Effects of Viscous Dissipation on Unsteady MHD Thermo Bioconvection Boundary Layer Flow of a Nanofluid Containing Gyrotactic Microorganisms along a Stretching Sheet
This paper presents a numerical study of the problem of unsteady thermo bioconvection boundary layer flow of a nanofluid containing gyrotactic microorganisms along a stretching sheet under the influence of magnetic field and viscous dissipation. With the help of usual transformation, the governing equations are transformed into unsteady nonlinear coupled partial differential equations. The numerical solution is obtained by using an explicit finite difference scheme. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. From the results it is found that both magnetic parameter and bioconvection Rayleigh number have positive effect on the dimensionless Nusselt number and density number of the motile microorgan-isms while the opposite behavior became clear in the case of Grashof number and Eckert number. The rescaled velocity, temperature, concentration and the density of motile microorganisms depend strongly on the governing parameters.
References
[1]
Gorla, R.S.R. and Hossain, A. (2013) Mixed Convective Boundary Layer Flow over a Vertical Cylinder Embedded in a Porous Medium Saturated with a Nanofluid. International Journal of Numerical Methods for Heat & Fluid Flow, 23, 1393-1405. https://doi.org/10.1108/HFF-03-2012-0064
[2]
Makinde, O.D. (2013) Effects of Viscous Dissipation and Newtonian Heating on Boundary-Layer Flow of Nanofluids over a Flat Plate. International Journal of Numerical Methods for Heat & Fluid Flow, 23, 1291-1303. https://doi.org/10.1108/HFF-12-2011-0258
[3]
Mustafa, M., Hayat, T. and Obaidat, S. (2013) Boundary Layer Flow of a Nanofluid over an Exponentially Stretching Sheet with Convective Boundary Conditions. International Journal of Numerical Methods for Heat & Fluid Flow, 23, 945-959. https://doi.org/10.1108/HFF-09-2011-0179
[4]
Kuznetsov, A. and Nield, D. (2010) Natural Convective Boundary-Layer Flow of a Nano-fluid past a Vertical Plate. International Journal of Thermal Sciences, 49, 243-247. https://doi.org/10.1016/j.ijthermalsci.2009.07.015
[5]
Khan, W.A. and Pop, I. (2010) Boundary-Layer Flow of a Nanofluid past a Stretching Sheet. International Journal of Heat and Mass Transfer, 53, 2477-2483. https://doi.org/10.1016/j.ijheatmasstransfer.2010.01.032
[6]
Bachok, N., Ishak, A. and Pop, I. (2010) Boundary Layer Flow of Nanofluids over a Moving Surface in a Flowing Fluid. International Journal of Thermal Sciences, 49, 1663-1668. https://doi.org/10.1016/j.ijthermalsci.2010.01.026
[7]
Sun, Q. and Pop, I. (2011) Free Convection in a Triangle Cavity Filled with a Porous Medium Saturated with Nanofluids with Flush Mounted Heater on the Wall. International Journal of Thermal Sciences, 50, 2141-2153. https://doi.org/10.1016/j.ijthermalsci.2011.06.005
[8]
Ferdows, M., Khan, M.S., Bég, O.A., Alam, M.M. and Azad, M.A.K. (2013) Numerical Study of Transient Magnetohydrodynamic Radiative Free Convection Nanofluid Flow from a Stretching Permeable Surface. Journal of Process Mechanical Engineering, 1-16.
[9]
Nadeem, S. and Lee, C. (2012) Boundary Layer Flow of Nanofluid over an Exponentially Stretching Surface. Nanoscale Research Letters, 7, 94. https://doi.org/10.1186/1556-276X-7-94
[10]
Na, T.Y. and Pop, I. (1996) Unsteady Flow past a Stretching Sheet. Mechanics Research Communications, 23, 413-422. https://doi.org/10.1016/0093-6413(96)00040-7
[11]
Bondareva, N.S., Sheremet, M.A. and Pop, I. (2015) Magnetic Field Effect on the Unsteady Natural Convection in a Right-Angle Trapezoidal Cavity Filled with a Nanofluid. International Journal of Numerical Methods for Heat & Fluid Flow, 25, 1924-1946. https://doi.org/10.1108/HFF-07-2014-0236
[12]
Ferdows, M., Khan, M.S., Alam, M.M. and Sun, S. (2012) MHD Mixed Convective Boundary Layer Flow of a Nanofluid through a Porous Medium Due to an Exponentially Stretching Sheet. Mathematical Problems in Engineering, 2012, Article ID: 408528.
[13]
Haile, E. and Shankar, B. (2014) Heat and Mass Transfer in the Boundary Layer of Unsteady Viscous Nanofluid along a Vertical Stretching Sheet. Journal of Computational Engineering, 2014, Article ID: 345153. https://doi.org/10.1155/2014/345153
[14]
Shehzad, S.A., Abdullah, Z., Abbasi, F.M., Hayat, T. and Alsaedi, A. (2016) Field Effect in Three-Dimensional Flow of an Oldroyd-B Nanofluid over a Radiative Surface. Journal of Magnetism and Magnetic Materials, 399, 97-108. https://doi.org/10.1016/j.jmmm.2015.09.001
[15]
Kuznetsove, A.V. (2006) Investigation of the Onset of Bioconvection in a Suspension of Oxytactic Microorganisms Subjected to High-Frequency Vertical Vibration. Theoretical and Computational Fluid Dynamics, 20, 73-87. https://doi.org/10.1007/s00162-006-0007-0
[16]
Mahdy, A. (2016) Natural Convection Boundary Layer Flow Due to Gyrotactic Microorganisms about Vertical Cone in Porous Media Saturated by a Nanofluid. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38, 67-76. https://doi.org/10.1007/s40430-015-0313-9
[17]
Hady, F.M., Mohamed, R.A., Mahdy, A. and Abo Zaid, O.A. (2016) Non-Darcy Natural Convection Boundary Layer Flow over a Vertical Cone in Porous Media Saturated with a Nanofluid Containing Gyrotactic Microorganisms with a Convective Boundary Condition. Journal of Nanofluids, 5, 765-773. https://doi.org/10.1166/jon.2016.1256
[18]
Uddin, M.J., Khan, W.A. and Ismail, A.I. (2012) Effect of Dissipation on Free Convective Flow of a Non-Newtonian Nanofluid in a Porous Medium with Gyrotactic Microorganisms. Journal of Nanoengineering and Nanosystems, 227, 11-18.
[19]
Kuznetsove, A.V. and Avramenko, A.A. (2003) Stability Analysis of Bioconvection of Gyrotactic Motile Microorganisms in a Fluid Saturated Porous Medium. Transport in Porous Media, 53, 95-104. https://doi.org/10.1023/A:1023582001592
[20]
Kuznetsov, A.V. (2006) The Onset of Thermo-Bioconvection in a Shallow Fluid Saturated Porous Layer Heated from Below in a Suspension of Oxytactic Microorganisms. European Journal of Mechanics—B/Fluids, 25, 223-233. https://doi.org/10.1016/j.euromechflu.2005.06.003
[21]
Mutuku, W.N. and Makinde, O.D. (2014) Hydromagnetic Bioconvection of Nanofluid over a Permeable Vertical Plate Due to Gyrotactic Microorganisms. Computers & Fluids, 95, 88-97. https://doi.org/10.1016/j.compfluid.2014.02.026
[22]
Khan, W.A. and Makindem, O.D. (2014) MHD Nanofluid Bioconvection Due to Gyrotactic Microorganisms over a Convectively Heat Stretching Sheet. International Journal of Thermal Sciences, 81, 118-124. https://doi.org/10.1016/j.ijthermalsci.2014.03.009
[23]
Jashim Uddin, M., Kabir, M.N. and Anwar Bégd, O. (2016) Computational Investigation of Stefan Blowing and Multiple-Slip Effects on Buoyancy-Driven Bioconvection Nanofluid Flow with Microorganisms. International Journal of Heat and Mass Transfer, 95, 116-130. https://doi.org/10.1016/j.ijheatmasstransfer.2015.11.015
[24]
Raees, A., Xu, H. and Liao, S. (2015) Unsteady Mixed Nano-Bioconvection Flow in a Horizontal Channel with Its Upper Plate Expanding or Contracting. International Journal of Heat and Mass Transfer, 86, 174-182. https://doi.org/10.1016/j.ijheatmasstransfer.2015.03.003
[25]
Khan, M.S., Karim, I., Ali, L.E. and Islam, A. (2012) Unsteady MHD Free Convection Boundary-Layer Flow of a Nanofluid along a Stretching Sheet with Thermal Radiation and Viscous Dissipation Effects. International Nano Letters, 2, 24. https://doi.org/10.1186/2228-5326-2-24
