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The aim of current communication is to investigate the flow features of Cross nanomaterial over stretched porous surface subject to activation energy and magnetic field. The idea of gyrotactic microorganisms is used to stabilize the nanoparticles in Cross fluid. Temperature relation is modeled considering thermal radiation and viscous dissipation. Furthermore, Bio-convection through mutual effects of thermophoresis and Brownian diffusion is also considered. Boundary layer assumptions are used to obtain the flow expressions. The obtained flow expressions are transformed into non-dimensional one using similarity transformations. Newton built in shooting technique code in Mathematica software is implemented to study the impact of potential parameters on velocity, temperature, concentration and concentration of microorganisms. Numerical computations for physical quantities such as skin friction, Nusselt, Sherwood and density numbers are also discussed. Important observations are highlighted at the end.

This article addresses the entropy generation in mixed convection magnetohydrodynamics Eyring–Powell nanofluid flow toward a permeable surface of a cylinder. The flow is modeled considering heat generation and chemical reaction aspects. The influence of buoyancy forces, magnetic field, and thermal radiation is also considered. Moreover, activation energy, viscous dissipation, and permeability effects on bio-nanofluid flow are assimilated in modeling of concentration and energy relations. Total entropy generation is modeled in view of the second thermodynamics law. The governing system of PDEs is deduced by incorporating boundary layer assumptions. Relevant transformations are used to reduce the dimensional flow model into a non-dimensional one. The built-in shooting technique and the NDSolve code in Mathematica software are used to handle the dimensionless flow expressions. Variation in velocity, temperature, concentration, motile micro-organisms, Bejan number, and entropy generation with respect to the involved parameters is scrutinized graphically. Surface drag force, heat transfer rate, mass transfer rate, and density number are further calculated and investigated. Important results are summarized at the end.

Various industrial operations involve frequent heating and cooling of electrical systems. In such circumstances, the development of relevant thermal devices is of extreme importance. During the development of thermal devices, the second law of thermodynamics plays an important role by means of entropy generation. Entropy generation should be reduced significantly for the efficient performance of the devices. The current paper reports an analytical study on micropolar fluid with entropy generation over a stretching surface. The influence of various physical parameters on velocity profile, microrotation profile, and temperature profile is investigated graphically. The impact of thermal radiation, porous medium, magnetic field, and viscous dissipation are also analyzed. Moreover, entropy generation and Bejan number are also illustrated graphically. Furthermore, the governing equations are solved by using HAM and code in MATHEMATICA software. It is concluded from this study that velocity and micro-rotation profile are reduced for higher values of magnetic and vortex viscosity parameter, respectively. For larger values of Eckert number and thermal radiation parameters, Bejan number and entropy generation are increased, respectively. These findings are useful in petroleum industries and engineering designs.

Present article addresses mixed convection magnetohydrodynamic Casson nanomaterial flow by stretchable cylinder. The effects of thermal, solutal and motile density stratifications at the boundary of the surface are accounted. Flow governing expressions are acquired considering aspects of permeability, thermal radiation, chemical reaction, viscous dissipation and activation energy. The obtained flow model is made dimensionless through transformations and then tackled by NDsolve code in Mathematica. Physical impacts of sundry variables on nanomaterial velocity, temperature distribution, volume fraction of microorganisms and mass concentration is investigated through plots. Furthermore, quantities of engineering interest like surface drag force, heat transfer rate, density number and Sherwood number are computed and analyzed. We observed that fluid velocity diminishes for higher curvature variable, Casson fluid material variable, Hartmann number and permeability parameter. Fluid temperature has a direct relation with Eckert number, thermophoresis variable, Brownian dispersal parameter, Prandtl number and Hartmann number. Volume fraction of gyrotactic microorganisms is decreasing function of bioconvection Lewis number, stratification parameter and bioconvection Peclet number. Detailed observations are itemized at the end.