Back
 OJFD  Vol.6 No.3 , September 2016
Homotopy Analysis of MHD Free Convective Micropolar Fluid Flow along a Vertical Surface Embedded in Non-Darcian Thermally-Stratified Medium
Abstract: The dynamics of steady, two-dimensional magnetohydrodynamics (MHD) free convective flow of micropolar fluid along a vertical porous surface embedded in a thermally stratified medium is investigated. The ratio of pressure drop caused by liquid-solid interactions to that of pressure drop caused by viscous resistance are equal; hence, the non-Darcy effect is properly accounted for in the momentum equation. The temperature at the wall and at the free stream which best accounts for thermal stratification are adopted. Similarity transformations are used to convert the nonlinear partial differential equation to a system of coupled non-linear ordinary differential equation and also to parameterize the governing equations. The approximate analytical solution of the corresponding BVP are obtained using Homotopy Analysis Method (HAM). The effects of stratification parameter, thermal radiation and other pertinent parameters on velocity, angular velocity and temperature profiles are shown graphically. It is observed that increase in the stratification parameter leads to decrease in both velocity and temperature distribution and also makes the microrotation distribution to increase near the plate and decrease away from the plate. The influence of both thermal stratification and exponential space dependent internal heat source on velocity, micro-rotation and temperature profiles are presented. The comparison of the solutions obtained using analytical techniques (HAM) and MATLAB package (bvp4c) is shown and a good agreement is observed.
Cite this paper: Kolade Koriko, O. , Oreyeni, T. , John Omowaye, A. and Lare Animasaun, I. (2016) Homotopy Analysis of MHD Free Convective Micropolar Fluid Flow along a Vertical Surface Embedded in Non-Darcian Thermally-Stratified Medium. Open Journal of Fluid Dynamics, 6, 198-221. doi: 10.4236/ojfd.2016.63016.
References

[1]   Dake, J.M.K. and Harleman, D.R.F. (1969) Thermal Stratification in Lakes: Analytical and Laboratory Studies. Water Resources Research, 5, 484-495.
http://dx.doi.org/10.1029/WR005i002p00484

[2]   Animasaun, I.L. (2015) Casson Fluid Flow of Variable Viscosity and Thermal Conductivity along Exponentially Stretching Sheet Embedded in a Thermally Stratified Medium with Exponentially Heat Generation. Journal of Heat and Mass Transfer, 2, 63-78.

[3]   Madhu, J., Rajasekhar, M.N. and Reddy, B.S (2015) Effects of Viscous Dissipation and Thermal Stratification on Chemical Reacting Fluid Flow over a Vertical Stretching Surface with Heat Source. Advances in Applied Science Research, 6, 59-65.

[4]   Hayat, T., Hussain, T., Shehzad, S.A. and Alsaedi, A. (2014) Thermal and Concentration Stratifications Effects in Radiative Flow of Jeffrey Fluid over a Stretching Sheet. PLoS ONE, 9, e107858.
http://dx.doi.org/10.1371/journal.pone.0107858

[5]   Mukhopadhyay, S. and Ishak, A. (2012) Mixed Convection Flow along a Stretching Cylinder in a Thermally Stratified Medium. Journal of Applied Mathematics, 2012, Article ID: 491695.
http://dx.doi.org/10.1155/2012/491695

[6]   Murthy, P.V.S.N. and El-Amin, M.F. (2011) Thermo-Diffusion Effect on Free Convection Heat and Mass Transfer in a Thermally Linearly Stratified Non-Darcy Porous Media. The Open Transport Phenomena Journal, 3, 49-55.
http://dx.doi.org/10.2174/1877729501103010049

[7]   Omowaye, A.J., Adegbie, K.S., Disu, A.B. and Animasaun, I.L. (2015) Heat and Mass Transfer of Upper Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Horizontal Melting Surface. Applied Mathematics, 6, 1362-1379.
http://dx.doi.org/10.4236/am.2015.68129

[8]   Eringen A.C. (1966) Theory of Micropolar Fluids. Journal of Mathematics and Mechanics, 16, 1-18.
http://dx.doi.org/10.1512/iumj.1967.16.16001

[9]   Lukaszewicz, G. (1999) Micropolar Fluids: Theory and Applications. Birkhauser, Boston.
http://dx.doi.org/10.1007/978-1-4612-0641-5

[10]   Mohammad, S., Fatima, A. and Abdur, R. (2013) MHD Viscous Flow of Micropolar Fluids Due to a Shrinking Sheet. International Journal of Emerging Technology and Advanced Engineering, 3, 651-658.

[11]   Mohammad, A. and Mohammad, S.A. (2013) Soret and Dufour Effects on Steady Free Convective in MHD Micropolar Fluid Flow, Mass and Heat Transfer with Hall Current. International Journal of Advancements in Research and Technology, 2, 130-138.

[12]   Umavathi, J.C. and Jaweriya, S. (2012) Mixed Convection Flow of a Micropolar Fluid with Concentration in a Vertical Channel in the Presence of Heat Source or Sink. International Journal of Mathematcal Archieve, 3, 10.

[13]   Thiagarajan, M. and Senthilkumar, K. (2014) A Semi Analytical Investigation on MHD Micropolar Fluid and Heat Transfer in a Permeable Porous Channel. United States of America Research Journal, 3, 9-17.

[14]   Jat, R.N., Saxena, V. and Rajotia, D. (2013) Mhd Flow and Heat Transfer Near the Stagnation Point of a Micropolar Fluid over a Stretching Surface with Heat Generation/Absorption. Indian Journal of Pure and Applied Physics, 51, 683-689.

[15]   Ravi, S.K., Singh, A.K., Singh, R.K. and Chamkha A.J. (2013) Transient Free Convective Flow of a Micropolar Fluid between Two Vertical Walls. International Journal of Industrial Mathematics, 5, 87-95.

[16]   Animasaun, I.L. (2016) Melting Heat and Mass Transfer in Stagnation Point Micropolar Fluid Flow of Temperature Dependent Fluid Viscosity and Thermal Conductivity at Constant Vortex Viscosity. Journal of the Egyptian Mathematical Society. In-Press.

[17]   Mohammed, S., Sankar, T. and Eddy, N.R. (2013) Thermal Radiation Effects on MHD Free Convection Flow of a Micropolar Fluid past a Stretching Surface Embedded in a Non-Darcian Porous Medium. Innovative Systems Design and Engineering, 4, 13.

[18]   Abo-Eldahab, E.M. and El Aziz, M.A. (2005) Flow and Heat Transfer in a Micropolar Fluid Past a Stretching Surface Embedded in a Non-Darcian Porous Medium with Uniform Free Stream. Applied Mathematics and Computation, 162, 881-899.
http://dx.doi.org/10.1016/j.amc.2003.12.129

[19]   RamReddy, C., Murthy, P.V.S.N., Chamka A.J. and Rashad, A.M. (2013) Influence of Viscous Dissipation on Free Convection in a Non-Darcy Porous Medium Saturated with Nanofluid in the Presence of Magnetic Field. The Open Transport Phenomena Journal, 5, 20-29.
http://dx.doi.org/10.2174/1877729501305010020

[20]   Bakier, A.Y. (2011) Natural Convection Heat and Mass Transfer in a Micropolar Fluid-Saturated Non-Darcy Porous Regime with Radiation and Thermophoresis Effects. Thermal Science, 15, 317-326.
http://dx.doi.org/10.2298/TSCI101026096B

[21]   Adhikari, A. and Maiti, A.K. (2014) Mhd Micropolar Fluid Flow towards a Vertical Surface in a Presence of Heat Source/Sink under Radiative Heat Flux. Journal of the International Mathematical Virtual Institute, 4, 1-25.

[22]   Animasaun, I.L, Adebile, E.A. and Fagbade, A.I. (2016) Casson Fluid Flow with Variable Thermo-Physical Property along Exponentially Stretching Sheet with Suction and Exponentially Decaying Internal Heat Generation Using the Homotopy Analysis Method. Journal of Nigeria Mathematical Society, 35, 1-17.
http://dx.doi.org/10.1016/j.jnnms.2015.02.001

[23]   Liao, S.J. (2003) Beyond Perturbation: Introduction to Homotopy Analysis Method. Chapman Hall/CRC Press, Boca Raton.

[24]   Hilton, P.J. (1953) An Introduction to Homotopy Theory. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511666278

 
 
Top