Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity

Ime Jimmy Uwanta; Halima Usman

doi:doi:10.11648/j.acm.20140302.12

| Peer-Reviewed

Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity

Ime Jimmy Uwanta, Halima Usman

Published in Applied and Computational Mathematics (Volume 3, Issue 2)

Received: 30 March 2014 Accepted: 22 April 2014 Published: 30 April 2014

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The objective of this paper is to study thermal conductivity and magnetic field intensity effects on heat and mass transfer flow over a vertical channel both numerically and analytically. The non-linear partial differential equations governing the flow are non-dimensionalised, simplified and solved using Crank Nicolson type of implicit finite difference method. To check the accuracy of the numerical solution, steady state solutions for velocity, temperature and concentration fields are obtained by using perturbation method. Graphical results for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number have been obtained, to show the effects of different parameters entering in the problem. Results from these study shows that velocity, temperature and concentration increases with the increase in the dimensionless time until they reach steady state value. Also, it was observed that the analytical and numerical solutions agree very well at large values of time.

Published in	Applied and Computational Mathematics (Volume 3, Issue 2)
DOI	10.11648/j.acm.20140302.12
Page(s)	48-56
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

Thermal Conductivity, Heat and Mass Transfer, Magnetic Field, Thermal Radiation

References

[1]	S. Ahmed, “Mathematical model of induced magnetic field with viscous/magnetic dissipation bounded by a porous vertical plate in presence of radiation,” International Journal of Applied Mathematics and Mechanics, vol. 8, no.1, pp. 86-104, 2012.
[2]	R. Azizian, E. Doroodchi, T. Mckrell, J. Buongiomo, L. W. Hu and B. Moghtaden, “Effect of magnetic field on laminar convec-tive heat transfer of magnetic nano fluids,” International Journal of Heat and Mass Transfer, vol. 68, pp. 94-109, 2014.
[3]	M. Q. Brewster. Thermal radiative transfer and properties, John Wiley and Sons. Inc, New York, 1992.
[4]	C. Y. Cheng, “Effect of magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media- an integral approach,” International Communications in Heat and Mass Transfer, vol. 26, no. 7, pp. 935-943, 1999.
[5]	E. M. Elbashbeshy, T. G. Emam, M. S. El-Azaba and K. M. Abdelgaber, “Effect of magnetic field on flow and heat transfer over a stretching horizontal cylinder in the presence of a heat source/sink with suction/ injection,” Applied Mechanical Engineering, vol. 1, no. 1, pp. 1-5, 2012.
[6]	H. L. Evans, “Mass transfer through laminar boundary layers,” International Journal of Heat and Mass Transfer, vol. 5, pp. 35-57, 1962.
[7]	M. S. Hosain and M. A. Samad, “Heat and mass transfer of an MHD free convection flow along a stretching sheet with chemical reac-tion, radiation and heat generation in presence of magnetic field,” Research Journal of Mathe-matics and Statistics, vol. 5, no. 1-2, pp. 5-17, 2013.
[8]	M. A. A. Mahmoud, “Thermal radia-tion effects on MHD flow of a micropolar fluid over a stretching sheet with variable thermal con-ductivity,” Physica A, vol. 375, pp. 401-410, 2007.
[9]	S. Noreen, T. Hayat, A. Alsaedi and M. Qasim, “Mixed convection heat and mass transfer in peristaltic flow with chemical reaction and inclined magnetic field,” Indian Journal of Physics, vol. 87, no. 9, pp. 889-896, 2013.
[10]	J. I. Oahimire and B.I. Olajuwon, “Hydromagnetic flow near a stagnation point on a stretching sheet with variable thermal conductivity and heat source/sink,” International Journal of Applied Science and Engineering, vol. 11, no. 3, pp. 331-341, 2013.
[11]	K. Parvin, “Review of Magnetohydro-dynamic flow heat and mass transfer characteristics in a fluid,” International Journal of Science and Research Publications, vol. 3, no. 11, pp. 1-3, 2013.
[12]	G. Patowary, “Effect of variable viscosity and thermal conductivity of micropolar fluid in a porous channel in presence of magnetic field,” International Journal for Basic Sciences and Social Sciences, vol. 1, no. 3, pp. 69-77, 2012.
[13]	M. Qasim, Z. H. Khan, W. A. Khan and I. A. Sha, “MHD boundary layer slip flow and heat transfer of Ferro fluid along a stretching cylinder with prescribed heat flux,” PLOS ONE, vol. 9, no. 1, pp. 1-6, 2014.
[14]	A. M. Salem, “Variable viscosity and thermal conductivity effects on MHD flow and heat transfer in visco elastic fluid over a stretching sheet,” Physics Letters A, vol. 369, no. 4, pp. 315-322, 2007.
[15]	M. A. Seddek and F. A. Salema, “The effects of tempera-ture dependent viscosity and thermal conductivity on unsteady MHD convective heat transfer past a semi-infinite vertical porous moving plate with variable suction,” Computational Material Sciences, vol. 40, no. 2, pp. 186-192, 2007.
[16]	P. R. Sharma and G. Singh, “Effects of variable thermal conductivity and heat source/sink on MHD flow near a stagnation point on a linearly stretching sheet,” Journal of Applied Fluid Mechanics, vol. 2, pp. 13-21, 2008.
[17]	E. M. Sparrow, E. R. Eckert and W. J. Minkowyez, “Transportation cooling in a magnetohydrodynamic stagnation point flow,” Applied Science Research, A, vol. 11, pp. 125-147, 1962.
[18]	H. Usman and I. J. Uwanta, “Effect of thermal conductivity on MHD heat and mass transfer flow past an infinite vertical plate with Soret and Dufour effects,” American Journal of Applied Mathematics, vol. 1, no. 3, pp. 28-38, 2013.
[19]	S. K. Venkateswalu, K. N. Suryanarayana and B. R. Reddy, “Finite difference analysis on convective heat transfer flow through a porous medium in a vertical channel with magnetic field,” International Journal of Applied Mathematics and Mechanics, vol. 7, no. 7, pp. 74-94, 2011.
[20]	T. Zhang and H. Huang, “Effect of local magnetic field on electrically conducting fluid flow and heat transfer,” Journal of heat transfer, vol. 135, no. 2, pp. 1-8, 2012.

Cite This Article

Plain Text BibTeX RIS

APA Style

Ime Jimmy Uwanta, Halima Usman. (2014). Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity. Applied and Computational Mathematics, 3(2), 48-56. https://doi.org/10.11648/j.acm.20140302.12

Copy | Download

ACS Style

Ime Jimmy Uwanta; Halima Usman. Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity. Appl. Comput. Math. 2014, 3(2), 48-56. doi: 10.11648/j.acm.20140302.12

Copy | Download

AMA Style

Ime Jimmy Uwanta, Halima Usman. Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity. Appl Comput Math. 2014;3(2):48-56. doi: 10.11648/j.acm.20140302.12

Copy | Download

@article{10.11648/j.acm.20140302.12,
  author = {Ime Jimmy Uwanta and Halima Usman},
  title = {Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {2},
  pages = {48-56},
  doi = {10.11648/j.acm.20140302.12},
  url = {https://doi.org/10.11648/j.acm.20140302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140302.12},
  abstract = {The objective of this paper is to study thermal conductivity and magnetic field intensity effects on heat and mass transfer flow over a vertical channel both numerically and analytically. The non-linear partial differential equations governing the flow are non-dimensionalised, simplified and solved using Crank Nicolson type of implicit finite difference method. To check the accuracy of the numerical solution, steady state solutions for velocity, temperature and concentration fields are obtained by using perturbation method. Graphical results for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number have been obtained, to show the effects of different parameters entering in the problem. Results from these study shows that velocity, temperature and concentration increases with the increase in the dimensionless time until they reach steady state value. Also, it was observed that the analytical and numerical solutions agree very well at large values of time.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity
AU  - Ime Jimmy Uwanta
AU  - Halima Usman
Y1  - 2014/04/30
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140302.12
DO  - 10.11648/j.acm.20140302.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 48
EP  - 56
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140302.12
AB  - The objective of this paper is to study thermal conductivity and magnetic field intensity effects on heat and mass transfer flow over a vertical channel both numerically and analytically. The non-linear partial differential equations governing the flow are non-dimensionalised, simplified and solved using Crank Nicolson type of implicit finite difference method. To check the accuracy of the numerical solution, steady state solutions for velocity, temperature and concentration fields are obtained by using perturbation method. Graphical results for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number have been obtained, to show the effects of different parameters entering in the problem. Results from these study shows that velocity, temperature and concentration increases with the increase in the dimensionless time until they reach steady state value. Also, it was observed that the analytical and numerical solutions agree very well at large values of time.
VL  - 3
IS  - 2
ER  -

Copy | Download

Author Information

Ime Jimmy Uwanta

Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
Halima Usman

Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Ime Jimmy Uwanta, Halima Usman. (2014). Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity. Applied and Computational Mathematics, 3(2), 48-56. https://doi.org/10.11648/j.acm.20140302.12

Copy | Download

ACS Style

Ime Jimmy Uwanta; Halima Usman. Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity. Appl. Comput. Math. 2014, 3(2), 48-56. doi: 10.11648/j.acm.20140302.12

Copy | Download

AMA Style

Ime Jimmy Uwanta, Halima Usman. Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity. Appl Comput Math. 2014;3(2):48-56. doi: 10.11648/j.acm.20140302.12

Copy | Download

@article{10.11648/j.acm.20140302.12,
  author = {Ime Jimmy Uwanta and Halima Usman},
  title = {Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {2},
  pages = {48-56},
  doi = {10.11648/j.acm.20140302.12},
  url = {https://doi.org/10.11648/j.acm.20140302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140302.12},
  abstract = {The objective of this paper is to study thermal conductivity and magnetic field intensity effects on heat and mass transfer flow over a vertical channel both numerically and analytically. The non-linear partial differential equations governing the flow are non-dimensionalised, simplified and solved using Crank Nicolson type of implicit finite difference method. To check the accuracy of the numerical solution, steady state solutions for velocity, temperature and concentration fields are obtained by using perturbation method. Graphical results for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number have been obtained, to show the effects of different parameters entering in the problem. Results from these study shows that velocity, temperature and concentration increases with the increase in the dimensionless time until they reach steady state value. Also, it was observed that the analytical and numerical solutions agree very well at large values of time.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Effect of Variable Thermal Conductivity on Heat and Mass Transfer Flow over a Vertical Channel with Magnetic Field Intensity
AU  - Ime Jimmy Uwanta
AU  - Halima Usman
Y1  - 2014/04/30
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140302.12
DO  - 10.11648/j.acm.20140302.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 48
EP  - 56
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140302.12
AB  - The objective of this paper is to study thermal conductivity and magnetic field intensity effects on heat and mass transfer flow over a vertical channel both numerically and analytically. The non-linear partial differential equations governing the flow are non-dimensionalised, simplified and solved using Crank Nicolson type of implicit finite difference method. To check the accuracy of the numerical solution, steady state solutions for velocity, temperature and concentration fields are obtained by using perturbation method. Graphical results for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number have been obtained, to show the effects of different parameters entering in the problem. Results from these study shows that velocity, temperature and concentration increases with the increase in the dimensionless time until they reach steady state value. Also, it was observed that the analytical and numerical solutions agree very well at large values of time.
VL  - 3
IS  - 2
ER  -

Copy | Download