Unsteady magnetoconvective flow of bionanofluid with zero mass flux boundary condition

Induced magnetic field stagnation point flow for unsteady two-dimensional laminar forced convection of water based nanofluid containing microorganisms along a vertical plate has been investigated. We have incorporated zero mass flux boundary condition to get physically realistic results. The boundary layer equations with three independent variables are transformed into a system of ordinary differential equations by using appropriate similarity transformations. The derived equations are then solved numerically by using Maple which use the fourth-fifth order Runge-Kutta-Fehlberg algorithm to solve the system of similarity differential equations. The effects of the governing parameters on the dimensionless velocity, induced magnetic field, temperature, nanoparticle volume fraction, density of motile microorganisms, skin friction coefficient, local Nusselt number and motile density of microorganisms transfer rate are illustrated graphically and tabular form. It is found that the controlling parameters strongly affect the fluid flow and heat transfer characteristics. We compare our numerical results with published results for some limiting cases and found excellent agreement

Free convection boundary layer flow of a nanofluid from a convectively heated vertical plate with linear momentum slip boundary condition

Two dimensional steady laminar boundary layer flow of a nanofluid over a convectively heated vertical flat plate with linear momentum slip boundary condition has been studied numerically. The governing boundary layer equations are non-dimensionalized and transformed into a two point boundary value problem of coupled nonlinear ordinary differential equations in similarity variable before being solved numerically. The resulting equations with corresponding boundary conditions have been solved numerically by Maple 13 which uses Runge-Kutta-Fehlberg fourth- fifth order numerical algorithm for solving nonlinear ordinary boundary value problems. Our analysis reveals that the similarity solution is possible if the convective heat transfer coefficient is directly proportional to x–1/4, where x is the axial distance from the leading edge of the plate. Solutions depend on the seven parameters: Prandtl number, buoyancy ratio, Brownian motion, thermophoresis, Lewis number, momentum slip and convective heat transfer. The effects of the governing parameters on the flow and heat transfer characteristics have been shown graphically and discussed. Comparisons of the present numerical solution with the existing results in the literature are made and our results are in very good agreement. Results for the skin friction factor, the reduced Nusselt and the Sherwood numbers are provided in tabular form for various values of the convective heat transfer parameter. It is found that the skin friction coefficint reduces with the momentum slip and the buoyancy ratio parameters whilst it enhances with the convective heat transfer parameter. It is also found that mass transfer rate enhances with the Lewis number and the convective heat transfer parameter whilst it falls with the thermophoresis parameter

Investigation of heat mass transfer for combined convective slips flow: a lie group analysis

The steady laminar combined convective flow with heat and mass transfer of a Newtonian viscous incompressible fluid over a permeable flat plate with linear hydrodynamic and thermal slips has been investigated numerically. The velocity of the external flow, the suction/injection velocity and the temperature of the plate surface are assumed to vary nonlinearly following the power law with the distance along the plate from the origin. Lie group analysis is used to develop the similarity transformations and the governing momentum, the energy conservation and the mass conservation equations are converted to a system of coupled nonlinear ordinary differential equations with the associated boundary conditions. The resulting equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method. The effects of hydrodynamic slip parameter (a), thermal slip parameter (b), suction/injection parameter (fw), power law parameter (m), buoyancy ratio parameter (N), Prandtl number (Pr) and Schmidt number (Sc) on the fluid flow, heat transfer and mass transfer characteristics are investigated and presented graphically. We have also shown the effects of the Reynolds number (Re) and the power law parameter (m) on the velocity slip and the thermal slip factors. Good agreement is found between the numerical results of the present paper and published results

Stefan blowing effect on bioconvective flow of nanofluid over a solid rotating stretchable disk

A mathematical model for the unsteady forced convection over rotating stretchable disk in nanofluid containing micro-organisms and taking into account Stefan blowing effect is presented theoretically and numerically. Appropriate transformations are used to transform the governing boundary layer equations into non-linear ordinary differential equations, before being solved numerically using the Runge-Kutta-Fehlberg method. The effect of the governing parameters on the dimensionless velocities, temperature, nanoparticle volume fraction (concentration), density of motile microorganisms as well as on the local skin friction, local Nusselt, Sherwood number and motile microorganisms numbers are thoroughly examined via graphs. It is observed that the Stefan blowing increases the local skin friction and reduces the heat transfer, mass transfer and microorganism transfer rates. The numerical results are in good agreement with those obtained from previous literature. Physical quantities results from this investigation show that the effects of higher disk stretching strength and suction case provides a good medium to enhance the heat, mass and microorganisms transfer compared to blowing case