Effect of Newtonian heating on bioconvection of nanofluid over stretching sheet with gyrotactic microorganisms

Transport processes in nanofluids and their importance in biomedical applications and process industries has gained considerable attention in recent decades [1, 2]. Bioconvection in a horizontal layer with heat and mass transfer of nanofluid containing gyrotactic microorganisms along a stretching sheet taking into account the Newtonian heating boundary condition is investigated numerically. In the modelling of nanofluid, both Brownian motion and thermophoresis effects are incorporated into the nonlinear differential equations. The governing equations are reduced to a system of couple non-linear ordinary differential equations for momentum, energy, nanoparticle concentration and dimensionless motile microorganism density, with using appropriate similarity transformations and then tackled numerically using the fifth order Rung-Kutta-Fehlberg scheme with shooting technique. Please download the full abstract below

A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM–Padé technique

AbstractIn this paper, the Adomian decomposition method and Padé approximants are integrated to study the deflection and pull-in instability of nanocantilever electromechanical switches. In a distributed parameter model, intermolecular forces, including Casimir forces, are taken into account considering their range of application. A closed form power series solution based on Adomian polynomials is obtained. The obtained analytic results are compared with numerical solution. The Adomian method is accurate for small deflections, but the results of a pull-in instability study demonstrate that the accuracy of the Adomian solution is not as good for small deflections. Thus, to increase the accuracy of the Adomian solution for the pull-in instability, the Adomian power series is converted to Padé approximants. The results of the present method are compared with the numerical results as well as those of the Adomian decomposition method and other methods reported in the literature. The results obtained using the ADM–Padé are remarkably accurate compared with the numerical results. The proposed technique can be easily extended to solve a wide range of instability problems. Finally, the minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to the intermolecular attractions, which is an important parameter for the pull-in instability of a nanocantilever actuator, are calculated using Adomian–Padé approximants

An Approximate Solution for a Simple Pendulum beyond the Small Angles Regimes Using Hybrid Artificial Neural Network and Particle Swarm Optimization Algorithm

AbstractSimple pendulum is the most popular example in mechanics. Study on the physics of simple pendulum is a key to understanding the nonlinear dynamics of many other systems. However, there is an exact analytical solution for this problem, but its exact solution is in the form of the Jacobi elliptic integral which it is hard for using in simple engineering manipulations. Hence, determining an accurate simple approximate solution is helpful. This study presents a new method by using hybrid neural networks and particle swarm optimization algorithm, in order to find a simple approximate solution for motion of a nonlinear pendulum beyond the small angles regime. The approximate solution is simple and powerful to converge to the exact solution. The results of the approximate solution are compared with exact solution and linear solution, using tables and graphs. Furthermore, the present method is expandable to solve complex pendulums

Homotopy study of magnetohydrodynamic mixed convection nanofluid multiple slip flow and heat transfer from a vertical cylinder with entropy generation

Stimulated by thermal optimization in magnetic materials process engineering, the present work investigates theoretically the entropy generation in mixed convection magnetohydrodynamic (MHD) flow of an electrically-conducting nanofluid from a vertical cylinder. The mathematical includes the effects of viscous dissipation and second order velocity slip and thermal slip. The cylindrical partial differential form of the two-component non-homogenous nanofluid model has been transformed into a system of coupled ordinary differential equations by applying similarity transformations. The effects of governing parameters with no-flux nanoparticle concentration have been examined on important quantities of interest. Furthermore the dimensionless form of the entropy generation number has also been evaluated using the powerful homotopy analysis method (HAM). The present analytical results achieve good correlation with numerical results. Entropy is found to be an increasing function of second order velocity slip, magnetic field and curvature parameter. Temperature is elevated with increasing curvature parameter and magnetic parameter whereas it is reduced with mixed convection parameter. The flow is accelerated with curvature parameter but decelerated with magnetic parameter. Heat transfer rate (Nusselt number) is enhanced with greater mixed convection parameter, curvature parameter and first order velocity slip parameter but reduced with increasing second order velocity slip parameter. Entropy generation is also increased with magnetic parameter, second order slip velocity parameter, curvature parameter, thermophoresis parameter, buoyancy parameter and Reynolds number whereas it is suppressed with higher first order velocity slip parameter, Brownian motion parameter and thermal slip parameter

Energy conversion under conjugate conduction, magneto-convection, diffusion and nonlinear radiation over a non-linearly stretching sheet with slip and multiple convective boundary conditions

Energy conversion under conduction, convection, diffusion and radiation has been studied for MHD free convection heat transfer of a steady laminar boundary-layer flow past a moving permeable non-linearly extrusion stretching sheet. The nonlinear Rosseland thermal radiation flux model, velocity slip, thermal and mass convective boundary conditions are considered to obtain a model with fundamental applications to real world energy systems. The Navier slip, thermal and mass convective boundary conditions are taken into account. Similarity differential equations with corresponding boundary conditions for the flow problem, are derived, using a scaling group of transformation. The transformed model is shown to be controlled by magnetic field, conduction-convection, convection-diffusion, suction/injection, radiation-conduction, temperature ratio, Prandtl number, Lewis number, buoyancy ratio and velocity slip parameters. The transformed non-dimensional boundary value problem comprises a system of nonlinear ordinary differential equations and physically realistic boundary conditions, and is solved numerically using the efficient Runge-Kutta-Fehlberg fourth fifth order numerical method, available in Maple17 symbolic software. Validation of results is achieved with previous simulations available in the published literature. The obtained results are displayed both in graphical and tabular form to exhibit the effect of the controlling parameters on the dimensionless velocity, temperature and concentration distributions. The current study has applications in high temperature materials processing utilizing magnetohydrodynamics, improved performance of MHD energy generator wall flows and also magnetic-microscale fluid devices

Influence of Stefan blowing on nanofluid flow submerged in microorganisms with leading edge accretion or ablation

The unsteady forced convective boundary layer flow of viscous incompressible fluid containing both nanoparticles and gyrotactic microorganisms, from a flat surface with leading edge accretion (or ablation), is investigated theoretically. Utilizing appropriate similarity transformations for the velocity, temperature, nanoparticle volume fraction and motile microorganism density, the governing conservation equations are rendered into a system of coupled, nonlinear, similarity ordinary differential equations. These equations, subjected to imposed boundary conditions, are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method in the MAPLE symbolic software. Good agreement between our computations and previous solutions is achieved. The effect of selected parameters on flow velocity, temperature, nano-particle volume fraction (concentration) and motile microorganism density function is investigated. Furthermore, tabular solutions are included for skin friction, wall heat transfer rate, nano-particle mass transfer rate and microorganism transfer rate. Applications of the study arise in advanced micro-flow devices to assess nanoparticle toxicity

Radiative and magnetohydrodynamics flow of third grade viscoelastic fluid past an isothermal inverted cone in the presence of heat generation/absorption

A mathematical analysis is presented to investigate the nonlinear, isothermal, steady-state, free convection boundary layer flow of an incompressible third grade viscoelastic fluid past an isothermal inverted cone in the presence of magnetohydrodynamic, thermal radiation and heat generation/absorption. The transformed conservation equations for linear momentum, heat and mass are solved numerically subject to the realistic boundary conditions using the second-order accurate implicit finite-difference Keller Box Method. The numerical code is validated with previous studies. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and low-density polymer materials processing

Finite element simulation of magnetohydrodynamic convective nanofluid slip flow in porous media with nonlinear radiation

A numerical investigation of two dimensional steady state laminar boundary layer flow of a viscous electrically-conducting nanofluid in the vicinity of a stretching ∕ shrinking porous flat plate located in a Darcian porous medium is performed. The nonlinear Rosseland radiation effect is taken into account. Velocity slip and thermal slip at the boundary as well as the newly developed zero mass flux boundary conditions are also implemented to achieve physically applicable results. The governing transport equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity transformations and these are then solved numerically using a variational finite element method (FEM). The influence of the governing parameters (Darcy number, magnetic field, velocity and thermal slip, temperature ratio, transpiration, Brownian motion, thermophoresis, Lewis number and Reynolds number) on the dimensionless velocity, temperature, nanoparticle volume fraction as well as on the skin friction, the heat transfer rates and the mass transfer rates are examined and illustrated in detail. The FEM code is validated with earlier studies for non-magnetic non-slip flow demonstrating close correlation. The present study is relevant to high-temperature nano-materials processing operations