Hindawi Mathematical Problems in Engineering Volume 2018, Article ID 6790420, 15 pages https://doi.org/10.1155/2018/6790420 Research Article Heat and Mass Transfer in Three-Dimensional Flow of an Oldroyd-B Nanofluid with Gyrotactic Micro-Organisms M. Sulaiman,1,2 Aamir Ali ,1 and S. Islam 2 1 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan 2Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, 23200, Pakistan Correspondence should be addressed to Aamir Ali; aamir
[email protected] Received 10 December 2017; Revised 28 February 2018; Accepted 29 April 2018; Published 6 September 2018 Academic Editor: Efstratios Tzirtzilakis Copyright © 2018 M. Sulaiman et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper discusses the three-dimensional fow of the gyrotactic bioconvection of an Oldroyd-B nanofuid over a stretching surface. Teory of microorganisms is utilized to stabilize the suspended nanoparticles through bioconvection induced by the efects of buoyancy forces. Analytic solution for the governing nonlinear equations is obtained by using homotopy analysis method (HAM). Te efects of involved parameters on velocity, temperature, nanoparticles concentration, and density of motile microorganisms are discussed graphically. Te 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 fuid parameters, i.e., relaxation time parameter �1 and retardation time parameter �2, have opposite efects on the velocity profle.