Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation

Ekakitie Omamoke; Emeka Amos; Kubugha Wilcox Bunonyo

doi:doi:10.11648/j.ajam.20200804.14

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Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation

Ekakitie Omamoke, Emeka Amos, Kubugha Wilcox Bunonyo

Published in American Journal of Applied Mathematics (Volume 8, Issue 4)

Received: 18 June 2020 Accepted: 3 July 2020 Published: 17 July 2020

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Abstract

This study analyzes radiation, viscous dissipation and heat source effects on magneto-hydrodynamic free convection flow, of a viscous incompressible fluid over an inclined porous plate. Applying the perturbation technique, the solution of a set of ordinary differential equations are gotten as a result of reducing the non-linear partial differential equations of motion, energy and diffusion, which is solved analytically for velocity, temperature and the concentration distribution. The effect of Radiation, viscous dissipation and heat source on the velocity, temperature, concentration, skin friction, heat transfer and rate of mass flux distribution is plotted graphically using Mathematica 12 software and discussed. It is observed that increased Magnetic field reduces the velocity profile, increases the temperature, skin friction and heat transfer profile. Increase in radiation reduces heat transfer causing a mixed effect on the velocity, temperature and skin friction while an increase in the heat source causes a turbulent effect on the velocity, temperature and skin friction profile. Increase in porosity reduces the velocity, temperature, skin friction and heat transfer profile and finally parameters such as Chemical reaction, Grashof concentration number and Schmidt number had no effect on the velocity, temperature, skin friction and heat transfer profile.

Published in	American Journal of Applied Mathematics (Volume 8, Issue 4)
DOI	10.11648/j.ajam.20200804.14
Page(s)	190-206
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), 2020. Published by Science Publishing Group

Keywords

Free Convection, Radiation, Viscous Dissipation, Heat Source, Inclined Plate, Porous Plate, Magneto Hydrodynamic (MHD)

References

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[3]	Mebine, P. (2007). Thermosolutal MHD Flow with Radiative Heat Transfer past an Oscillating Plate. Advances in Theoretical and Applied Mathematics, 2, 3, pp 217-231.
[4]	Venkateswarlu, M., (2015), Unsteady MHD free convective Heat and Mass Transfer in a Boundary Layer Flow Past a vertical Permeable plate with Thermal Radiation and Chemical Reaction. Internal Conference of Computational Heat and Mass Transfer, Procedia Engineering 127, 791 – 799.
[5]	Sankar, Reddy, Sudheer, Babu, M., Narayana, P. V. and Umamaheswara, Reddy, D., (2011). Radiation and Chemical Reaction Effect on an Unsteady MHD Convection Flow Past a Vertical Moving Porous Plate Embedded in a Porous Medium with Viscous Dissipation, Advances in Applied Research, 2 (5):226-239, ISBN:0976-8610.
[6]	Durga, Prasad, P., Kiran, Kumar, R. V. M. S. and Varma, S. V. K., (2016). Heat and Mass Transfer for the MHD Flow of Nano-Fluid with Radiation Absorption, Ain Shams Engineering Journal, www.sciencedirect.com.
[7]	Madhusudhana, Rao, B., Raju, M. C., Viswanath, Reddy, G. and Varma, S. V. K., (2013). Unsteady MHD Free Convective Double Diffusive and Dissipative Visco-Elastic Fluid Flow in Porous Medium with Suction, International Journal of Advances in Science and Technology, Volume 7, number 2, ISSN: 2229-5216.
[8]	Venkateswarlu, M., Venkata, Lakshmi, D. and Naga, Malleswara, Rao, K., (2016). Soret, Hall Current, Rotation, Chemical Reaction and Thermal Radiation Effects on Unsteady MHD Heat and Mass Transfer Natural Convection Flow Past an Accelerated Vertical Plate. J. KSIAM, Volume 20, number 3, pp 203-224, DOI-10.12941.
[9]	Harinath, Reddy, S., Raju, M. C. and Reddy, Keshava, E., (2016). Soret and Defour Effects on Radiation Absorption Fluid in the Presence of Exponentially Varying Temperature and Concentration in a Conducting Field, Special Topics and Reviews in Porous Media-An International Journal 7(2):115-129.
[10]	Rojaa, T., Sankar, Reddy, B. and Bhaskar, Reddy, (2013). Radiation and Chemical Reaction Effect on MHD Free Convection Flow of a Micro-polar Fluid Bounded by Vertical Infinite Surface with Viscous Dissipation and Constant Suction, International Journal of Advanced Research, IJOAR.org, Volume 1, Issue 3, ISSN: 2320-9135.
[11]	Venkateswarlu, M., Ramana, Reddy, G. V. and Lakshmi, D. V., (2013). Unsteady MHD Flow of a Viscous Fluid Past a Vertical Porous Plate under Oscillatory Suction Velocity, Advances in Applied Research, 4(6):52-67, ISSN: 0976-8610.
[12]	Ojemeri, G., Onwabuya, I. O. and Abdusalam, S., Effect of Soret and Radial Magnetic Field of a Free Convective Slip Flow in a Viscous Reactive Fluid Towards a Vertical Porous Cylinder, Continental Journal of Applied Sciences, 14 (1): 25-45 DOI:10.5281, ISSN: 1597-9928.
[13]	Reddy, M. G. and Reddy, N. B., (2009). Radiation and Mass Transfer Effects on Unsteady MHD Free Convection Flow of an Incompressible Viscous Fluid Past a Moving Vertical Cylinder, Journal of Applied Mathematics and Mechanics, Volume 6, pp 96-110.
[14]	Rammana, Reddy, J. V., Sugunamma, V., Sandeep, N. and Sulochana, C., (2016). Influence of Chemical Reaction, Radiation and Rotation on MHD Nano Fluid Flow Past a Permeable Flat Plate in Porous Medium, Journal of the Nigerian Mathematical Society, Volume 35, pp 48-65.
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[18]	Ekakitie, Omamoke and Emeka, Amos, (2020). The Impact of Chemical Reaction and Heat Source on MHD Free Convection Flow over an Inclined Porous Surface, Internal Journal of Scientific and Research Publication, Volume 10, Issue 5, ISSN:2250-3153, DOI: 10.29322/IJSRP.10.05.2020.P10103.

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APA Style

Ekakitie Omamoke, Emeka Amos, Kubugha Wilcox Bunonyo. (2020). Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation. American Journal of Applied Mathematics, 8(4), 190-206. https://doi.org/10.11648/j.ajam.20200804.14

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ACS Style

Ekakitie Omamoke; Emeka Amos; Kubugha Wilcox Bunonyo. Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation. Am. J. Appl. Math. 2020, 8(4), 190-206. doi: 10.11648/j.ajam.20200804.14

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AMA Style

Ekakitie Omamoke, Emeka Amos, Kubugha Wilcox Bunonyo. Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation. Am J Appl Math. 2020;8(4):190-206. doi: 10.11648/j.ajam.20200804.14

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@article{10.11648/j.ajam.20200804.14,
  author = {Ekakitie Omamoke and Emeka Amos and Kubugha Wilcox Bunonyo},
  title = {Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation},
  journal = {American Journal of Applied Mathematics},
  volume = {8},
  number = {4},
  pages = {190-206},
  doi = {10.11648/j.ajam.20200804.14},
  url = {https://doi.org/10.11648/j.ajam.20200804.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20200804.14},
  abstract = {This study analyzes radiation, viscous dissipation and heat source effects on magneto-hydrodynamic free convection flow, of a viscous incompressible fluid over an inclined porous plate. Applying the perturbation technique, the solution of a set of ordinary differential equations are gotten as a result of reducing the non-linear partial differential equations of motion, energy and diffusion, which is solved analytically for velocity, temperature and the concentration distribution. The effect of Radiation, viscous dissipation and heat source on the velocity, temperature, concentration, skin friction, heat transfer and rate of mass flux distribution is plotted graphically using Mathematica 12 software and discussed. It is observed that increased Magnetic field reduces the velocity profile, increases the temperature, skin friction and heat transfer profile. Increase in radiation reduces heat transfer causing a mixed effect on the velocity, temperature and skin friction while an increase in the heat source causes a turbulent effect on the velocity, temperature and skin friction profile. Increase in porosity reduces the velocity, temperature, skin friction and heat transfer profile and finally parameters such as Chemical reaction, Grashof concentration number and Schmidt number had no effect on the velocity, temperature, skin friction and heat transfer profile.},
 year = {2020}
}

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TY  - JOUR
T1  - Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation
AU  - Ekakitie Omamoke
AU  - Emeka Amos
AU  - Kubugha Wilcox Bunonyo
Y1  - 2020/07/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ajam.20200804.14
DO  - 10.11648/j.ajam.20200804.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 190
EP  - 206
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20200804.14
AB  - This study analyzes radiation, viscous dissipation and heat source effects on magneto-hydrodynamic free convection flow, of a viscous incompressible fluid over an inclined porous plate. Applying the perturbation technique, the solution of a set of ordinary differential equations are gotten as a result of reducing the non-linear partial differential equations of motion, energy and diffusion, which is solved analytically for velocity, temperature and the concentration distribution. The effect of Radiation, viscous dissipation and heat source on the velocity, temperature, concentration, skin friction, heat transfer and rate of mass flux distribution is plotted graphically using Mathematica 12 software and discussed. It is observed that increased Magnetic field reduces the velocity profile, increases the temperature, skin friction and heat transfer profile. Increase in radiation reduces heat transfer causing a mixed effect on the velocity, temperature and skin friction while an increase in the heat source causes a turbulent effect on the velocity, temperature and skin friction profile. Increase in porosity reduces the velocity, temperature, skin friction and heat transfer profile and finally parameters such as Chemical reaction, Grashof concentration number and Schmidt number had no effect on the velocity, temperature, skin friction and heat transfer profile.
VL  - 8
IS  - 4
ER  -

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Author Information

Ekakitie Omamoke

Department of Mathematics, Bayelsa Medical University, Yenagoa, Nigeria
Emeka Amos

Department of Mathematics, Rivers State University, Port Harcourt, Nigeria
Kubugha Wilcox Bunonyo

Department of Mathematics and Statistics, Federal University Otuoke, Yenagoa, Nigeria

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Plain Text BibTeX RIS

APA Style

Ekakitie Omamoke, Emeka Amos, Kubugha Wilcox Bunonyo. (2020). Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation. American Journal of Applied Mathematics, 8(4), 190-206. https://doi.org/10.11648/j.ajam.20200804.14

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ACS Style

Ekakitie Omamoke; Emeka Amos; Kubugha Wilcox Bunonyo. Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation. Am. J. Appl. Math. 2020, 8(4), 190-206. doi: 10.11648/j.ajam.20200804.14

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AMA Style

Ekakitie Omamoke, Emeka Amos, Kubugha Wilcox Bunonyo. Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation. Am J Appl Math. 2020;8(4):190-206. doi: 10.11648/j.ajam.20200804.14

Copy | Download

@article{10.11648/j.ajam.20200804.14,
  author = {Ekakitie Omamoke and Emeka Amos and Kubugha Wilcox Bunonyo},
  title = {Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation},
  journal = {American Journal of Applied Mathematics},
  volume = {8},
  number = {4},
  pages = {190-206},
  doi = {10.11648/j.ajam.20200804.14},
  url = {https://doi.org/10.11648/j.ajam.20200804.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20200804.14},
  abstract = {This study analyzes radiation, viscous dissipation and heat source effects on magneto-hydrodynamic free convection flow, of a viscous incompressible fluid over an inclined porous plate. Applying the perturbation technique, the solution of a set of ordinary differential equations are gotten as a result of reducing the non-linear partial differential equations of motion, energy and diffusion, which is solved analytically for velocity, temperature and the concentration distribution. The effect of Radiation, viscous dissipation and heat source on the velocity, temperature, concentration, skin friction, heat transfer and rate of mass flux distribution is plotted graphically using Mathematica 12 software and discussed. It is observed that increased Magnetic field reduces the velocity profile, increases the temperature, skin friction and heat transfer profile. Increase in radiation reduces heat transfer causing a mixed effect on the velocity, temperature and skin friction while an increase in the heat source causes a turbulent effect on the velocity, temperature and skin friction profile. Increase in porosity reduces the velocity, temperature, skin friction and heat transfer profile and finally parameters such as Chemical reaction, Grashof concentration number and Schmidt number had no effect on the velocity, temperature, skin friction and heat transfer profile.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Radiation and Heat Source Effects on MHD Free Convection Flow over an Inclined Porous Plate in the Presence of Viscous Dissipation
AU  - Ekakitie Omamoke
AU  - Emeka Amos
AU  - Kubugha Wilcox Bunonyo
Y1  - 2020/07/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ajam.20200804.14
DO  - 10.11648/j.ajam.20200804.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 190
EP  - 206
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20200804.14
AB  - This study analyzes radiation, viscous dissipation and heat source effects on magneto-hydrodynamic free convection flow, of a viscous incompressible fluid over an inclined porous plate. Applying the perturbation technique, the solution of a set of ordinary differential equations are gotten as a result of reducing the non-linear partial differential equations of motion, energy and diffusion, which is solved analytically for velocity, temperature and the concentration distribution. The effect of Radiation, viscous dissipation and heat source on the velocity, temperature, concentration, skin friction, heat transfer and rate of mass flux distribution is plotted graphically using Mathematica 12 software and discussed. It is observed that increased Magnetic field reduces the velocity profile, increases the temperature, skin friction and heat transfer profile. Increase in radiation reduces heat transfer causing a mixed effect on the velocity, temperature and skin friction while an increase in the heat source causes a turbulent effect on the velocity, temperature and skin friction profile. Increase in porosity reduces the velocity, temperature, skin friction and heat transfer profile and finally parameters such as Chemical reaction, Grashof concentration number and Schmidt number had no effect on the velocity, temperature, skin friction and heat transfer profile.
VL  - 8
IS  - 4
ER  -

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