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.ResultsA 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.ConclusionThe 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 of m, M and Le. The skin friction coefficient increases with increasing m and M . 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.
Highlights
The flow over a porous wedge, in the presence of viscous dissipation and Joule heating, has been investigated
A careful literature survey reveals that to date, no study is available which considers the boundary layer flow of a nanofluid over a wedge in presence of microorganisms. To fill up this gap, we present here a mathematical study analyzing the flow of a nanofluid over a porous wedge in the presence of gyrotactic microorganisms
Results and discussion we highlight the influence of some relevant parameters on the velocity, temperature, concentration and motile microorganisms density profiles with the help of graphs
Summary
The flow over a porous wedge, in the presence of viscous dissipation and Joule heating, has been investigated. Scientists and researchers are keenly working on the ways to improve the heat transfer characteristics of the fluids used in everyday life. For this purpose, many theoretical as well as practical studies have been presented over the years. The proposed model uses nanoparticles to improve the heat transfer characteristics of the fluids like water, kerosene and the other traditional fluids. He proved that the thermal properties of these fluids (termed as base fluids) can be enhanced by the addition of nano particles (Choi et al 2001). Some of the most relevant and useful ones can be seen in (Sheikholeslami and Ellahi 2015a, b; Ellahi et al 2015; Khan et al 2015; Mohyud-Din et al 2015a, b; Gul et al 2015a, b) and the references therein
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