Analysis of Unsteady Flow and Heat Transfer of Nanofluid Using Blasius–Rayleigh–Stokes Variable

This article investigates the unsteady flow and heat transfer analyses of a viscous-based nanofluid over a moving surface emerging from a moving slot. This new form of boundary layer flow resembles with the boundary layer flow over a stretching/shrinking surface depending on the motion of the moving slot. The governing partial differential equations are transformed to correct similar form using the Blasius–Rayleigh–Stokes variable. The transformed equations are solved numerically. Existence of dual solutions is observed for a certain range of moving slot parameter. The range of dual solution is strongly influenced by Brownian and thermophoretic diffusion of nanoparticles.

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Numerical solutions of three-dimensional boundary layer flow and heat transfer past a permeable shrinking surface in a Cu-water nanofluid

10.1063/1.4882487 ◽

2014 ◽

Cited By ~ 1

Author(s):

Mohd Amin Mohd Noor ◽

Roslinda Nazar ◽

Khamisah Jafar ◽

Ioan Pop

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Boundary Layer Flow ◽

Numerical Solutions ◽

Three Dimensional ◽

Flow And Heat Transfer ◽

Dimensional Boundary ◽

Layer Flow ◽

Shrinking Surface

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Boundary layer flow and heat transfer past a permeable shrinking surface embedded in a porous medium with a second-order slip: A stability analysis

Applied Thermal Engineering ◽

10.1016/j.applthermaleng.2016.08.080 ◽

2017 ◽

Vol 115 ◽

pp. 1407-1411 ◽

Cited By ~ 18

Author(s):

Mohd Hafizi Mat Yasin ◽

Anuar Ishak ◽

Ioan Pop

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Porous Medium ◽

Stability Analysis ◽

Boundary Layer Flow ◽

Second Order ◽

Flow And Heat Transfer ◽

Layer Flow ◽

Shrinking Surface

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Boundary layer flow of a nanofluid past a permeable exponentially shrinking surface with convective boundary condition using Buongiorno’s model

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-12-2013-0361 ◽

2015 ◽

Vol 25 (2) ◽

pp. 299-319 ◽

Cited By ~ 35

Author(s):

M.M. Rahman ◽

Alin V. Rosca ◽

I. Pop

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Boundary Condition ◽

Partial Differential Equations ◽

Differential Equations ◽

Skin Friction ◽

Boundary Layer Flow ◽

Content Type ◽

Layer Flow ◽

Shrinking Surface

Purpose – The purpose of this paper is to numerically solve the problem of steady boundary layer flow of a nanofluid past a permeable exponentially shrinking surface with convective surface condition. The Buongiorno’s mathematical nanofluid model has been used. Design/methodology/approach – Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the governing parameters, stretching/shrinking parameter λ, suction parameter s, Prandtl number Pr, Lewis number Le, Biot number, the Brownian motion parameter Nb and the thermophoresis parameter Nt, using the bvp4c function from Matlab. The effects of these parameters on the reduced skin friction coefficient, heat transfer from the surface of the sheet, Sherwood number, dimensionless velocity, and temperature and nanoparticles volume fraction distributions are presented in tables and graphs, and are in details discussed. Findings – Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the shrinking case (λ<0). A stability analysis has been performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible. In addition, it is shown that for a regular fluid (Nb=Nt=0) a very good agreement exists between the present numerical results and those reported in the open literature. Research limitations/implications – The problem is formulated for an incompressible nanofluid with no chemical reactions, dilute mixture, negligible viscous dissipation, negligible radiative heat transfer and a new boundary condition is imposed on nanoparticles and base fluid locally in thermal equilibrium. The analysis reveals that the boundary layer separates from the plate. Beyond the turning point it is not possible to get the solution based on the boundary-layer approximations. To obtain further solutions, the full basic partial differential equations have to be solved. Originality/value – The present results are original and new for the boundary-layer flow and heat transfer past a shrinking sheet in a nanofluid. Therefore, this study would be important for the researchers working in the relatively new area of nanofluids in order to become familiar with the flow behavior and properties of such nanofluids. The results show that in the presence of suction the dual solutions may exist for the flow of a nanofluid over an exponentially shrinking as well as stretching surface.

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