The present paper deals with the multiple solutions and their stability analy- sis of non-Newtonian micropolar nanofluid slip flow past a shrinking sheet in the presence of a passively controlled nanoparticle boundary...The present paper deals with the multiple solutions and their stability analy- sis of non-Newtonian micropolar nanofluid slip flow past a shrinking sheet in the presence of a passively controlled nanoparticle boundary condition. The Lie group transformation is used to find the similarity transformations which transform the governing transport equations to a system of coupled ordinary differential equations with boundary condi- tions. These coupled set of ordinary differential equation is then solved using the Runge- Kutta-Fehlberg fourth-fifth order （RKF45） method and the ode15s solver in MATLAB. For stability analysis, the eigenvalue problem is solved to check the physically realizable solution. The upper branch is found to be stable, whereas the lower branch is unsta- ble. The critical values （turning points） for suction （0 〈 sc 〈 s） and the shrinking parameter （Xc 〈 X 〈 0） are also shown graphically for both no-slip and multiple-slip conditions. Multiple regression analysis for the stable solution is carried out to inves- tigate the impact of various pertinent parameters on heat transfer rates, The Nusselt number is found to be a decreasing function of the thermophoresis and Brownian motion parameters.展开更多
The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group ...The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.展开更多
基金Project supported by Universiti Sains Malaysia(No.1001/PMATHS/811252)
文摘The present paper deals with the multiple solutions and their stability analy- sis of non-Newtonian micropolar nanofluid slip flow past a shrinking sheet in the presence of a passively controlled nanoparticle boundary condition. The Lie group transformation is used to find the similarity transformations which transform the governing transport equations to a system of coupled ordinary differential equations with boundary condi- tions. These coupled set of ordinary differential equation is then solved using the Runge- Kutta-Fehlberg fourth-fifth order （RKF45） method and the ode15s solver in MATLAB. For stability analysis, the eigenvalue problem is solved to check the physically realizable solution. The upper branch is found to be stable, whereas the lower branch is unsta- ble. The critical values （turning points） for suction （0 〈 sc 〈 s） and the shrinking parameter （Xc 〈 X 〈 0） are also shown graphically for both no-slip and multiple-slip conditions. Multiple regression analysis for the stable solution is carried out to inves- tigate the impact of various pertinent parameters on heat transfer rates, The Nusselt number is found to be a decreasing function of the thermophoresis and Brownian motion parameters.
基金Project supported by the National Natural Science Foundation of China (No. 50936003)the Open Project of State Key Laboratory for Advanced Metals and Materials and the Research Foundation of Engineering Research Institute of University of Science and Technology Beijing (No. 2009Z-02)
文摘The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.
