This paper is about the stagnation point flow and mass transfer with chemical reaction past a stretching/shrinking cylinder. The governing partial differential equations in cylindrical form are transformed into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using a shooting method. Results for the skin friction coefficient, Schmidt number, velocity profiles as well as concentration profiles are presented for different values of the governing parameters. Effects of the curvature parameter, stretching/shrinking parameter and Schmidt number on the flow and mass transfer characteristics are examined. The study indicates that dual solutions exist for the shrinking cylinder but for the stretching cylinder, the solution is unique. It is observed that the surface shear stress and the mass transfer rate at the surface increase as the curvature parameter increases.
The mathematical model of the two-dimensional steady stagnation-point flow over a stretching or shrinking sheet of nanofluid in the presence of the Soret and Dufour effects and of second-order slip at the boundary was considered in this paper. The partial differential equations were transformed into the ordinary differential equations by applying a suitable similarity transformation. The numerical results were obtained by using bvp4c codes in Matlab. The skin friction coefficient, heat transfer coefficient, mass transfer coefficient, as well as the velocity, temperature, and concentration profiles were presented graphically for different values of slip parameters, Soret effect, Dufour effect, Brownian motion parameter, and thermophoresis parameter. A dual solution was obtained in this present paper. The presence of the slip parameters (first-and second-order slip parameters) was found to expand the range of solutions. However, the presence of the slip parameters led to a decrease in the skin friction coefficient, whereas the heat transfer coefficient increased. Besides that, a larger Soret effect (smallest Dufour effect) led to the decrement of the heat transfer coefficient. The effects of the Brownian motion and thermophoresis parameters on the heat transfer coefficient were also studied in this paper. A stability analysis was performed in this paper to verify the stability of the solutions obtained.
The stagnation-point boundary-layer flow and heat transfer over an exponentially stretching/shrinking cylinder is studied. The governing partial differential equations in cylindrical form are first transformed into ordinary differential equations which are then solved numerically using a shooting method. Results for the skin friction coefficient, local Nusselt number, velocity and temperature profiles are presented and discussed in detail. The effects of the stretching/shrinking parameter ɛ and the curvature parameter γ on the fluid flow and heat transfer characteristics are also examined. It is found that the solutions for a shrinking cylinder are non-unique and that the surface shear stress and the heat transfer rate at the surface increase as the curvature parameter increases.
This article focuses on the boundary layer for an axisymmetric flow and heat transfer of a nanofluid past a moving slender needle with single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). In this study, the streamlines of the flow are symmetrically located along the needle’s surface. Water and kerosene are two types of base fluids that are considered in this study. This analysis is presented with needle thickness, the ratio of velocity, nanoparticle volume fraction, and Prandtl number. The partial differential equations (PDEs) are transformed into dimensionless ordinary differential equations (ODEs) by adopting relevant similarity transformations. The bvp4c package is implemented in MATLAB R2018a to solve the governing dimensionless problems numerically. The behaviors of various sundry variables on the flow and heat transfer are observed and elaborated further. The magnitude of the skin friction, heat transfer rate, as well as velocity and temperature distributions are demonstrated in graphical form and discussed. It is worth mentioning that kerosene-based CNTs have the largest skin friction coefficient and heat transfer rate compared to water-based CNTs. The thin wall of the needle and the single-walled carbon nanotubes also contributes to high drag force and heat transfer rate on the surface. It is revealed from the stability analysis that the first solution exhibits a stable flow. Obtained results are also matched with the present data in the restricting situation, and excellent agreement is noticed.
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