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Heat and Mass Transfer in Three-Dimensional Flow of an Oldroyd-B Nanofluid with Gyrotactic Micro-Organisms

This paper discusses the three-dimensional flow of the gyrotactic bioconvection of an Oldroyd-B nanofluid over a stretching surface. Theory of microorganisms is utilized to stabilize the suspended nanoparticles through bioconvection induced by the effects of buoyancy forces. Analytic solution for the governing nonlinear equations is obtained by using homotopy analysis method (HAM). The effects of involved parameters on velocity, temperature, nanoparticles concentration, and density of motile microorganisms are discussed graphically. The local Nusselt, Sherwood, and motile microorganisms numbers are also analyzed graphically. Several known results have been pointed out as the particular cases of the present analysis. It is found that the non-Newtonian fluid parameters, i.e., relaxation time parameterβ1and retardation time parameterβ2, have opposite effects on the velocity profile. The velocity of the fluid and boundary layer thickness decreases for increasing relaxation time while it decreases for increasing retardation time effects.