Numerical modeling and spatial stability analysis of the wall jet flow of nanofluids with thermophoresis and brownian effects

Amin Jafarimoghaddam ^a,*, Fatemeh Shafizadeh ^b

a. Independent Researcher, Tehran, Iran (Previously at the Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran
         b. Department of Chemical Engineering, Babol Noshirvani University of Technology, Babol, Iran

Abstract: The present work describes similarity solution to a general scheme for the wall jet flow of nanofluids, accounting both the similarity branches (say upper and lower), allowed with respect to the suction and moving wall conditions in the context of Glauert type e-jets. Before proceeding with this, a spatial stability analysis is performed to check the stability of the similarity modes. Results indicated that the upper similarity branch is possibly stable; whilst, the lower branch is not likely to reside in actual physics. The governing transport equations of mass and energy subject to a general two-phase modeling framework were transformed into similarity equations. The involved equations were then solved numerically employing the standard 4th order Runge-Kutta together with shooting technique. The influence of the involved parameters is shown graphically and in a detailed manner. In the last section, it is presented closed-form algebraic solution to the energy equation for the base fluids with a general convective boundary condition.  

Keywords: Wall jet flow of nanofluids; Two-phase modeling; Spatial stability analysis; Similarity solution; Numerical modeling