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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.

Nanofluids are produced by suspending nanoparticles made up of metal carbides, nitrides and carbon nanotubes in heat transferring fluids (e.g. water, oil, ethylene glycol, polymer solution and Bio-fluids), the thermal conductivity of these fluids plays a crucial role on the heat transfer coefficient between the heat transfer medium and the heat transfer surface. Nanoparticles are the particles (that have the random movement in the nanofluid called Brownian motion) with diameter less than 100 nm. By pointing out that the use of solid particles as an additive suspended into the base fluids is a manner for increasing the heat transfer rate. Thus, nanofluid is a highly effective method of enhancing heat transfer. Gorla and Hossain [

MHD (Magneto-hydrodynamics) is the science of the motion of electrically conducting fluids under the influence of applied magnetic forces [

Bioconvection is a phenomenon in which physical laws that govern smaller scales lead to a phenomenon visible on a larger scale [

Consider a tow-dimensional unsteady thermo bioconvection laminar boundary layer flow of a viscous incompressible, electrically conducting nanofluid containing gyrotactic microorganisms past a vertical stretching sheet under the influence of a uniform transversely applied magnetic felid and viscous dissipation. Bioconvection induced flow only take place in a dilute suspension of nanoparticles. The presence of nanoparticles is assumed to have no effect on the direction in which microorganisms swim and on their swimming velocity. We choose the coordinate system

the

Using the Oberbeck?Boussinesq approximation, the boundary-layer approximations of the continuity, momentum, energy, nanoparticle concentration and conservation for microorganisms equations are:

where

The initial and boundary conditions are:

By substituting the following dimensionless quantities:

into Equations (1)-(5) gives the following dimensionless equations:

where the Grashof number

The dimensionless form of the initial and boundary conditions are:

The dimensionless form of the local Nusselt number, density number of the motile microorganisms and Skin-friction coefficient, respectively is defined as:

where, the local Reynolds number

The explicit finite difference method is used to solve the unsteady nonlinear coupled partial differential Equations (8)-(12) with initial and boundary conditions (13) and (14). The dimensionless equations are solved for the dependent variables

tained. Let

subject to initial and boundary conditions

where

where

Parameters | Khan et al. [ | Present results |
---|---|---|

0.9541 | 0.9541395 | |

0.3667 | 0.3559093 | |

0.1359 | 0.1386993 |

In the following section, the numerical solutions of our problem are discussed and displayed by graphic. The effects of the governing physical parameters on the dimensionlesss velocity, temperature, nanoparticle volume fraction and density of motile microorganisms are illustrated in Figures 2-13.

Figures 2-4 present the effect of magnetic parameter

and bioconvection Rayleigh number

The effects of Grashof number

after

Hady, F.M., Mahdy, A., Mohamed, R.A. and Zaid, O.A.A. (2016) Effects of Viscous Dissipation on Unsteady MHD Thermo Bioconvection Boundary Layer Flow of a Nanofluid Containing Gyrotactic Microorganisms along a Stretching Sheet. World Journal of Mechanics, 6, 505-526. http://dx.doi.org/10.4236/wjm.2016.612035