Scaling group transformation for MHD boundary layer flow over permeable stretching sheet in presence of slip flow with Newtonian heating effects

Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.

Biomathematical model for gyrotactic free-forced bioconvection with oxygen diffusion in near-wall transport within a porous medium fuel cell

Bioconvection has shown significant promise for environmentally friendly,sustainable“green”fuel cell technologies.The improved design of such systems requires continuous refinements in biomatheatical modeling in conjunction with laboratory and fieldtesting.Motivated by exploring deeper the near-wall transport phenomena involved inbio-inspired fuel cells,in the present paper,we examine analytically and numericallythe combined free-forced convective steady boundary layer flow from a solid verticalflat plate embedded in a Darcian porous medium containing gyrotactic microorganisms.Gyrotaxis is one of the many taxes exhibited in biological microscale transport,andother examples include magneto-taxis,photo-taxis,chemotaxis and geo-taxis (reflecting the response of microorganisms to magnetic field,light,chemical concentration orgravity,respectively). The bioconvection fuel cell also contains difusing oxygen specicswhich mimics the cathodic behavior in a proton exchange membrane(PEM) systei.Thevertical wall is maintained at isosolutal (constant oxygen volume fraction and motilemicroorganism density) and iso-thermal conditions. Wall values of these quantities aresustained at higher values than the ambient temperature and concentration of oxygenand biological microorganism specics.Similarity transformations are applied to renderthe governing partial differential equations for mass,momentum,energy,oxygen speciesand microorganism species density into a system of ordinary differential equations. Theemerging eight order nonlinear coupled,ordinary differential boundary value problemfeatures several important dimensionless control parameters,namely Lewis number(Le),buoyancy ratio paraneter i.e. ratio of oxygen species buoyancy force to thermal buoy-ancy force(Nr), bioconvection Rayleigh number(Rb), bioconvection Lewis number(Lb),bioconvection Peclet number(Pe) and the mixed convection parameter(e) spanning theentire range of free and forced convection. The transformed nonlinear system of equationswith boundary conditions is solved numerically by a finite difference met.hod with centraldifferencing,tridiagonal matrix manipulation and an iterative procedure.Computationsare validated with the symbolic Maple 14.0 software.The influence of buoyancy andbioconvection parameters on the dimensionless temperature,velocity,oxygen concentration and motile microorganism density distribution,Nusselt,Sherwood and gradient ofmotile microorganism density are studied. The work clearly shows the benefit of utilizingbiological organisms in fuel cell design and presents a logical biomathematical modeling framework for simulating such systems.In particular,the deployment of gyrotacticmicroorganisns is shown to stimulate improved transport characteristics in heat andmormentum at the fuel cell wall.

Three-dimensional biomagnetic Maxwell fluid flow over a stretching surface in presence of heat source/sink

The present paper deals with the study of three-dimensional boundary layer flow of biomagnetic Maxwell fluid over a plane horizontal surface stretched linearly along two mutually perpendicular directions. Basic principles of magnetohydrodynamics (MHD) and ferro-hydrodynamics (FHD) have been employed. The effect of heat generation/absorption has been taken into consideration. The study is theoretical and is conducted by using a combination of approximate and numerical techniques. By using the method of similarity transformation, the governing nonlinear partial differential equations are converted into a set of coupled ordinary differential equations. In the sequel, a suitable numerical method has been developed to solve the coupled differential equations. The accuracy of the numerical method has been checked by comparing the numerical results with those of an earlier study reported in available literatures. Effects of various parameters involved in the study, viz. the magnetohydrodynamic and ferromagnetic parameters, Deborah number, stretching ratio and heat generation on the fluid flow profiles are investigated and the results have been presented graphically. Variations of the skin friction, heat transfer rate and relative wall pressure with change in hydrodynamic and ferromagnetic parameters have also been illustrated. It is found that due to the influence of the Kelvin force, the velocity component in xx-direction is greater than the corresponding one in the hydrodynamic case, but the opposite is true for the velocity component in the yy-direction. We also found that the temperature of the fluid for hydrodynamic flow is greater than that for MHD or FHD flow. It is even greater for BFD flows. The numerical results of the study reveal that the characteristics of blood flow are significantly affected by the presence of a magnetic field.

Natural convective flow of a magneto-micropolar fluid along a vertical plate

This paper presents a numerical study of natural convective flow of an electrically conducting viscous micropolar fluid past a vertical plate. Internal heat generation (IHG) versus without IHG in the medium are discussed in the context of corresponding similarity solutions. Results are presented in terms of velocity, angular velocity, temperature, skin friction in tabular forms, local wall-coupled stress, and Nusselt number. Computations have been accomplished by parametrizing the micropolar, micro-rotation, magnetic field, suction parameters, and the Prandtl number. Several critical issues are addressed at the end of the paper with reference to a previous study by El-Hakiem. The study is relevant to high-temperature electromagnetic materials fabrication systems.