Dual solution for double-diffusive mixed convection opposing flow through a vertical cylinder saturated in a Darcy porous media containing gyrotactic microorganisms.

The steady mixed convection flow towards an isothermal permeable vertical cylinder nested in a fluid-saturated porous medium is studied. The Darcy model is applied to observe bioconvection through porous media. The suspension of gyrotactic microorganisms is considered for various applications in bioconvection. Appropriate similarity variables are opted to attain the dimensionless form of governing equations. The resulting momentum, energy, concentration, and motile microorganism density equations are then solved numerically. The resulting dual solutions are graphically visualized and physically analyzed. The results indicate that depending on the systems' parameters, dual solutions exist in opposing flow beyond a critical point where both solutions are connected. Our results were also compared with existing literature.

Effects of thermal slip and chemical reaction on free convective nanofluid from a horizontal plate embedded in a porous media.

We consider a two-dimensional, uniform, incompressible and free convection flow of a nano-fluid along a plane. The plate is located facing upward about the porous medium. Throughout the investigation, thermal slip, chemical reaction, heat emission/absorption is considered. In the modeling of nano-fluid we have considered the dynamic effect along with the Brownian and thermophoresis. In obtaining the governing equations, including the boundary conditions, an appropriate scaling is applied. The governing momentum equations, including thermal energy and nanoparticles equations are translated into a group of nonlinear ODEs by using Lie symmetry group transformation. The transformed equations are then solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order. The numerical results of velocity, temperature, and nanoparticle volume fraction profiles for varied physical parameters will be discussed and analyzed at the end. The discussion also includes the local Nusselt and the local Sherwood numbers against several of the systems' physical parameters. It is found that the velocity and temperature decrease with thermal slip and heat absorption whilst it increases by increasing heat generation and chemical reaction order. Our present results will be compared with similar existing literature results.

Numerical study of nano-biofilm stagnation flow from a nonlinear stretching/shrinking surface with variable nanofluid and bioconvection transport properties.

A mathematical model is developed for stagnation point flow toward a stretching or shrinking sheet of liquid nano-biofilm containing spherical nano-particles and bioconvecting gyrotactic micro-organisms. Variable transport properties of the liquid (viscosity, thermal conductivity, nano-particle species diffusivity) and micro-organisms (species diffusivity) are considered. Buongiorno's two-component nanoscale model is deployed and spherical nanoparticles in a dilute nanofluid considered. Using a similarity transformation, the nonlinear systems of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a central space finite difference method in the CodeBlocks Fortran platform. Graphical plots for the distribution of reduced skin friction coefficient, reduced Nusselt number, reduced Sherwood number and the reduced local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms are presented for the influence of wall velocity power-law index (m), viscosity parameter [Formula: see text], thermal conductivity parameter (c4), nano-particle mass diffusivity (c6), micro-organism species diffusivity (c8), thermophoresis parameter [Formula: see text], Brownian motion parameter [Formula: see text], Lewis number [Formula: see text], bioconvection Schmidt number [Formula: see text], bioconvection constant (σ) and bioconvection Péclet number [Formula: see text]. Validation of the solutions via comparison related to previous simpler models is included. Further verification of the general model is conducted with the Adomian decomposition method (ADM). Extensive interpretation of the physics is included. Skin friction is elevated with viscosity parameter ([Formula: see text] whereas it is suppressed with greater Lewis number and thermophoresis parameter. Temperatures are elevated with increasing thermal conductivity parameter ([Formula: see text] whereas Nusselt numbers are reduced. Nano-particle volume fraction (concentration) is enhanced with increasing nano-particle mass diffusivity parameter ([Formula: see text]) whereas it is markedly reduced with greater Lewis number (Le) and Brownian motion parameter (Nb). With increasing stretching/shrinking velocity power-law exponent ([Formula: see text] skin friction is decreased whereas Nusselt number and Sherwood number are both elevated. Motile microorganism density is boosted strongly with increasing micro-organism diffusivity parameter ([Formula: see text]) and Brownian motion parameter (Nb) but reduced considerably with greater bioconvection Schmidt number (Sc) and bioconvection Péclet number (Pe). The simulations find applications in deposition processes in nano-bio-coating manufacturing processes.

Dual solutions in biomagnetic fluid flow and heat transfer over a nonlinear stretching/shrinking sheet: Application of lie group transformation method.

Of concern in the paper is a theoretical investigation of boundary layer flow of a biomagnetic fluid and heat transfer on a stretching/shrinking sheet in the presence of a magnetic dipole. The problem has been treated mathematically by using Lie group transformation. The governing nonlinear partial differential equations are thereby reduced to a system of coupled nonlinear ordinary differential equations subject to associated boundary conditions. The resulting equations subject to boundary conditions are solved numerically by using bvp4c function available in MATLAB software. The plots for variations of velocity, temperature, skin friction and heat transfer rate have been drawn and adequate discussion has been made. The study reveals that the problem considered admits of dual solutions in particular ranges of values of the suction parameter and nonlinear stretching/shrinking parameter. A stability analysis has also been carried out and presented in the paper. This enables one to determine which solution is stable that can be realized physically, and which is not. The results of the present study have been compared with those reported by previous investigators to ascertain the validity/reliability of the computational results.