Numerical Approach to a Mathematical Modeling of Bioconvection Due to Gyrotactic Micro-Organisms over a Nonlinear Inclined Stretching Sheet
The water-based bioconvection of a nanofluid
containing motile gyrotactic micro-organisms over nonlinear
inclined stretching sheet has been investigated. The governing
nonlinear boundary layer equations of the model are reduced to a
system of ordinary differential equations via Oberbeck-Boussinesq
approximation and similarity transformations. Further, the modified
set of equations with associated boundary conditions are solved using
Finite Element Method. The impact of various pertinent parameters
on the velocity, temperature, nanoparticles concentration, density of
motile micro-organisms profiles are obtained and analyzed in details.
The results show that with the increase in angle of inclination δ,
velocity decreases while temperature, nanoparticles concentration,
a density of motile micro-organisms increases. Additionally, the
skin friction coefficient, Nusselt number, Sherwood number, density
number are computed for various thermophysical parameters. It
is noticed that increasing Brownian motion and thermophoresis
parameter leads to an increase in temperature of fluid which results
in a reduction in Nusselt number. On the contrary, Sherwood number
rises with an increase in Brownian motion and thermophoresis
parameter. The findings have been validated by comparing the
results of special cases with existing studies.
[1] E. M. Abo-Eldahab, M. A. E. Aziz, Blowing/suction effect on
hydromagnetic heat transfer by mixed convection from an inclined
continuously stretching surface with internal heat generation/absorption,
International Journal of Thermal Sciences, vol. 43 (7), 2004, pp. 709 –
719.
[2] B. C. Sakiadis, Boundary-layer behavior on continuous solid surfaces:
I. boundary-layer equations for two-dimensional and axisymmetric flow,
AIChE Journal, vol. 7 (1), 1961, pp. 26–28.
[3] P. S. Gupta, A. S. Gupta, Heat and mass transfer on a stretching sheet
with suction or blowing, The Canadian Journal of Chemical Engineering,
vol. 55 (6), 1977, pp. 744–746.
[4] E. M. A. Elbashbeshy, Heat transfer over a stretching surface with
variable surface heat flux, Journal of Physics D: Applied Physics,
vol. 31 (16), 1998, pp. 19-51.
[5] C.-K. Chen, M.-I. Char, Heat transfer of a continuous, stretching
surface with suction or blowing, Journal of Mathematical Analysis and
Applications, vol. 135 (2), 1988, pp. 568 – 580.
[6] T. C. Chiam, Micropolar fluid flow over a stretching sheet, ZAMM
- Journal of Applied Mathematics and Mechanics / Zeitschrift
fr Angewandte Mathematik und Mechanik, vol. 62 (10), 1982,
pp. 565–568.
[7] I. Hassanien, R. S. R. Gorla, Mixed convection boundary layer flow
of a micropolar fluid near a stagnation point on a horizontal cylinder,
International Journal of Engineering Science, vol. 28 (2), 1990, pp. 153
– 161.
[8] N. Kelson, A. Desseaux, Effect of surface conditions on flow of a
micropolar fluid driven by a porous stretching sheet, International
Journal of Engineering Science vol. 39 (16), 2001, pp. 1881 – 1897.
[9] W. Khan, I. Pop, Boundary-layer flow of a nanofluid past a stretching
sheet, International Journal of Heat and Mass Transfer, vol. 53 (1112),
2010, pp. 2477 – 2483.
[10] N. Hill, T. Pedley, Bioconvection, Fluid Dynamics Research,
vol. 37 (12), 2005, pp. 1 – 20, biofluiddynamics.
[11] A. Avramenko, A. Kuznetsov, Stability of a suspension of gyrotactic
microorganisms in superimposed fluid and porous layers, International
Communications in Heat and Mass Transfer, vol. 31 (8), 2004, pp. 1057
– 1066.
[12] T. J. Pedley, N. A. Hill, J. O. Kessler (1988), The growth
of bioconvection patterns in a uniform suspension of gyrotactic
micro-organisms, Journal of Fluid Mechanics, vol. 195, 1988,
pp. 223237.
[13] S. Ghorai, N. A. Hill (2000), Wavelengths of gyrotactic plumes in
bioconvection, Bulletin of Mathematical Biology, vol. 62 (3), 2000,
pp. 429–450. [14] Li H, Liu S, Dai Z, Bao J, Yang X, Applications of nanomaterials
in electrochemical enzyme biosensors, Sensors, vol. 9, 2009,
pp. 8547–8561.
[15] H. S. Z. A. Munir, J. Wang, Dynamics of capturing process of multiple
magnetic nanoparticles in a flow through microfluidic bioseparation
system, IET Nanobiotechnol, vol. 3, 2009, pp. 55–64.
[16] D. Huh, B. D. Matthews, A. Mammoto, M. Montoya-Zavala, H. Y.
Hsin, D. E. Ingber, Reconstituting organ-level lung functions on a chip,
Science, vol. 328 (5986), 2010, pp. 1662–1668.
[17] A. Kuznetsov, The onset of nanofluid bioconvection in a suspension
containing both nanoparticles and gyrotactic microorganisms,
International Communications in Heat and Mass Transfer, vol. 37 (10),
2010, pp. 1421 – 1425.
[18] A. Kuznetsov, D. Nield, Double-diffusive natural convective
boundary-layer flow of a nanofluid past a vertical plate, International
Journal of Thermal Sciences, vol. 50 (5), 2011, pp. 712 – 717.
[19] A. Aziz, W. Khan, I. Pop, Free convection boundary layer flow past
a horizontal flat plate embedded in porous medium filled by nanofluid
containing gyrotactic microorganisms, International Journal of Thermal
Sciences, vol. 56, 2012, pp. 48 – 57.
[20] W. Khan, O. Makinde, {MHD} nanofluid bioconvection due to
gyrotactic microorganisms over a convectively heat stretching sheet,
International Journal of Thermal Sciences, vol. 81, 2014, pp. 118 –
124.
[21] S. A. M. Mehryan, F. Moradi Kashkooli, M. Soltani, K. Raahemifar,
Fluid flow and heat transfer analysis of a nanofluid containing motile
gyrotactic micro-organisms passing a nonlinear stretching vertical sheet
in the presence of a non-uniform magnetic field; numerical approach,
PLOS ONE, vol. 11 (6), 2016, pp. 1–32.
[22] P. Rana, R. Bhargava, Flow and heat transfer of a nanofluid over a
nonlinearly stretching sheet: A numerical study, Communications in
Nonlinear Science and Numerical Simulation, vol. 17 (1), 2012, pp. 212
– 226.
[23] W. N. Mutuku, O. D. Makinde, Hydromagnetic bioconvection
of nanofluid over a permeable vertical plate due to gyrotactic
microorganisms, Computers & Fluids, vol. 95, 2014, pp. 88 – 97.
[1] E. M. Abo-Eldahab, M. A. E. Aziz, Blowing/suction effect on
hydromagnetic heat transfer by mixed convection from an inclined
continuously stretching surface with internal heat generation/absorption,
International Journal of Thermal Sciences, vol. 43 (7), 2004, pp. 709 –
719.
[2] B. C. Sakiadis, Boundary-layer behavior on continuous solid surfaces:
I. boundary-layer equations for two-dimensional and axisymmetric flow,
AIChE Journal, vol. 7 (1), 1961, pp. 26–28.
[3] P. S. Gupta, A. S. Gupta, Heat and mass transfer on a stretching sheet
with suction or blowing, The Canadian Journal of Chemical Engineering,
vol. 55 (6), 1977, pp. 744–746.
[4] E. M. A. Elbashbeshy, Heat transfer over a stretching surface with
variable surface heat flux, Journal of Physics D: Applied Physics,
vol. 31 (16), 1998, pp. 19-51.
[5] C.-K. Chen, M.-I. Char, Heat transfer of a continuous, stretching
surface with suction or blowing, Journal of Mathematical Analysis and
Applications, vol. 135 (2), 1988, pp. 568 – 580.
[6] T. C. Chiam, Micropolar fluid flow over a stretching sheet, ZAMM
- Journal of Applied Mathematics and Mechanics / Zeitschrift
fr Angewandte Mathematik und Mechanik, vol. 62 (10), 1982,
pp. 565–568.
[7] I. Hassanien, R. S. R. Gorla, Mixed convection boundary layer flow
of a micropolar fluid near a stagnation point on a horizontal cylinder,
International Journal of Engineering Science, vol. 28 (2), 1990, pp. 153
– 161.
[8] N. Kelson, A. Desseaux, Effect of surface conditions on flow of a
micropolar fluid driven by a porous stretching sheet, International
Journal of Engineering Science vol. 39 (16), 2001, pp. 1881 – 1897.
[9] W. Khan, I. Pop, Boundary-layer flow of a nanofluid past a stretching
sheet, International Journal of Heat and Mass Transfer, vol. 53 (1112),
2010, pp. 2477 – 2483.
[10] N. Hill, T. Pedley, Bioconvection, Fluid Dynamics Research,
vol. 37 (12), 2005, pp. 1 – 20, biofluiddynamics.
[11] A. Avramenko, A. Kuznetsov, Stability of a suspension of gyrotactic
microorganisms in superimposed fluid and porous layers, International
Communications in Heat and Mass Transfer, vol. 31 (8), 2004, pp. 1057
– 1066.
[12] T. J. Pedley, N. A. Hill, J. O. Kessler (1988), The growth
of bioconvection patterns in a uniform suspension of gyrotactic
micro-organisms, Journal of Fluid Mechanics, vol. 195, 1988,
pp. 223237.
[13] S. Ghorai, N. A. Hill (2000), Wavelengths of gyrotactic plumes in
bioconvection, Bulletin of Mathematical Biology, vol. 62 (3), 2000,
pp. 429–450. [14] Li H, Liu S, Dai Z, Bao J, Yang X, Applications of nanomaterials
in electrochemical enzyme biosensors, Sensors, vol. 9, 2009,
pp. 8547–8561.
[15] H. S. Z. A. Munir, J. Wang, Dynamics of capturing process of multiple
magnetic nanoparticles in a flow through microfluidic bioseparation
system, IET Nanobiotechnol, vol. 3, 2009, pp. 55–64.
[16] D. Huh, B. D. Matthews, A. Mammoto, M. Montoya-Zavala, H. Y.
Hsin, D. E. Ingber, Reconstituting organ-level lung functions on a chip,
Science, vol. 328 (5986), 2010, pp. 1662–1668.
[17] A. Kuznetsov, The onset of nanofluid bioconvection in a suspension
containing both nanoparticles and gyrotactic microorganisms,
International Communications in Heat and Mass Transfer, vol. 37 (10),
2010, pp. 1421 – 1425.
[18] A. Kuznetsov, D. Nield, Double-diffusive natural convective
boundary-layer flow of a nanofluid past a vertical plate, International
Journal of Thermal Sciences, vol. 50 (5), 2011, pp. 712 – 717.
[19] A. Aziz, W. Khan, I. Pop, Free convection boundary layer flow past
a horizontal flat plate embedded in porous medium filled by nanofluid
containing gyrotactic microorganisms, International Journal of Thermal
Sciences, vol. 56, 2012, pp. 48 – 57.
[20] W. Khan, O. Makinde, {MHD} nanofluid bioconvection due to
gyrotactic microorganisms over a convectively heat stretching sheet,
International Journal of Thermal Sciences, vol. 81, 2014, pp. 118 –
124.
[21] S. A. M. Mehryan, F. Moradi Kashkooli, M. Soltani, K. Raahemifar,
Fluid flow and heat transfer analysis of a nanofluid containing motile
gyrotactic micro-organisms passing a nonlinear stretching vertical sheet
in the presence of a non-uniform magnetic field; numerical approach,
PLOS ONE, vol. 11 (6), 2016, pp. 1–32.
[22] P. Rana, R. Bhargava, Flow and heat transfer of a nanofluid over a
nonlinearly stretching sheet: A numerical study, Communications in
Nonlinear Science and Numerical Simulation, vol. 17 (1), 2012, pp. 212
– 226.
[23] W. N. Mutuku, O. D. Makinde, Hydromagnetic bioconvection
of nanofluid over a permeable vertical plate due to gyrotactic
microorganisms, Computers & Fluids, vol. 95, 2014, pp. 88 – 97.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:77882", author = "Madhu Aneja and Sapna Sharma", title = "Numerical Approach to a Mathematical Modeling of Bioconvection Due to Gyrotactic Micro-Organisms over a Nonlinear Inclined Stretching Sheet", abstract = "The water-based bioconvection of a nanofluid
containing motile gyrotactic micro-organisms over nonlinear
inclined stretching sheet has been investigated. The governing
nonlinear boundary layer equations of the model are reduced to a
system of ordinary differential equations via Oberbeck-Boussinesq
approximation and similarity transformations. Further, the modified
set of equations with associated boundary conditions are solved using
Finite Element Method. The impact of various pertinent parameters
on the velocity, temperature, nanoparticles concentration, density of
motile micro-organisms profiles are obtained and analyzed in details.
The results show that with the increase in angle of inclination δ,
velocity decreases while temperature, nanoparticles concentration,
a density of motile micro-organisms increases. Additionally, the
skin friction coefficient, Nusselt number, Sherwood number, density
number are computed for various thermophysical parameters. It
is noticed that increasing Brownian motion and thermophoresis
parameter leads to an increase in temperature of fluid which results
in a reduction in Nusselt number. On the contrary, Sherwood number
rises with an increase in Brownian motion and thermophoresis
parameter. The findings have been validated by comparing the
results of special cases with existing studies.", keywords = "Bioconvection, inclined stretching sheet, Gyrotactic
micro-organisms, Brownian motion, thermophoresis, finite element
method.", volume = "12", number = "9", pages = "174-9", }
