title: Influence of viscous dissipation and Joule heating on MHD bio-convection flow over a porous wedge in the presence of nanoparticles and gyrotactic microorganisms.
abstract: BACKGROUND
  The flow over a porous wedge, in the presence of viscous dissipation and Joule heating, has been investigated. The wedge is assumed to be saturated with nanofluid containing gyrotactic microorganisms. For the flow, magneto-hydrodynamic effects are also taken into consideration. The problem is formulated by using the passive control model. The partial differential equations, governing the flow, are transformed into a set of ordinary differential equations by employing some suitable similarity transformations.
  
  
  RESULTS
  A numerical scheme, called Runge-Kutta-Fehlberg method, has been used to obtain the local similarity solutions for the system. Variations in the velocity, temperature, concentration and motile micro-organisms density profiles are highlighted with the help of graphs. The expressions for skin friction coefficient, Nusselt number, Sherwood number and motile micro-organisms density number are obtained and plotted accordingly. For the validity of the obtained results, a comparison with already existing results (special cases) is also presented.
  
  
  CONCLUSIONS
  The magnetic field increases the velocity of the fluid. Injection at the walls can be used to reduce the velocity boundary layer thickness. Thermal boundary layer thickness can be reduced by using the magnetic field and the suction at the wall. The motile microorganisms density profile is an increasing function of the bioconvection Pecket number and bioconvection constant. The same is a decreasing function ofm,MandLe. The skin friction coefficient increases with increasingmand [Formula: see text]. Nusselt number and the density number of motile microorganisms are higher for the case of suction as compared to the injection case. The density number of motile microorganisms is an increasing function for all the involved parameters.
authors.affiliation: COMSSATS Institute of Information Technology, Abbottabad, Pakistan.
authors.forename: Umar
authors.initials: U
authors.lastname: Khan
authors.affiliation: Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Taxila, Pakistan.
authors.forename: Naveed
authors.initials: N
authors.lastname: Ahmed
authors.affiliation: Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Taxila, Pakistan.
authors.forename: Syed Tauseef
authors.initials: ST
authors.lastname: Mohyud-Din
keywords: Gyrotactic microorganisms; Joule heating; Nanofluids; Numerical solution; Porous wedge; Viscous dissipation