Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity

Adamu Gizachew; Bandari Shankar

doi:doi:10.11648/j.aas.20180303.13

| Peer-Reviewed

Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity

Adamu Gizachew, Bandari Shankar

Published in Advances in Applied Sciences (Volume 3, Issue 3)

Received: 19 July 2018 Accepted: 13 August 2018 Published: 6 September 2018

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this study, we have developed an analytic model to analyze the influence of velocity slip parameter and heat source on magneto hydrodynamics (MHD) heat and mass transfer of a Jeffery fluid which conducts electricity on a stretching surface. Both temperature and concentration are assumed to be in power low form. The existing partial differential equations (PDEs) is changed into a structure of ordinary differential equations (ODE's) by using a similarity variable. For computing the transformed equation, we used an analytical method named as Optimal Homotopy Asymptotic Method (OHAM). The influence of different dimensionless parameters on the velocity, temperature, concentration and as well as the coefficient of skin friction, Nusselt number and Sherwood number were evaluated using graphs and tables. It is observed that the velocity slip parameter (k) and the Deborah number (β) have opposite effects on the velocity distributions of the fluid flow. However, the effects of heat source parameter (δ) and thermal radiation parameter (R) on the temperature profile is similar. To be confident about the accuracy of this analytic method, the values of Nusselt number (Mu_x) solved numerically is compared with the previously published works done before and the comparison is found to be in a very good agreement.

Published in	Advances in Applied Sciences (Volume 3, Issue 3)
DOI	10.11648/j.aas.20180303.13
Page(s)	34-42
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), 2018. Published by Science Publishing Group

Keywords

Stretching Sheet, Slip Parameter, Heat Source, Thermal Radiation, Chemical Reaction, OHAM

References

[1]	B. C. Sakiadis, “boundary layer surface on continuous solid surface: L Boundary layer equations for two dimensional and ax symmetric flow,” J Am Inst Chem.Eng, 1961, 7: 26–8.
[2]	L.J. Crane, “Flow past a stretching plate,” Z Angew Math Phys, 1970, 21:645–647.
[3]	B.Dutta, P. Roy, and A. Gupta, “Temperature field in the flow over a stretching sheet with uniform heat flux,” Int. J Commun. Heat.MassTransf, 1985, 12: 89–94.
[4]	P. Gupta and A. Gupta, “Heat and mass transfer on a stretching sheet with suction or blowing,” Can.J.Chem. Eng, 1977,55: 744–746.
[5]	C. Chen and M. Char, “Heat transfer of a continuous stretching surface with suction or blowing,” J.Math.Anal. Appl, 1988, 135: 568–580.
[6]	M. Salleh, R. Nazar, and I. Pop, “Boundary layer flow and heat transfer over a stretching sheet with Newtonian heating,” J. Taiwan Inst. Chem. Eng.,2010, 41: 651–655.
[7]	P. Babu, J.A. Rao, and S. Sheri, “Radiation Effect on Mhd Heat and Mass Transfer Flow over a Shrinking Sheet with Mass Suction,” J. Appl. Fluid Mech., 2014, 7(4): 641–650.
[8]	N. S. Akbar, S. Nadeem, R.U. Haq, and Z.H. Khan, “Radiation effects on MHD stagnation point flow of nanofluid towards a stretching surface with convective boundary condition,” Chin J Aeronaut, 2013, 26: 1389–97.
[9]	B. C. Rout and S. R. Mishra, “Thermal energy transport on MHD nanofluid flow over a stretching surface: A comparative study,” Eng. Sci. Technol. an Int. J., 2018, 21: 60–69.
[10]	N. S. Akbar, S. Nadeem, R. U. Haq, and Z. H. Khan, “Dual solutions in MHD stagnation point flow of a Prandtl fluid impinging on a shrinking sheet,” Appl Math Mech, 2014, 35: 813–20.
[11]	O. D. Makinde and S. R. Mishra, “On Stagnation Point Flow of Variable Viscosity Nanofluids Past a Stretching Surface with Radiative Heat,” Int. J. Appl. Comput. Math., 2017, 3: 561-578
[12]	D. Pal and G. Mandal, “Influence of Lorentz Force and Thermal Radiation on Heat Transfer of Nanofluids Over a Stretching Sheet with Velocity–Thermal Slip,” Int. J. Appl. Comput. Math., 2017, 3(4): 3001-3020.
[13]	D. Pal and N. Roy, “Influence of Brownian Motion and Thermal Radiation on Heat Transfer of a Nanofluid Over Stretching Sheet with Slip Velocity,” Int. J. Appl. Comput. Math,2017, 3(4): 3355–3377.
[14]	Y. S. Daniel, Z. A. Aziz, Z. Ismail, and F. Salah, “Effects of slip and convective conditions on MHD flow of nanofluid over a porous nonlinear stretching/shrinking sheet,” Aust. J. Mech. Eng., 2017.
[15]	M. Sheikholeslami, H.. Ashorynejad, D.. Ganji, and A. Kolahdooz, “Investigation of rotating MHD viscous flow and heat transfer between stretching and porous surfaces using analytical method,” Math probl Eng, 2011: 1–17.
[16]	G. Adamu and B. Shankar, “MHD Flow of Non-Newtonian Viscoelastic Fluid on Stretching Sheet With The Effect of Slip Velocity,” Int. J. Eng. Manuf. Sci., 2018, 8(1): 1–14.
[17]	P. V. S. Narayana and D. H. Babu, “Numerical study of MHD heat and mass transfer of a Jeffrey fluid over a stretching sheet with chemical reaction and thermal radiation,” J. Taiwan Inst. Chem. Eng.,2016,59: 18–25.
[18]	K. Ammad and A. Ishak, “Magnetohydrodynamic (MHD) Jeffrey fluid over a stretching vertical surface in a porous medium,” Propuls. Power Res., 2017, 6(4): 269–276.
[19]	M. Qasim, “Heat and mass transfer in a Jeffrey fluid over a stretching sheet with heat source/sink,” Alex Eng J, 2013, 52: 571–575.
[20]	K. Das, N. Acharya, and P.. Kundu, “Radiative flow of MHD Jeffrey fluid past a stretching sheet with surface slip and melting heat transfer,” Alexandria Eng. J., 2015, 54: 815–821.
[21]	A. Zeeshan and A. Majeed, “Heat transfer analysis of Jeffery fluid flow over a stretching sheet with suction/injection and magnetic dipole effect,” Alexandria Eng. J., 2016, 55: 2171–2181.
[22]	S. Nadeem, R. Mehmood, and N. Akbar, “Non orthogonal stagnation point flow of a nano non-Newtonian fluid towards a stretching surface with heat transfer,” Int. J. Heat.Mass Transf., 2013, 57: 679–689.
[23]	S. Nadeem, Noreen, and S. Akbar, “Peristaltic flow of a Jeffrey fluid with variable viscosity in an asymmetric channel,”,Z. Natur schung A, 2009,64a: 713–722.
[24]	M. Khan, F. Iftikhar, and A. Anjum, “Some unsteady flows of a Jeffrey fluid between two side walls over a plane wall,” Z.Natur sch, 2011, 66: 745–752.
[25]	T. Hayat, S. Asad, M. Qasim, and A. Hendi, “Boundary layer flow of a Jeffrey fluid with convective boundary conditions,” Int. J.Numer. Methods Fluids, 2012, 69AD: 1350–1362.
[26]	T.Hayat, S.. Shehzad, M. Qasim, and S. Obaidt, “Thermal radiation effects on the mixed convection stagnation-point flow in a Jeffery fluid,” Z. Natur sch, 2011, 66: 606–614.
[27]	V.Marinca, N. Herisan, C. Bota, and B. Marinca, “An optimal homotopy asymptotic method applied to the steady flow of fourth-grade fluid past a porous plate,” Appl Math Lett, 2009, 22: 245–251.
[28]	T.Hayat, S.. Shehzad, M. Qasim, and S. Obaidat, “radiative flow of Jeffery fluid in a porous medium with power law heat flux and heat source,” Nucl Eng, 2012, 243: 15–19.
[29]	M.Qasim, “Heat and mass transfer in a Jeffrey fluid over a stretching sheet with heat source/sink,” Alexandria Eng. J., 2013, 52: 571–575.
[30]	C. H. Chen, “Laminar mixed convection adjacent to vertical continuously stretching sheets,” Heat Mass Transf., 1998, 33: 471–476.

Cite This Article

Plain Text BibTeX RIS

APA Style

Adamu Gizachew, Bandari Shankar. (2018). Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity. Advances in Applied Sciences, 3(3), 34-42. https://doi.org/10.11648/j.aas.20180303.13

Copy | Download

ACS Style

Adamu Gizachew; Bandari Shankar. Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity. Adv. Appl. Sci. 2018, 3(3), 34-42. doi: 10.11648/j.aas.20180303.13

Copy | Download

AMA Style

Adamu Gizachew, Bandari Shankar. Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity. Adv Appl Sci. 2018;3(3):34-42. doi: 10.11648/j.aas.20180303.13

Copy | Download

@article{10.11648/j.aas.20180303.13,
  author = {Adamu Gizachew and Bandari Shankar},
  title = {Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity},
  journal = {Advances in Applied Sciences},
  volume = {3},
  number = {3},
  pages = {34-42},
  doi = {10.11648/j.aas.20180303.13},
  url = {https://doi.org/10.11648/j.aas.20180303.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.aas.20180303.13},
  abstract = {In this study, we have developed an analytic model to analyze the influence of velocity slip parameter and heat source on magneto hydrodynamics (MHD) heat and mass transfer of a Jeffery fluid which conducts electricity on a stretching surface. Both temperature and concentration are assumed to be in power low form. The existing partial differential equations (PDEs) is changed into a structure of ordinary differential equations (ODE's) by using a similarity variable. For computing the transformed equation, we used an analytical method named as Optimal Homotopy Asymptotic Method (OHAM). The influence of different dimensionless parameters on the velocity, temperature, concentration and as well as the coefficient of skin friction, Nusselt number and Sherwood number were evaluated using graphs and tables. It is observed that the velocity slip parameter (k) and the Deborah number (β) have opposite effects on the velocity distributions of the fluid flow. However, the effects of heat source parameter (δ) and thermal radiation parameter (R) on the temperature profile is similar. To be confident about the accuracy of this analytic method, the values of Nusselt number (Mux) solved numerically is compared with the previously published works done before and the comparison is found to be in a very good agreement.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity
AU  - Adamu Gizachew
AU  - Bandari Shankar
Y1  - 2018/09/06
PY  - 2018
N1  - https://doi.org/10.11648/j.aas.20180303.13
DO  - 10.11648/j.aas.20180303.13
T2  - Advances in Applied Sciences
JF  - Advances in Applied Sciences
JO  - Advances in Applied Sciences
SP  - 34
EP  - 42
PB  - Science Publishing Group
SN  - 2575-1514
UR  - https://doi.org/10.11648/j.aas.20180303.13
AB  - In this study, we have developed an analytic model to analyze the influence of velocity slip parameter and heat source on magneto hydrodynamics (MHD) heat and mass transfer of a Jeffery fluid which conducts electricity on a stretching surface. Both temperature and concentration are assumed to be in power low form. The existing partial differential equations (PDEs) is changed into a structure of ordinary differential equations (ODE's) by using a similarity variable. For computing the transformed equation, we used an analytical method named as Optimal Homotopy Asymptotic Method (OHAM). The influence of different dimensionless parameters on the velocity, temperature, concentration and as well as the coefficient of skin friction, Nusselt number and Sherwood number were evaluated using graphs and tables. It is observed that the velocity slip parameter (k) and the Deborah number (β) have opposite effects on the velocity distributions of the fluid flow. However, the effects of heat source parameter (δ) and thermal radiation parameter (R) on the temperature profile is similar. To be confident about the accuracy of this analytic method, the values of Nusselt number (Mux) solved numerically is compared with the previously published works done before and the comparison is found to be in a very good agreement.
VL  - 3
IS  - 3
ER  -

Copy | Download

Author Information

Adamu Gizachew

Department of Mathematics, College of Science, Osmania University, Hyderabad, India
Bandari Shankar

Department of Mathematics, College of Science, Osmania University, Hyderabad, India

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Adamu Gizachew, Bandari Shankar. (2018). Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity. Advances in Applied Sciences, 3(3), 34-42. https://doi.org/10.11648/j.aas.20180303.13

Copy | Download

ACS Style

Adamu Gizachew; Bandari Shankar. Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity. Adv. Appl. Sci. 2018, 3(3), 34-42. doi: 10.11648/j.aas.20180303.13

Copy | Download

AMA Style

Adamu Gizachew, Bandari Shankar. Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity. Adv Appl Sci. 2018;3(3):34-42. doi: 10.11648/j.aas.20180303.13

Copy | Download

@article{10.11648/j.aas.20180303.13,
  author = {Adamu Gizachew and Bandari Shankar},
  title = {Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity},
  journal = {Advances in Applied Sciences},
  volume = {3},
  number = {3},
  pages = {34-42},
  doi = {10.11648/j.aas.20180303.13},
  url = {https://doi.org/10.11648/j.aas.20180303.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.aas.20180303.13},
  abstract = {In this study, we have developed an analytic model to analyze the influence of velocity slip parameter and heat source on magneto hydrodynamics (MHD) heat and mass transfer of a Jeffery fluid which conducts electricity on a stretching surface. Both temperature and concentration are assumed to be in power low form. The existing partial differential equations (PDEs) is changed into a structure of ordinary differential equations (ODE's) by using a similarity variable. For computing the transformed equation, we used an analytical method named as Optimal Homotopy Asymptotic Method (OHAM). The influence of different dimensionless parameters on the velocity, temperature, concentration and as well as the coefficient of skin friction, Nusselt number and Sherwood number were evaluated using graphs and tables. It is observed that the velocity slip parameter (k) and the Deborah number (β) have opposite effects on the velocity distributions of the fluid flow. However, the effects of heat source parameter (δ) and thermal radiation parameter (R) on the temperature profile is similar. To be confident about the accuracy of this analytic method, the values of Nusselt number (Mux) solved numerically is compared with the previously published works done before and the comparison is found to be in a very good agreement.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Analytical Solutions of an MHD Heat and Mass Transfer of a Jeffery Fluid Flow over a Stretching Sheet with the Effect of Slip Velocity
AU  - Adamu Gizachew
AU  - Bandari Shankar
Y1  - 2018/09/06
PY  - 2018
N1  - https://doi.org/10.11648/j.aas.20180303.13
DO  - 10.11648/j.aas.20180303.13
T2  - Advances in Applied Sciences
JF  - Advances in Applied Sciences
JO  - Advances in Applied Sciences
SP  - 34
EP  - 42
PB  - Science Publishing Group
SN  - 2575-1514
UR  - https://doi.org/10.11648/j.aas.20180303.13
AB  - In this study, we have developed an analytic model to analyze the influence of velocity slip parameter and heat source on magneto hydrodynamics (MHD) heat and mass transfer of a Jeffery fluid which conducts electricity on a stretching surface. Both temperature and concentration are assumed to be in power low form. The existing partial differential equations (PDEs) is changed into a structure of ordinary differential equations (ODE's) by using a similarity variable. For computing the transformed equation, we used an analytical method named as Optimal Homotopy Asymptotic Method (OHAM). The influence of different dimensionless parameters on the velocity, temperature, concentration and as well as the coefficient of skin friction, Nusselt number and Sherwood number were evaluated using graphs and tables. It is observed that the velocity slip parameter (k) and the Deborah number (β) have opposite effects on the velocity distributions of the fluid flow. However, the effects of heat source parameter (δ) and thermal radiation parameter (R) on the temperature profile is similar. To be confident about the accuracy of this analytic method, the values of Nusselt number (Mux) solved numerically is compared with the previously published works done before and the comparison is found to be in a very good agreement.
VL  - 3
IS  - 3
ER  -

Copy | Download