In this article, we probe the multiple-slip effects on magnetohydrodynamic unsteady Casson nano-fluid flow over a penetrable stretching sheet, sheet entrenched in a porous medium with thermo-diffusion effect, and injection/suction in the presence of heat source. The flow is engendered due to the unsteady time-dependent stretching sheet retained inside the porous medium. The leading non-linear partial differential equations are transmuted in the system of coupled nonlinear ordinary differential equations by using appropriate transformations, then the transformed equations are solved by using the variational finite element method numerically. The velocity, temperature, solutal concentration, and nano-particles concentration, as well as the rate of heat transfer, the skin friction coefficient, and Sherwood number for solutal concentration, are presented for several physical parameters. Next, the effects of these various physical parameters are conferred with graphs and tables. The exact values of flow velocity, skin friction, and Nusselt number are compared with a numerical solution acquired with the finite element method (FEM), and also with numerical results accessible in literature. In the end, we rationalize the convergence of the finite element numerical solution, and the calculations are carried out by reducing the mesh size. Appl. Sci. 2019, 9, 5217 2 of 21 partial velocity slip can occur on the stretching boundary. In an assortment of industry procedures, the influences of slip can crop-up at the boundary of pipes, surfaces, and walls. The Navier Stoke velocity slip conditions are customary to approach in the study of slip phenomenon.There are hundreds of applications in industries and engineering, and magneto-hydrodynamic fluid flows through stretching sheet have achieved much importance in recent days, according to Mabbod et al. [3]. Applications as well as the liquid coating on the photographic films, boundary layers throughout the liquid film in the concentration procedure, and the aerodynamic excrescence of plastic sheets exist. With this, the extensive range of applications of magnetohydrodynamic flow that can be found in copious fields like in electronic cooling process, in boilers, heat lagging, and metal extrusion, geothermal system, nuclear process, micro-magnetohydrodynamic pumps, underground water system, in energy storage units, biological conveyance, and in the thermal energy procedure has played a very important role. Unsteady flow due to the stretching sheet has been scrutinized by Pop and Na [4]. Afterward, Sheridan et al. [5] investigated the significance of variable wall temperature and variable heat flux in the boundary layer flow over the unsteady stretching surface with similarity transformation. An unsteady stagnation point flow of the viscous fluid caused by a stretching sheet under the influence of slip condition has been reported by Bhattacharyya et al. [6]. The impact of the magnetic field on the two-dimensional flow of nano-fluid with and without slip condition was conferred b...

This article explores the impact of a magnetic dipole on the heat transfer phenomena of different nano-particles Fe (ferromagnetic) and Fe 3 O 4 (Ferrimagnetic) dispersed in a base fluid (60% water + 40% ethylene glycol) on micro-polar fluid flow over a stretching sheet. A magnetic dipole in the presence of the ferrities of nano-particles plays an important role in controlling the thermal and momentum boundary layers. The use of magnetic nano-particles is to control the flow and heat transfer process through an external magnetic field. The governing system of partial differential equations is transformed into a system of coupled nonlinear ordinary differential equations by using appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The impact of different physical parameters on the velocity, the temperature, the Nusselt number, and the skin friction coefficient is shown. The velocity profile decreases in the order Fe (ferromagnetic fluid) and Fe 3 O 4 (ferrimagnetic fluid). Furthermore, it was observed that the Nusselt number is decreasing with the increasing values of boundary parameter (δ), while there is controversy with respect to the increasing values of radiation parameter (N). Additionally, it was observed that the ferromagnetic case gained maximum thermal conductivity, as compared to ferrimagnetic case. In the end, the convergence of the finite element solution was observed; the calculations were found by reducing the mesh size.Coatings 2020, 10, 170 2 of 20 metals, etc.). Such attention is the due to their credible applications in heat transfer, innovative magnetic constituents, and microelectronic freezing. Magnetic nano-fluids create a different kind of nano-fluid that shows both fluidic and magnetic properties. These fluids interest researchers and scientists because they have several applications in the field of bio-medicine, chemical engineering, micro-electro-mechanical, compounds, colored stains, the refinement of melted metals, shock absorbers, pumps, etc. [1][2][3][4]. The transfer of heat is the elementary feature of the vast utilization via applications, which are subjected to the thermal conductivity of operational liquids, and include procedures with the capability of thermal utilization and erection. There are many periodicals on nano-fluids that seek to recognize their behavior so that it can be utilized wherever the transfer of heat enhancement is overriding, such as in several manufacturing appliances such as transportation, nuclear-powered reactors, and electronics and in bio-medicine and nutrition. Nano-fluid has been found wherever the heat transfer might be reduced or enhanced. Wen [5] represents the insufficient caring of the structure and mechanism of nano-fluids and their applications.The suspension of particles is instigated by Brownian motion. Under normal conditions, the particles will not settle down. The magnetism of nano-scaled ferromagnetic particles has been truncated during surfactant van ...

In this article, the intention is to explore the flow of a magneto-hydrodynamic (MHD) bioconvective micro-polar Nanofluid restraining microorganism. The numerical solution of 2-D laminar bioconvective boundary layer flow of micro-polar nanofluids are presented. The phenomena of multi-slip, convective thermal and Solutal boundary conditions have been integrated. A system of non-linear partial differential equations are transformed into the system of coupled nonlinear ordinary differential equations by applying appropriate transformations, the transformed equations are then solved by applying the variational finite element method (FEM). The fascinating features of assorted velocity parameter, microrotation, temperature, microorganism compactness, solutal and nanoparticles concentration have been inspected. The rate of heat transfer, the skin friction coefficient, couple stress and Sherwood number for microorganisms have also been discussed graphically and numerically. The investigations illustrated that increase in material parameters causes a reduction in microorganism compactness, concentration and temperature. As a result of enhancement in the unsteadiness parameter, the fluid velocity, concentration of microorganisms and the temperature are observed to be declines. Energy and microorganism compactness profile affected by the improvement in the buoyancy ratio parameter. As the improvement in results of buoyancy ratio parameter effects on improvement in the energy and the microorganism compactness profile while the velocity profile is condensed. In the end, rationalized convergence of the finite element solution has been inspected; the computations are found out via depreciating the mesh size.

The present work examines the effect of different magnetic nanoparticles and the heat transfer phenomena over the stretching sheet with thermal stratification and slips effect. The mixture of water (H 2 O) and ethylene glycol (C 2 H 6 O 2 ) is used as base fluid whereas the paramagnetic, diamagnetic, and ferromagnetic ferrites are taken as nanoparticles. In the presence of ferrite nanoparticles, the magnetic dipole has a significant effect in controlling the rate of heat transfer and the thermal boundary layers. By using suitable similarity transformations, the system of partial differential equations is transformed into nonlinear ordinary differential equations. The numerical solution of resulting equations is found out by using the variational finite element method. The effect of numerous emerging parameters on velocity, temperature, and micro-rotation velocity are represented graphically and analyzed numerically. It has been noticed that comparatively the diamagnetic ferrites have gained maximum thermal conductivity relative to the other nanoparticles. It was also observed that the thermal conduction of nanoparticles increases with the variation of volume fraction. Moreover, with increasing values of thermal stratification the thermal boundary layer thickness decreases and the heat transfer rate increases at the surface. Furthermore, the validation of code and the accuracy of the numerical technique has been confirmed by the assessment of current results with earlier studies.

The role of women in economic development and the global environment is vital for progressing them towards the United Nations sustainable development goal (SDG-5) that emphasized the need to empower women in every walk of life. The study examines women’s autonomy in the sustainable development agenda under China’s open innovation system from 1975 to 2019. The study employed an autoregressive distributed lag (ARDL) model, vector autoregressive (VAR) Granger causality, and innovation accounting matrix to estimate parameters. The existing data are summarized and collated in the context of China to explain as a correlational study. The results show that women’s autonomy moderated with technology spills over to decrease greenhouse gas (GHG) emissions and substantiate the hump-shaped relationship between them. The increased spending on research and development (R&D) activities, patent publications, and renewable energy consumption empowers women to be equipped with the latest sustainable technologies to improve environmental quality. The pollution haven hypothesis verifies a given country, where trade liberalization policies tend to increase polluting industries to set up their plants that engaged in dirty production that exacerbate GHG emissions. The causality estimates confirmed that technological innovations and renewable energy consumption leads to women’s autonomy. In contrast, females’ share in the labor force participation rate leads to an increase in renewable energy consumption. Thus, it is evident that there is a positive role of women in the country’s sustainable development.