Mixed convection flow and heat transfer in a vertical channel filled with composite porous medium using Robin boundary conditions is analyzed. The flow is modeled using the Darcy-Lapwood-Brinkman model. The viscous and Darcy dissipation terms are included in energy equation. The plate exchanges heat with an external fluid. Both the conditions of equal and different reference temperature of the external fluid are considered. The governing equations are coupled and non-linear because of inclusion of dissipation terms and buoyancy forces. The equations are solved using perturbation method valid for small values of perturbation parameter. However, the restriction on the perturbation parameter is relaxed by finding the solutions of governing equations by using Differential Transform Method. The effects of various parameters such as mixed convection parameter, porous parameter, viscosity ratio, width ratio, conductivity ratio and the Biot numbers on the flow are discussed. The percentage of error between perturbation method and differential transformation method increases as the perturbation parameter increases for both equal and unequal Biot numbers.
| Published in | American Journal of Applied Mathematics (Volume 2, Issue 4) |
| DOI | 10.11648/j.ajam.20140204.11 |
| Page(s) | 96-110 |
| 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), 2014. Published by Science Publishing Group |
Mixed Convection, Composite Porous Medium, Perturbation Method, Differential Transform Method, Robin Boundary Condition
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APA Style
Jada Prathap Kumar, Jawali Channabasappa Umavathi, Yadav Ramarao. (2014). Free and Forced Convective Flow in a Vertical Channel Filled with Composite Porous Medium Using Robin Boundary Conditions. American Journal of Applied Mathematics, 2(4), 96-110. https://doi.org/10.11648/j.ajam.20140204.11
ACS Style
Jada Prathap Kumar; Jawali Channabasappa Umavathi; Yadav Ramarao. Free and Forced Convective Flow in a Vertical Channel Filled with Composite Porous Medium Using Robin Boundary Conditions. Am. J. Appl. Math. 2014, 2(4), 96-110. doi: 10.11648/j.ajam.20140204.11
AMA Style
Jada Prathap Kumar, Jawali Channabasappa Umavathi, Yadav Ramarao. Free and Forced Convective Flow in a Vertical Channel Filled with Composite Porous Medium Using Robin Boundary Conditions. Am J Appl Math. 2014;2(4):96-110. doi: 10.11648/j.ajam.20140204.11
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Download@article{10.11648/j.ajam.20140204.11,
author = {Jada Prathap Kumar and Jawali Channabasappa Umavathi and Yadav Ramarao},
title = {Free and Forced Convective Flow in a Vertical Channel Filled with Composite Porous Medium Using Robin Boundary Conditions},
journal = {American Journal of Applied Mathematics},
volume = {2},
number = {4},
pages = {96-110},
doi = {10.11648/j.ajam.20140204.11},
url = {https://doi.org/10.11648/j.ajam.20140204.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140204.11},
abstract = {Mixed convection flow and heat transfer in a vertical channel filled with composite porous medium using Robin boundary conditions is analyzed. The flow is modeled using the Darcy-Lapwood-Brinkman model. The viscous and Darcy dissipation terms are included in energy equation. The plate exchanges heat with an external fluid. Both the conditions of equal and different reference temperature of the external fluid are considered. The governing equations are coupled and non-linear because of inclusion of dissipation terms and buoyancy forces. The equations are solved using perturbation method valid for small values of perturbation parameter. However, the restriction on the perturbation parameter is relaxed by finding the solutions of governing equations by using Differential Transform Method. The effects of various parameters such as mixed convection parameter, porous parameter, viscosity ratio, width ratio, conductivity ratio and the Biot numbers on the flow are discussed. The percentage of error between perturbation method and differential transformation method increases as the perturbation parameter increases for both equal and unequal Biot numbers.},
year = {2014}
}
TY - JOUR T1 - Free and Forced Convective Flow in a Vertical Channel Filled with Composite Porous Medium Using Robin Boundary Conditions AU - Jada Prathap Kumar AU - Jawali Channabasappa Umavathi AU - Yadav Ramarao Y1 - 2014/07/30 PY - 2014 N1 - https://doi.org/10.11648/j.ajam.20140204.11 DO - 10.11648/j.ajam.20140204.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 96 EP - 110 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20140204.11 AB - Mixed convection flow and heat transfer in a vertical channel filled with composite porous medium using Robin boundary conditions is analyzed. The flow is modeled using the Darcy-Lapwood-Brinkman model. The viscous and Darcy dissipation terms are included in energy equation. The plate exchanges heat with an external fluid. Both the conditions of equal and different reference temperature of the external fluid are considered. The governing equations are coupled and non-linear because of inclusion of dissipation terms and buoyancy forces. The equations are solved using perturbation method valid for small values of perturbation parameter. However, the restriction on the perturbation parameter is relaxed by finding the solutions of governing equations by using Differential Transform Method. The effects of various parameters such as mixed convection parameter, porous parameter, viscosity ratio, width ratio, conductivity ratio and the Biot numbers on the flow are discussed. The percentage of error between perturbation method and differential transformation method increases as the perturbation parameter increases for both equal and unequal Biot numbers. VL - 2 IS - 4 ER -
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