Two-component modeling for non-Newtonian nanofluid slip flow and heat transfer over sheet： Lie group approach

• Published in: Applied mathematics and mechanics 2016-10, Vol.37 (10), p.1325-1340
• Main Authors: Rana, P., Uddin, M. J., Gupta, Y., Ismail, A. I. M.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Boundary conditions; Classical Mechanics; Differential equations; Fluid- and Aerodynamics; Heat transfer; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nanofluids; Nanoparticles; Non Newtonian flow; Partial Differential Equations; Runge-Kutta method; Stability analysis
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-016-2140-9

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.