Existence and uniqueness results for a nonlinear differential equation arising in stagnation point flow in a porous medium

We establish existence and uniqueness results over the semi-infinite interval [0, ∞) for a class of nonlinear third-order ordinary differential equations arising in the stagnation point flow in a porous medium.     

Flow and heat transfer in a moving fluid over a moving non-isothermal surface

Heat transfer characteristics for a boundary layer forced convective flow past a moving parallel flat non-isothermal surface in the presence of heat source/sink are obtained. The cases of surface temperature varying directly or inversely with power-law exponent are considered. The similarity solutions are obtained. The numerical results are validated by comparing them with the available results in the literature for some special cases. It is found that dual solutions exist when the surface and the fluid move in the opposite directions. Furthermore, exact and analytical solutions are provided for some parametric regimes.     

Diffusion of chemically reactive species in Casson fluid flow over an unsteady permeable stretching surface

In this paper we investigate the two-dimensional flow of a non-Newtonian fluid over an unsteady stretching permeable surface. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First-order constructive/destructive chemical reaction is considered. With the help of a shooting method, numerical solutions for a class of nonlinear coupled differential equations subject to appropriate boundary conditions are obtained. For the steady flow, the exact solution is obtained. The flow features and the mass transfer characteristics for different values of the governing parameters are analyzed and discussed in detail.     

MHD Carreau nanoliquid flow over a nonlinear stretching surface

The Dufour and Soret impacts on magnetohydrodynamic Carreau nanoliquid past a nonlinearly stretching sheet are investigated. Variations in viscosity, heat conductivity, and convective boundary conditions are considered. Suitable similarity conversions are utilized to design the governing equations nondimensional. The Optimal Homotopy Analysis Method is employed to resolve the dimensionless equations. Graphs and tables are utilized to illustrate the impacts of the relevant factors over velocity, temperature, concentration, and streamlines. For the variations of different parameters, numerical values for Nusselt number, Sherwood number, and skin friction are provided in a table. The observed results are in good agreement with the previous literature findings. Furthermore, the current research shows that when the Dufour number increases, the temperature distributions get narrower. However, with increasing Soret number, the concentration distribution has the opposite effect. One of the important outcomes of the current study is that by increasing the Weissenberg number for shear-thinning fluids, one can improve the velocity field.     

Coupled effect of multislips and activation energy in a micropolar nanoliquid on a convectively heated elongated surface

This research communication explores the impact of wall slips along with the suspension of nanomaterials in a chemically reactive micropolar liquid stream on a stretched surface with convective heating. Activation of energy is analyzed through the modified Arrhenius function. Radiative heat flux with nonlinearity and temperature-dependent thermal source (sink) are considered in the heat transmission process. The Cattaneo–Christov approach featuring the time of thermal relaxation is employed. Successive application of scaling analysis followed by the Runge–Kutta–Fehlberg numerical approach delivered computational solutions for the partial differential equations delineating the problem under study. The response of flow variables for different values of various emerged physical variables is elaborated in detail via graphical and numerical presentations. Comparison of the outcome of the current analysis for certain cases is in accordance with the outcomes available in the literature. The findings reveal that pairs of velocity, microrotation, temperature, and species concentration oppositely reacted to both parameters of slip. The temperature of the nanofluid is improved by 18.5%, for specified values of radiation and temperature ratio parameters over that of the pure base liquid. Activation energy augments concentration. The drag coefficient declines with growing thermal and solutal Grashof numbers. Sherwood number is enhanced for higher values of the temperature difference and chemical reaction parameters.     

The effect of variable viscosity on the flow and heat transfer of a viscous Agwater and Cu-water nanofluids

A numerical study is carried out to study the effects of the temperature dependent viscosity on the flow and heat transfer of a nanofluid over a flat surface in the presence of viscous dissipation. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, and are solved numerically by the Keller-box method. The numerical results indicate that the effect of nanoparticle volume fraction is to increase the heat transfer and hence enhance the thermal boundary layer thickness. This is true even in the presence of variable viscosity and the viscous dissipation. Furthermore, the results obtained for heat transfer characteristics with nanoparticles reveal many interesting behaviors that warrant further study on the effects of the "nano-solid-particles".     

Transport of thermal energy in the magnetohydrodynamic oblique stagnation point flow in a hybrid nanofluid with nanoparticle shape effect

In the present paper, the augmented heat characteristics of a hybrid nanofluid which is a blend of Al₂O₃ (alumina) and Ag (silver) in the host hybrid fluid (C₂H₆O₂-H₂O) (50%–50%) impinging obliquely on an elastic surface with magnetic lines of force are investigated. The properties of the nanofluid are assessed through the computational solutions established with the aid of the popular Runge–Kutta–Fehlberg fifth-order (RKF 5) numerical technique. Outputs of the analysis reveal that the rate of thermal energy transport in the hybrid (mono) nanofluid is enhanced by 11.5% (5.8%) by using blade-shaped nanoparticles in comparison to that of the spherical particles. Stream contours of both nanofluids are inclined to the left (right) of the stagnation-point for positive (negative) values of the stagnation flow parameter.     

Boundary layer flow past a stretching/shrinking surface beneath an external uniform shear flow with a convective surface boundary condition in a nanofluid

The problem of a steady boundary layer shear flow over a stretching/shrinking sheet in a nanofluid is studied numerically. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique. Two types of nanofluids, namely, Cu-water and Ag-water are used. The effects of nanoparticle volume fraction, the type of nanoparticles, the convective parameter, and the thermal conductivity on the heat transfer characteristics are discussed. It is found that the heat transfer rate at the surface increases with increasing nanoparticle volume fraction while it decreases with the convective parameter. Moreover, the heat transfer rate at the surface of Cu-water nanofluid is higher than that at the surface of Ag-water nanofluid even though the thermal conductivity of Ag is higher than that of Cu.     

Effect of thermophoresis and Brownian motion on the melting heat transfer of a Jeffrey fluid near a stagnation point towards a stretching surface: Buongiorno's model

This analysis intends to address the coupled effect of phase change heat transfer, thermal radiation, and viscous heating on the MHD flow of an incompressible chemically reactive nanofluid in the vicinity of the stagnation point toward the stretching surface, taking a Jeffrey fluid as the base fluid. Convergent analytical solutions for the nonlinear boundary layer equations are obtained by the successive application of scaling variables and the highly efficacious homotopy analysis method. Error analysis is implemented to endorse the convergence of the solutions. Through parametric examination, influence of various physical parameters occurring in analysis of the profiles of velocity, temperature, and nanoparticle concentration, coefficient of surface drag, rates of mass and heat transfer is explored pictorially. The Deborah number and the melting parameter are found to enhance velocity, and the associated momentum boundary layers are thicker, whereas the magnetic field depreciates the flow rate. Temperature is observed to enhance with the thermophoresis parameter, Prandtl number and Eckert number, whereas a reduction is seen with the thermal radiation parameter and Brownian motion parameter. Nanoparticle concentration is depleted by the chemical reaction parameter, the thermophoresis parameter, and the Lewis number.