Three-dimensional mixed convection stagnation-point flow past a vertical surface with second-order slip velocity

This study is concerned with the three-dimensional (3D) stagnation-point for the mixed convection flow past a vertical surface considering the first-order and second-order velocity slips. To the authors' knowledge, this is the first study presenting this very interesting analysis. Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations (ODEs) by using appropriate similarity transformation. These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language. The effects of the governing parameters on the non-dimensional velocity profiles, temperature profiles, skin friction coefficients, and the local Nusselt number are presented in detail through a series of graphs and tables. Interestingly, it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation. The numerical computations of the present work are compared with those from other research available in specific situations, and an excellent consensus is observed. Another exciting feature for this work is the existence of dual solutions. An important remark is that the dual solutions exist for both assisting and opposing flows. A linear stability analysis is performed showing that one solution is stable and the other solution is not stable. We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics. These effects are depicted in graphs and discussed in this paper. The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow, as well as on the heat transfer characteristics.

Automated summary

This study presents a detailed analysis of the three-dimensional stagnation-point for mixed convection flow past a vertical surface with first-order and second-order velocity slips. The governing equations are transformed into ordinary differential equations using a similarity transformation and numerically solved using MATLAB. The effects of governing parameters on various flow and heat transfer characteristics are presented in graphs and tables. The study also reveals the existence of dual solutions for both assisting and opposing flows, with one solution being stable and the other unstable. The results emphasize the strong influence of mixed convection and velocity slip parameters on the flow characteristics.