Unsteady two-dimensional flows of a nanofluid over a vertical plate with time-exponential temperature

Abstract

A two dimensional natural convective flow of nanofluid over a vertical plate in the presence of time-exponential temperature has been studied analytically. We have incorporated the effects of thermophoresis and Brownian motion in the considered nanofluid model. Moreover on the boundary of plate, it is assumed that the volumetric concentration of nanoparticles is passively controlled. The non-linear coupled governing equations have been solved with the help of the modified simple function equation method. Exact expressions for the concentration, temperature and velocity distribution profile have been established. Numerical computations are carried out in order to see the influence of different physical parameters like Lewis number, Pradtl number, buoyancy ratio parameter, thermophoresis parameter and Brownian motion parameter on the volumetric concentration of nanoparticles, temperature and velocity distribution profile and results are illustrated graphically and with tables. It is found that for decreasing values of the Brownian diffusion coefficient, therefore for increasing values of the Lewis number, the values of temperature and of particles concentration decrease. The temperature decreases with Prandtl number; while the nanoparticles concentration increases with Prandtl number (the thermal diffusivity has different influence on temperature and concentration).

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“…Many definitions of fractional derivatives are available. Yang's monograph offers a comprehensive study of various fractional derivative systems [33], with widespread applications as fractional wire [34], fractional vibration [35], fractional fluid [36], electromechanical fractional MHD [37], electromagnetic fractional flux, fractional thermoelasticity [38], soliton dynamics [39] and fractional KdV equation [40]. He et al [41] proposed the partial complex transformation to turn the fractional differential equation into the classic differential partner of Jumarie's alteration of Riemann-Liouville derivative.…”