurul Farahain, Mohammad
author_facet Nurul Asyiqin, Mat Yaman
Nur Asiah, Mohd Makhatar
Mohd Rijal, Ilias
Abdul Rahman, Mohd Kasim
Nurul Farahain, Mohammad
author_sort Nurul Asyiqin, Mat Yaman
title Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel
title_short Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel
title_full Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel
title_fullStr Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel
title_full_unstemmed Non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel
title_sort non-darcy newtonian liquid flow with internal heat generation using boundary conditions of the third kind of fully developed mixed convection in a vertical channel
publisher Semarak Ilmu Publishing
publishDate 2023
url http://umpir.ump.edu.my/id/eprint/40944/1/Non-darcy%20newtonian%20liquid%20flow%20with%20internal%20heat%20generation.pdf
http://umpir.ump.edu.my/id/eprint/40944/
https://doi.org/10.37934/cfdl.15.10.5270
https://doi.org/10.37934/cfdl.15.10.5270
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score 13.244413

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