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Research Papers: Porous Media

Magnetohydrodynamics and Soret Effects on Bioconvection in a Porous Medium Saturated With a Nanofluid Containing Gyrotactic Microorganisms

[+] Author and Article Information
S. Shaw, P. Sibanda

School of Mathematics,
Statistics & Computer Science,
University of KwaZulu-Natal, P/Bag X01,
Scottsville, Pietermaritzburg 3209,
South Africa

A. Sutradhar

Department of Mathematics,
Indian Institute of Technology,
Kharagpur 721 302, India

P. V. S. N. Murthy

Department of Mathematics,
Indian Institute of Technology,
Kharagpur 721 302, India
e-mail: pvsnm@maths.iitkgp.ernet.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 4, 2012; final manuscript received October 23, 2013; published online February 26, 2014. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 136(5), 052601 (Feb 26, 2014) (10 pages) Paper No: HT-12-1647; doi: 10.1115/1.4026039 History: Received December 04, 2012; Revised October 23, 2013

We investigate the bioconvection of gyrotactic microorganism near the boundary layer region of an inclined semi infinite permeable plate embedded in a porous medium filled with a water-based nanofluid containing motile microorganisms. The model for the nanofluid incorporates Brownian motion, thermophoresis, also Soret effect and magnetic field effect are considered in the study. The governing partial differential equations for momentum, heat, solute concentration, nanoparticle volume fraction, and microorganism conservation are reduced to a set of nonlinear ordinary differential equations using similarity transformations and solved numerically. The effects of the bioconvection parameters on the thermal, solutal, nanoparticle concentration, and the density of the micro-organisms are analyzed. A comparative analysis of our results with previously reported results in the literature is given. Some interesting phenomena are observed for the local Nusselt and Sherwood number. It is shown that the Péclet number and the bioconvection Rayleigh number highly influence the local Nusselt and Sherwood numbers. For Péclet numbers less than 1, the local Nusselt and Sherwood number increase with the bioconvection Lewis number. However, both the heat and mass transfer rates decrease with bioconvection Lewis number for higher values of the Péclet number.

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References

Choi, S. U. S., 1995, “Enhancing Thermal Conductivity of Fluids With Nanoparticles,” Developments and Applications of Non-Newtonian Flows, Vol. 99, D. A.Siginerm, H. P.Wang, eds., ASME, New York.
Ebrahimi, S., Sabbaghzadeh, J., Lajevardi, M., and Hadi, I., 2010, “Cooling Performance of a Microchannel Heat Sink With Nanofluids Containing Cylindrical Nanoparticles (Carbon Nanotubes),” Heat Mass Transfer, 46, pp. 549–553. [CrossRef]
Wu, X., Wu, H., and Cheng, P., 2009, “Pressure Drop and Heat Transfer of Al2O3–H2O Nanofluids Through Silicon Microchannels,” J. Micromech. Microeng., 19, p. 105020. [CrossRef]
Do, K. H., and Jang, S. P., 2010, “Effect of Nanofluids on the Thermal Performance of a Flat Micro Heat Pipe With A Rectangular Grooved Wick,” Int. J. Heat Mass Transfer, 53, pp. 2183–2192. [CrossRef]
Fan, X., Chen, H., Ding, Y., Plucinski, P. K., and Lapkin, A. A., 2008, “Potential of Nanofluids to Further Intensify Microreactors,” Green Chem., 10, pp. 670–677. [CrossRef]
Das, S. K., Choi, S. U. S., Wu, W., and Pradeep, T., 2007, Nanofluids: Science and Technology, Wiley, New York.
Wager, H., 1911, “On the Effect of Gravity Upon the Movements and Aggregation of Euglena viridis, Ehrb., and Other Micro-Organisms,” Philos. Trans. R. Soc. London, Ser. B, 201, pp. 333–390. [CrossRef]
Platt, J. R., 1961, “Bioconvection Pattern in Cultures of Free-Swimming Organism,” Science, 133, pp. 1766–1767. [CrossRef] [PubMed]
Plesset, M. S., and Winet, H., 1974, “Bioconvection Patterns in Swimming Micro-Organism Cultures As an Example of Rayleigh-Taylor Instability,” Nature, 248, pp. 441–443. [CrossRef] [PubMed]
Pedley, T. J., Hill, N. A., and Kessler, J. O., 1988, “The Growth of Bioconvection Patterns in a Uniform Suspension of Gyrotactic Micro-Organisms,” J. Fluid Mech., 195, pp. 223–338. [CrossRef] [PubMed]
Pedley, T. J., and Kessler, J. O., 1992, “Hydrodynamic Phenomena in Suspensions of Swimming Micro-Organisms,” Annu. Rev. Fluid Mech., 24, pp. 313–358. [CrossRef]
Kuznetsov, A. V., and Avramenko, A. A., 2004, “Effect of Small Particles on the Stability of Bioconvection in a Suspension of Gyrotactic Microorganisms in a Layer of Finite Depth,” Int. Commun. Heat Mass Transfer, 31, pp. 1–10. [CrossRef]
Geng, P., and Kuznetsov, A. V., 2005, “Introducing the Concept of effective diffusivity to Evaluate the Effect of Bioconvection on Small Solid Particles,” Int. J. Transp. Phenom., 7, pp. 321–338.
Kuznetsov, A. V., and Geng, P., 2005, “The Interaction of Bioconvection Caused by Gyrotactic Micro-Organisms and Settling of Small Solid Particles,” Int. J. Numer. Methods Heat Fluid Flow, 15, pp. 328–347. [CrossRef]
Kuznetsov, A. V., 2011, “Non-Oscillatory and Oscillatory Nanofluid Bio-Thermal Convection in a Horizontal Layer of Finite Depth,” Eur. J. Mech. B/Fluids, 30, pp. 156–165. [CrossRef]
Kuznetsov, A. V., 2012, “Nanofluid Bioconvection: Interaction of Microorganisms Oxytactic Upswimming, Nanoparticle Distribution, and Heating/Cooling From Below,” Theor. Comput. Fluid Dyn., 26, pp. 291–310. [CrossRef]
Anoop, K. B., Sundararajan, T., and Das, S. K., 2009, “Effect of Particel Size on the Convective Heat Transfer in Nanofluid in the Developing Region,” Int. J. Heat Mass Transfer, 52, pp. 2189–2195. [CrossRef]
Kohno, M., Yamazaki, M., Kimura, I., and Wada, M., 2000, “Effect of Static Magnetic Fields on Bacteria: Streptococcus mutans, Staphylococcus aureus, and Escherichia coli,” Pathophysiology, 7, pp. 143–148. [CrossRef] [PubMed]
Strašák, L., Vetterl, V., and Šmarda, J., 2002, “Effects of Low-Frequency Magnetic Fields on Bacteria Escherichia coli,” Bioelectrochem, 55, pp. 161–164. [CrossRef]
Fojt, L., Strašák, L., Vetterl, V., and Šmarda, J., 2004, “Comparison of the Low-Frequency Magnetic Field Effects on Bacteria Escherichia coli, Leclercia adecarboxylata and Staphylococcus aureus,” Bioelectrochem., 63, pp. 337–341. [CrossRef]
Sarkar, A. K., Georgiou, G., and Sharma, M. M., 1994, “Transport of Bacteria in Porous Media: I. An Experimental Investigation,” Biotech. Bioengng., 44, pp. 489–497. [CrossRef]
Sarkar, A. K., Georgiou, G., and Sharma, M. M., 1994, “Transport of Bacteria in Porous Media: II. A Model for Convective Transport and Growth,” Biotech. Bioengng., 44, pp. 499–508. [CrossRef]
Hill, N. A., and Bees, M. A., 2002, “Taylor Dispersion of Gyrotactic Swimming Micro-Organisms in a Linear Flow,” Phys. Fluids, 14, pp. 2598–2605. [CrossRef]
Kuznetsov, A. V., 2010, “The Onset of Nanofluid Bioconvection in a Suspension Containing Both Nanoparticles and Gyrotactic Microorganisms,” Int. Commun. Heat Mass Transfer, 37, pp. 1421–1425. [CrossRef]
Kuznetsov, A. V., 2011, “Bio-Thermal Convection Induced by Two Different Species of Microorganisms,” Int. Commun. Heat Mass Transfer, 38, pp. 548–553. [CrossRef]
Aziz, A., Khan, W. A., and Pop, I., 2012, “Free Convection Boundary Layer Flow Past a Horizontal Flate Plate Embedded in Porous Medium Filled by Nanofluid Containing Gyrotactic Microorganisms,” Int. J. Thermal Sci., 56, pp. 48–57. [CrossRef]
Hillesdon, A. J., and Pedley, T. J., 2010, “Instability of Uniform Micro-Organism Suspensions Revisited,” J. Fluid Mech.647, pp. 335–359. [CrossRef]
Kuznetsov, A. V., 2011, “Nanofluid Bio-Thermal Convection: Simultaneous Effects of Gyrotactic and Oxytactic Microorganisms,” Fluid Dyn. Res., 43, p. 055505. [CrossRef]
Nield, D. A., and Kuznetsov, A. V., 2009, “Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid,” Int. J. Heat Mass Transfer, 52, pp. 5796–5801. [CrossRef]
Kuznetsov, A. V., and Nield, D. A., 2010, “The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium,” Transp. Porous Media, 85, pp. 941–951. [CrossRef]
Kuznetsov, A. V., 2012, “Nanofluid Bioconvection in Porous Media: Oxytactic Microorganisms,” J. Porous Media, 15, pp. 233–248. [CrossRef]
Gorla, R. S. R., and Chamkha, A., 2011, “Natural Convective Boundary Layer Flow Over a Horizontal Plate Embedded in a Porous Medium Saturated With A Nanofluid,” J. Mod. Phys., 2, pp. 62–71. [CrossRef]
Nield, D. A., and Kuznetsov, A. V., 2009, “The Cheng-Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid,” Int. J. Heat Mass Transfer, 52, pp. 5792–5795. [CrossRef]
Nield, D. A., and Kuznetsov, A. V., 2011, “The Cheng-Minkowycz Problem for the Double-Diffusive Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid,” Int. J. Heat Mass Transfer, 54, pp. 374–378. [CrossRef]
Kuznetsov, A. V., 2005, “Thermo-Bioconvection in a Suspension of Oxytactic Bacteria,” Int. Commun. Heat Mass Transfer, 32, pp. 991–999. [CrossRef]
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,” Eur. J. Mech. B/Fluids, 25, pp. 223–233. [CrossRef]
Kameswaran, P. K., Narayana, M., Sibanda, P., and Murthy, P. V. S. N., 2013, “Hydromagnetic Nanofluid Flow Due to a Stretching or Shrinking Sheet With Viscous Dissipation and Chemical Reaction Effects,” Int. J. Heat Mass Transfer, 55, pp. 7587–7595. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of the present problem

Grahic Jump Location
Fig. 2

The velocity profiles for different (a) Ha,fw (Nr = 1,Nc = 0.1,Rb = 1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Le = 1,Lb = 5,Pe = 3,τ0 = 1) (b) Nr,Rb (Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Le = 1,Lb = 5,Pe = 3,τ0 = 1,fw = 0.5) (c) Sr,Ln (Ha = 0.5,Nr = 1,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Lb = 5,Pe = 3,τ0 = 1,fw = 0.5) (d) Pe,Lb (Ha = 0.5,Nc = 0.1,Nr = 1,Rb = 1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Le = 1,τ0 = 1,fw = 0.5)

Grahic Jump Location
Fig. 3

The temperature profiles for different (a) Ha,fw (Nr = 1,Rb = 1) (b) Nr,Rb (Ha = 0.5,fw = 0.5) with Nc = 0.1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Le = 1,Lb = 5,Pe = 3,τ0 = 1

Grahic Jump Location
Fig. 4

The effect of the parameters Nt and Le on (a) temperature profiles (b) nanoparticle concentration profiles with Nc = 0.1,Nr = 0.1,Rb = 0.1,Nb = 0.1,Nt = 0.1,Ln = 1,Sr = 0.8,Lb = 1,Pe = 1,τ0 = 1

Grahic Jump Location
Fig. 5

The solute concentration profiles for different (a) Ha,fw (Sr = 0.8,Ln = 1) (b) Sr,Ln (Ha = 0.5,fw = 0.5) with Nc = 0.1,Nr = 1,Rb = 1,Nb = 0.1,Nt = 0.1,Le = 1,Lb = 5,Pe = 3,τ0 = 1

Grahic Jump Location
Fig. 6

The microorganism concentration profiles for different (a) Nt,Le (Pe = 1,Lb = 1,Rb = 0.1,Nr = 0.1) (b) Pe,Lb (Nt = 0.1,Le = 1,Nr = 1,Sr = 0.8,Ln = 1) with Ha = 0.5,Nc = 0.1,Nb = 0.1,Sr = 0.8

Grahic Jump Location
Fig. 7

Local Nusselt number for different (a) Nr,Sr (Pe = 3,Rb = 1) (b) Pe,Rb (Nr = 1,Sr = 0.8) with Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Ln = 1,Lb = 1,τ0 = 1

Grahic Jump Location
Fig. 8

Local Sherwood number for different (a) Nr,Sr (Pe = 3,Rb = 1) (b) Pe,Rb (Nr = 1,Sr = 0.8) with Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Ln = 1,Lb = 1,τ0 = 1

Grahic Jump Location
Fig. 9

The local nanoparticle volume fraction for different (a) Nr,Sr (Pe = 3,Rb = 1) (b) Pe,Rb (Nr = 1,Sr = 0.8) with Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Ln = 1,Lb = 1,τ0 = 1

Grahic Jump Location
Fig. 10

Local density of motile microorganisms for different (a) Pe,Rb with Ha = 0.5,Nc = 0.1,Nb = 0.1,Nt = 0.1,Le = 1,Ln = 1,Lb = 1,τ0 = 1

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