Microorganism cells movement in fluid is universal and affects many ecological and biological processes, including infection, reproduction and marine life ecosystem. There are many biological and medical applications that require understanding of transport process in nanofluids containing suspension of microorganism. The present problem deals with the bioconvection of Casson nanofluid containing suspension of motile gyrotactic microorganisms over inclined stretching sheet in the presence of thermal radiation, viscous dissipation, and chemical reaction and magnetic field. At the surface, influence of the thermo-solutal Marangoni convection and suction / injection impact are considered. The governing equations are solved numerically by using fourth order Runge-Kutta method with shooting technique. Impact of the major pertinent parameters on the velocity, temperature, nanoparticles concentration and density of the motile microorganism is illustrated graphically. Finally, correlation of various crucial parameters on skin friction, local Nusselt number, Sherwood number and local motile microorganism density number are displayed through graphs and tables.

In this paper, we investigate the influence of melting on mixed convection heat and mass transfer from vertical flat plate in a non-Newtonian fluid-saturated non-Darcy porous medium including the prominent Soret effect. The wall and the ambient medium are maintained at constant but different levels of temperature and concentration such that the heat and mass transfer occurs from the wall to the medium. The Ostwald–de Waele power law model is used to characterize the non-Newtonian fluid behavior. A similarity solution for the transformed governing equations is obtained. The numerical computation is carried out for various values of the nondimensional physical parameters. The variation of temperature, concentration, and heat and mass transfer coefficients with the power law index, mixed convection parameter, inertia parameter, melting parameter, Soret number, buoyancy ratio, and Lewis number is discussed for a wide range of values of these parameters.

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Microorganisms play a vital role in understanding the ecological system. The motions of micororganisms are self‐propelled while the impact of thermophoresis and Brownian motion property of nanoparticle shows more challenges in biotechnological and medical applications. The present problem is based on the understanding of double‐dispensed bioconvection for a Casson nanofluid flow over a stretching sheet. Suction phenomenon is introduced at the surface of the stretching sheet along with the convective boundary condition. The convection and movement of the microorganisms are assisted by an applied magnetic field, nonlinear thermal radiation, and first‐order chemical reaction. The governing equations are highly coupled and thus we used the spectral quasilinearization method to solve the governing equations. The study of the residual errors on the systemic parameters had given a confidence with the present results. The final outcomes are displayed through graphs and tables. The thermal dispersion coefficient shows a positive response in the temperature while a similar response is observed for the concentration with solutal dispersion coefficient. The response is reversible for the heat transfer rate at the surface with thermal dispersion coefficient. The density of the motile microorganism at the surface decreases with increase in the Casson number, thermal dispersion coefficient, and solute dispersion coefficient, while an opposite phenomenon was observed with increase in the density ratio of the motile microorganism.

This paper investigates the influence of the effect of viscous dissipation and radiation on natural convection heat transfer from vertical flat plate in a non-Darcy porous media saturated with non-Newtonian fluid of variable viscosity. The wall and the ambient medium are maintained at constant but different levels of temperature. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The viscosity of the fluid is assumed to follow Reynolds viscosity model. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing equations in their non-similar form are solved numerically by local non-similarity method. The effects of variable viscosity, viscous dissipation, radiation and the power-law index parameters on the velocity and temperature profiles as well as on the heat transfer coefficient are analyzed.