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The aim of present work is to study the flow and heat transport structures of hybrid nanoparticles in a moving material. Two types of hybrid nanoparticles have been chosen namely Al₂O₃-Cu and Al₂O₃-Ag nanoparticles (90%) within 10% of pure water.

Leading governing equations are transformed through similarity technique and then computed for numerical illustration by applying RKF method.

The author observed that the skin friction value of Al₂O₃-Cu/water case is lesser in comparison to the values of Nusselt number for Al₂O₃-Ag/water nanoparticles.

There exist no such study which addressed such phenomenon.

The purpose of this paper is to discuss the 3D micropolar hybrid (Ag-CuO/H₂O) nanofluid past rapid moving surface, where porous medium has been considered.

The model of problem was represented by highly partial differential equations which were deduced by using suitable approximations (boundary layer). Then, the governing model was converted into five combined ordinary differential equations applying proper similarity transformations. Therefore, the eminent iterative Runge–Kutta–Fehlberg method (RKF45) has been applied to solve the resulting equations.

Higher values of vortex viscosity, spin gradient viscosity and micro-inertia density parameters are reduced in horizontal direction, whereas opposite behaviour is noticed for vertical direction.

The work has not been done in the area of hybrid micropolar nanofluid. Hence, this article culminates to probe how to improve the thermal conduction and fluid flow in 3D boundary layer flow of micropolar mixture of nanoparticles driven by rapidly moving plate with convective boundary condition.

The purpose of this paper is to study the steady biomagnetic hybrid nanofluid (HNF) of oxytactic microorganisms taking place over a thin needle with a magnetic field using the modified Buongiorno’s nanoliquid model.

On applying the appropriate similarity transformations, the governing partial differential equations were transformed into a set of ordinary differential equations. These equations have been then solved numerically using Runge–Kutta–Fehlberg method of fourth–fifth order programming in MAPLE software. Features of the velocity profiles, temperature distribution, reduced skin friction coefficient, reduced Nusselt number and microorganisms’ flux, for different values of the governing parameters were analyzed and discussed.

It was observed that as the needle thickness and solid volume fraction increase, the temperature rises, but the velocity field decreases. For a higher Peclet number, the motile microorganism curve increases, and for a higher Schmidt number, the concentration curve rises.

On applying the modified Buongiorno’s model, the present results are original and new for the study of HNF flow and heat transfer past a permeable thin needle.

This study aims to investigate the flow behavior of aluminum oxide–water nanofluid with variable viscosity flowing through the microchannel parallel with the ground, with low aspect ratio. The study focuses on the first and second law analyses of Poiseuille flow using water as the base fluid with alumina nanoparticles suspended in it. Combined effects of thermal radiation, viscous dissipation, variable viscosity, nanoparticle shape factor and volume fraction on the thermal performance are studied and the in-built irreversibility in the process is examined.

The governing equations with dimensions are reduced to non-dimensional equations by using dimensionless quantities. Then, the Runge–Kutta–Fehlberg shooting scheme tackles the present non-linear equations.

The outcomes of the present analysis reveal that the activation energy parameter with its increase, depletes the exergetic effectiveness of the system, thus defending the fact to keep the activation energy parameter the lowest as possible for the system efficiency. In addition, thermal radiation and Biot number enhance the release of heat energy, thereby cooling the system. Bejan number graph exhibits the decreasing behavior for the increased nanoparticle shape factor, whereas the temperature enhances with the rise in nanoparticle shape factor.

The effects of nanoparticle shape factor in Poiseuille flow for alumina–water nanoliquid in low aspect ratio microchannel is inspected at the earliest. Exergetic effectiveness of the system is studied and heat transfer characteristics are explored for thermal radiation effect and activation energy parameter. Besides, BeηSphere>BeηBlades.

The purpose of this paper is to numerically study the boundary layer problem for the case of two-dimensional flow of dusty fluid over a shrinking surface in the presence of the fluid suction at the surface.

The governing equations of the problem are reduced to the system of ordinary differential equations using the similarity transformation and then solved using the bvp4c method in the Matlab software.

The effects of the drag coefficient parameter L, the fluid–particle interaction parameter δ, the suction parameter s and the particle loading parameter ω on the flow of the permeable shrinking sheet are investigated. It is found that the aforementioned parameters have different effects in the shrinking sheet flow. This study has also succeeded in discovering the second solution, and through the stability analysis, it is suggested that the solution is unstable and not physically realizable in practice.

The current findings add to a growing body of literature on the boundary layer problem in the dusty fluid. The dusty fluid is significant in various practical applications such as in the transporting suspended powdered materials through pipes, propulsion and combustion in rockets, the flow of blood in arteries, wastewater treatment and as corrosive particles in engine oil flow.

Even though the dusty fluid problem has been extensively studied in the flow of the stretching sheet, limited findings can be found over a shrinking flow. In fact, this is the first study to discover the second solution in the dusty fluid problem.

This paper aims to address the problem of double-diffusive magnetohydrodynamics (MHD) non-Darcy convective flow of heat and mass transfer over a stretching sheet embedded in a thermally-stratified porous medium. The controlling parameters such as chemical reaction parameter, permeability parameter, etc., are extensively discussed and illustrated in this paper.

With the help of appropriate similarity variables, the governing partial differential equations are converted into ordinary differential equations. The transformed equations are solved using the spectral homotopy analysis method (SHAM). SHAM is a numerical method, which uses Chebyshev pseudospectral and homotopy analysis method in solving science and engineering problems.

The effects of all controlling parameters are presented using graphical representations. The results revealed that the applied magnetic field in the transverse direction to the flow gives rise to a resistive force called Lorentz. This force tends to reduce the flow of an electrically conducting fluid in the problem of heat and mass transfer. As a result, the fluid velocity reduces in the boundary layer. Also, the suction increases the velocity, temperature, and concentration of the fluid, respectively. The present results can be used in complex problems dealing with double-diffusive MHD non-Darcy convective flow of heat and mass transfer.

The uniqueness of this paper is the examination of double-diffusive MHD non-Darcy convective flow of heat and mass transfer. It is considered over a stretching sheet embedded in a thermally-stratified porous medium. To the best of the knowledge, a problem of this type has not been considered in the past. A novel method called SHAM is used to solve this modelled problem. The novelty of this method is its accuracy and fastness in computation.

The purpose of this paper is to study the effects of thermal radiation and homogeneous-heterogeneous reactions in the three-dimensional hybrid nanofluid flow past a permeable stretching/shrinking sheet.

The combination of aluminum oxide (Al₂O₃) and copper (Cu) nanoparticles with total volumetric concentration is numerically analyzed using the existing correlations of hybrid nanofluid. With the consideration that both homogeneous and heterogeneous reactions are isothermal while the diffusion coefficients of both autocatalyst and reactant are same, the governing model is simplified into a set of differential (similarity) equations.

Using the bvp4c solver, dual solutions are presented, and the stability analysis certifies the physical/real solution. The findings show that the suction parameter is requisite to induce the steady solution for shrinking parameter. Besides, the fluid concentration owing to the shrinking sheet is diminished with the addition of surface reaction.

The present findings are novel and can be a reference point to other researchers to further analyze the heat transfer performance and stability of the working fluids.

This study aims to present an analysis on heat transfer attributes of fluid-particle interaction over a permeable elastic sheet. The fluid streaming on the sheet is Casson fluid (CF) with uniform distribution of dust particles.

The basic steady equations of the CF and dust phases are in the form of partial differential equations (PDEs) which are remodeled into ordinary ones with the aid of similarity transformations. In addition to analytical solution, numerical solution is obtained for the reduced coupled non-linear ordinary differential equations (ODEs) to validate the results.

The solution seems to be influenced by significant physical parameters such as CF parameter, magnetic parameter, suction parameter, fluid particle interaction parameter, Prandtl number, Eckert number and number density. The impact of these parameters on flow field and temperature for both fluid and dust phases is presented in the form of graphs and discussed in detail. The effect on skin friction coefficient and heat transfer rate is also presented in tabular form. It has been observed that an increase in the CF parameter curtails the fluid velocity as well as the particle velocity however enhances the heat transfer rate at the wall. Furthermore, comparison of the numerical and analytical solution is also made and found to be in excellent agreement.

Although the analysis of dusty fluid flow has been widely examined, however, the present study obtained both analytical and numerical results of power law temperature distribution in dusty Casson fluid under the influence of magnetic field which are new and original for such type of flow.

In financial analysis, forecasting often involves regressing one time series variable on another. However, to ensure that the models are correctly specified, one needs to first test for stationarity, co‐integration and causality. In testing for causality, the variables should be stationary. If non‐stationary, one can estimate the model in difference form, unless the variables are co‐integrated. This article determines whether cash flow and earnings variables are stationary, and which variable causes the other, using econometric analysis. In most cases, cash flow variables are found to cause earnings variables. This is so when the models are estimated in levels. However, when estimated in first differences, the causal relationship tends to be reversed such that earnings cause cash flows. Further study is recommended, whereby panel data could be used to improve the power of the tests.