# BIOCONVECTION HEAT TRANSFER OF A NANOFLUID OVER A STRETCHING SHEET WITH VELOCITY SLIP AND TEMPERATURE JUMP

## Main Article Content

## Abstract

This paper presents an investigation for bioconvection heat transfer of a nanofluid containing gyrotactic microorganisms over a stretching sheet, in which the effects of radiation, velocity slip and temperature jump are taken into account. The nonlinear governing equations are reduced into four ordinary differential equations by similarity transformations and solved by Homotopy Analysis Method (HAM), which is verified with numerical results in good agree. Results indicate that the density of motile microorganisms and gyrotactic microorganisms increase with bioconvection Rayleigh number, while decrease with increasing in bioconvection Péclet number and bioconvection Lewis number. It is also found that the Nusselt number, Sherwood number and gyrotactic microorganisms density depend strongly on the buoyancy, nanofluids and bioconvection parameters.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2132>. Date accessed: 14 dec. 2017. doi: https://doi.org/10.2298/TSCI150424128S.

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Accepted 2017-03-13

Published 2017-03-13

## References

[2] Nazar, R., et al., Unsteady Boundary Layer Flow in the Region of the Stagnation-point on a Stretching Sheet, International Journal of Engineering Science, 42 (2004), pp. 1241-1253

[3] Buongiorno, J., Convective Transport in Nanofluids, ASME Journal of Heat Transfer, 128 (2006), pp. 240-251

[4] Chamkha, A. J., Ismael, M.A., Conjugate Heat Transfer in a Porous Cavity Filled with Nanofluids and Heated by a Triangular Thick Wall, International Journal of Thermal Sciences, 67 (2013), pp. 135-151

[5] Xu, H., et al., Analysis of Mixed Convection Flow of a Nanofluid in a Vertical Channel with the Buongiorno Mathematical Model, International Communications in Heat and Mass Transfer, 44 (2013), pp. 15-22

[6] Rahman, M. M., et al., The Role of a Convective Surface in Models of the Radiative Heat Transfer in Nanofluids, Nuclear Engineering and Design, 275 (2014), pp. 382-392

[7] Alam, M. S., Hossain, S. C., Effects of Viscous Dissipation and Joule Heating on Hydromagnetic Forced Convective Heat and Mass Transfer Flow of a Nanofluid along a Nonlinear Stretching Surface with Convective Boundary Condition, Journal of Engineering e-Transaction, 8 (1), pp. 01-09

[8] Kuznetsov, A. V., Nield, D. A., Natural Convective Boundary-layer Flow of a Nanofluid past a Vertical Plate, International Journal of Thermal Science, 49 (2010), pp. 243-247

[9] Makinde, O. D., Aziz, A., Boundary Layer Flow of a Nanofluid past a Stretching Sheet with a Convective Boundary Condition, International Journal of Thermal Sciences, 50 (2011), pp. 1326-1332

[10] Dulal, P., Combined Effects of Non-uniform Heat Source/Sink and Thermal Radiation on Heat Transfer over an Unsteady Stretching Permeable Surface, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), pp. 1890-1904

[11] Anbuchezhian, N., et al., Thermophoresis and Brownian Motion Effects on Boundary-Layer Flow of a Nanofluid in the Presence of Thermal Stratification Due to Solar Energy, Applied Mathematics and Mechanics, 33 (2012), pp. 765-780

[12] Mushtaq, A., et al., Nonlinear Radiative Heat Transfer in the Flow of Nanofluid Due to Solar Energy: A Numerical Study, Journal of the Taiwan Institute of Chemical Engineers, 45 (2014), pp. 1176-1183

[13] Malvandi, A., et al., Slip Effects on Unsteady Stagnation Point Flow of a Nanofluid over a Stretching Sheet, Powder Technology, 253 (2014), pp. 377–384

[14] Behseresht, A., et al., Natural-convection Heat and Mass Transfer from a Vertical Cone in Porous Media Filled with Nanofluids Using the Practical Ranges of Nanofluids Thermo-physical Properties, Chemical Engineering Research and Design, 92 (2014), pp. 447-452

[15] Noghrehabadi, A., et al., Analyze of Fluid Flow and Heat Transfer of Nanofluids over a Stretching Sheet near the Extrusion Slit, Computers & Fluids, 100 (2014), pp. 227-236

[16] Rahman, M.M., et al., Boundary Layer Flow of a Nanofluid past a Permeable Exponentially Shrinking/Stretching Surface with Second Order Slip Using Buongiorno’s Model, International Journal of Heat and Mass Transfer,77 (2014), pp. 1133-1143.

[17] Kuznetsov, A. V., Non-oscillatory and Oscillatory Nanofluid Bio-thermal Convection in a Horizontal Layer of Finite Depth, European Journal of Mechanics-B/Fluids, 30 (2011), pp. 156-165

[18] Khan, W. A., Makinde, O. D., MHD Nanofluid Bioconvection Due to Gyrotactic Microorganisms over a Convectively Heat Stretching Sheet, International Journal of Thermal Sciences, 81 (2014), pp. 118-124

[19] Xu, H., Pop, I., Fully Developed Mixed Convection Flow in a Horizontal Channel Filled by a Nanofluid Containing Both Nanoparticles and Gyrotactic Microorganisms, European Journal of Mechanics B/Fluids, 46 (2014), pp. 37-45

[20] Khan, W. A., et al., MHD Boundary Layer Flow of a Nanofluid Containing Gyrotactic Microorganisms past a Vertical Plate with Navier Slip, International Journal of Heat and Mass Transfer, 74 (2014), pp. 285–291

[21] Xu, H., Pop, I., Mixed Convection Flow of a Nanofluid over a Stretching Surface With Uniform Free Stream in the Presence of both Nanoparticles and Gyrotactic Microorganisms, International Journal of Heat and Mass Transfer, 75 (2014), pp. 610-623

[22] Zheng, L.C., et al., MHD Flow and Heat Transfer over a Porous Shrinking Surface with Velocity Slip and Temperature Jump, Mathematical and Computer Modelling, 56(5) (2012), pp. 133-144

[23] Liao S. J., An approximate solution technique not depending on small parameters: a special example, International Journal of Non-Linear Mechanics, 30(3) (1995), pp. 371-380

[24] Liao S. J., Homotopy analysis method: a new analytic method for nonlinear problems, Applied Mathematics and Mechanics, 19(10) (1998), pp. 957-962

[25] Liao S. J., Beyond perturbation: introduction to the homotopy analysis method [M], CRC press, 2003

[26] Liao S. J., On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation, 147(2) (2004), pp. 499-513

[27] Liao S. J., Notes on the homotopy analysis method: some definitions and theorems, Communications in Nonlinear Science and Numerical Simulation, 14(4) (2009), pp. 983-997

[28] Zheng L.C., et al., Flow and Radiation Heat Transfer of a Nanofluid over a Stretching Sheet with Velocity Slip and Temperature Jump in Porous Medium, Journal of the Franklin Institute, 350 (2013), pp. 990-1007