Conservation laws and conserved quantities for laminar two-dimensional and radial jets

A systematic way to derive the conserved quantities for the liquid jet, free jet and wall jet using conservation laws is presented. Both two-dimensional and radial jets are considered. The jet flows are described by Prandtl’s momentum boundary layer equation and the continuity equation. The multiplier approach (also know as variational derivative approach) is first applied to construct a basis of conserved vectors for the system. The basis consists of two conserved vectors. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived for the liquid jet and the free jet. The multiplier approach is then applied to construct a basis of conserved vectors for the third-order partial differential equation for the stream function. The basis consists of two local conserved vectors one of which is a non-local conserved vector for the system. The conserved quantities for the free jet and the wall jet are derived from the corresponding conservation laws and boundary conditions. The approach gives a unified treatment to the derivation of conserved quantities for jet flows and may lead to a new classification of jets through conserved vectors and their multipliers.     

Efficient Removal of Pb(II) from Aqueous Medium Using Chemically Modified Silica Monolith

The adsorptive removal of lead (II) from aqueous medium was carried out by chemically modified silica monolith particles. Porous silica monolith particles were prepared by the sol-gel method and their surface modification was carried out using trimethoxy silyl propyl urea (TSPU) to prepare inorganic–organic hybrid adsorbent. The resultant adsorbent was evaluated for the removal of lead (Pb) from aqueous medium. The effect of pH, adsorbent dose, metal ion concentration and adsorption time was determined. It was found that the optimum conditions for adsorption of lead (Pb) were pH 5, adsorbent dose of 0.4 g/L, Pb(II) ions concentration of 500 mg/L and adsorption time of 1 h. The adsorbent chemically modified SM was characterized by scanning electron microscopy (SEM), BET/BJH and thermo gravimetric analysis (TGA). The percent adsorption of Pb(II) onto chemically modified silica monolith particles was 98%. An isotherm study showed that the adsorption data of Pb(II) onto chemically modified SM was fully fitted with the Freundlich and Langmuir isotherm models. It was found from kinetic study that the adsorption of Pb(II) followed a pseudo second-order model. Moreover, thermodynamic study suggests that the adsorption of Pb(II) is spontaneous and exothermic. The adsorption capacity of chemically modified SM for Pb(II) ions was 792 mg/g which is quite high as compared to the traditional adsorbents. The adsorbent chemically modified SM was regenerated, used again three times for the adsorption of Pb(II) ions and it was found that the adsorption capacity of the regenerated adsorbent was only dropped by 7%. Due to high adsorption capacity chemically modified silica monolith particles could be used as an effective adsorbent for the removal of heavy metals from wastewater.     

Microorganisms swimming through radiative Sutterby nanofluid over stretchable cylinder: Hydrodynamic effect

In the present article, radiative Sutterby nanofluid flow over a stretchable cylinder is considered. The suspended swimming microorganisms have been deliberated in the fluid analysis. Different processes such as Brownian motion, thermophoresis, Joules heating, and viscous dissipation have been inspected in the presences of stratification parameters. The solutions for flow profiles have been obtained via optimal homotopy analysis method. Impacts of different physical involved variables on non-dimensional velocity, temperature, nanofluid concentration, and concentration of density of swimming microorganisms have been debated. Coefficient of skin friction, local Nusselt number, Sherwood number, and density of motile organisms have been calculated. The results reveal that Sutterby fluid parameter enhances the skin friction and has a reverse impact on the velocity, while an increase in stratification causes a declination in the flow boundary layers. The temperature of the flow is also seen to be boosted by the increment in Brownian motion parameter. Analysis of entropy generation shows that the concentration difference parameter maximizes the entropy and minimizes the dimensionless Bejan number.     

Optimization of the numerical treatment of the Darcy–Forchheimer flow of Ree–Eyring fluid with chemical reaction by using artificial neural networks

In this study, Darcy Forchheimer flow paradigm, which is a useful paradigm in fields such as petroleum engineering where high flow velocity effects are common, has been analyzed with artificial intelligence approach. In this context, first of all, Darcy–Forchheimer flow of Ree–Eyring fluid along a permeable stretching surface with convective boundary conditions has been examined and heat and mass transfer mechanisms have been investigated by including the effect of chemical process, heat generation/absorption, and activation energy. Cattaneo–Christov heat flux model has been used to analyze heat transfer properties. Within the scope of optimizing Darcy–Forchheimer flow of Ree–Eyring fluid; three different artificial neural network models have been developed to predict Nusselt number, Sherwood number, and skin friction coefficient values. The developed artificial neural network model has been able to predict Nusselt number, Sherwood number, and skin friction coefficient values with high accuracy. The findings obtained as a result of the study showed that artificial neural networks are an ideal tool that can be used to model Darcy–Forchheimer Ree–Eyring fluid flow towards a permeable stretch layer with activation energy and a convective boundary condition.