Dual nature solution of water functionalized copper nanoparticles along a permeable shrinking cylinder: FDM approach

摘要

Present framework is established to deal the characteristics of axisymmetric mixed convection flow with heat transfer of water based copper (Cu-water) nanofluid along a porous shrinking cylinder with slip effects. The physical problem is modeled in the form of set of partial differential equations (PDEs) including conservation of mass, momentum and energy equations along with defined boundary conditions. Such PDEs are adapted to ordinary differential equations (ODES) by utilizing similarity transformation technique. System of equations is emerged with the expressions of nanoparticle and based fluid. Numerical solution of governing ODEs is sought by using Finite Difference Method (FDM) against the range of several pertinent physical parameters. Base fluid (water) is analyzed in the presence of nanoparticles. The model encounters buoyancy opposing and assisting flow regions. Present study reveals that the solution in the assisting flow region is unique whereas multiple solutions exist in the opposing flow region. The results also indicate the existence of multiple solutions for certain amount of mass suction parameter. Moreover, increase in slip parameters and nanoparticle volume fraction enhances the range of suction parameter where the similarity solutions exist. It is further found that due to increase of nanoparticle volume fraction the skin friction increases whereas heat transfer rate decreases. (C) 2018 Elsevier Ltd. All rights reserved.