Convective Transport in a Binary Nanofluid Saturated Porous Layer: A Nonlinear Approach

Abstract

Nonlinear analysis of a binary nanofluid saturated rotating porous layer is performed in the present article. While the porous medium complies with the Brinkman model, Brownian motion and thermoporesis of nanoparticles introduce additional nonlinear effects for the heat transport in the nanofluid. The thermal energy equations include the diffusion and cross-diffusion terms. For a flat fluid layer contained between two free boundaries, an exact analytic solution is obtained using one term Galerkin method. The critical Rayleigh number for the linear onset of instability is determined numerically. Nonlinear analysis using a truncated Fourier series, has been done in terms of the Nusselt numbers'. The behavior of the concentration and thermal Nusselt numbers is investigated numerically by solving the finite amplitude equations. The results obtained have been presented graphically and discussed in detail.

Nonlinear thermal convection in a viscoelastic nanofluid saturated porous medium under gravity modulation

“…The comparison is also made for with or without modulation, modulation case is more in heat and mass transport than in unmodulated case, these results conform the results obtained by Bhadauria and Kiran [51]. For un-modulation case one can see the paper of Agarwal et al [29]. But, for Newtonian fluid saturated porous medium case Srivastava et al [60] show the quite opposite results for weak nonlinear convection using Ginzburg-Landau model.…”

“…In general the following modes ð1; 1Þ is for stream function, ð0; 2Þ for temperature and ð1; 1Þ for nanoparticle concentration, which means only two terms have been considered (also see the studies of [27][28][29][30][31][32][33]) in order to study heat and mass transfer. The reader may note that, here is first nonlinear effects are accounted and further terms may slightly be addition to the nonlinear effects.…”

“…Their experiment showed that a smaller particle size exhibits better friction reduction with particle size ranging from 59 to 220 nm. Some other studies related to the nanofluids are given by [22][23][24][25][26][27][28][29][30][31][32] and corresponding introduction therein.…”

Rayleigh–Bénard instability in nanofluids: a comprehensive review

“…In this paper, numerical calculations were performed in order to obtain the terms. Agarwal et al [62] studied non-linear convection in binary nanofluid layer saturating porous medium in terms of Nusselt number and found that initially the effect of time on Nusselt number is oscillatory while it becomes steady as the time increases. Yadav et al [63] explored the thermal conductivity and viscosity variations effects on binary nanofluid convection in porous medium.…”

Onset of Convection in Porous Medium Saturated by Viscoelastic Nanofluid: More Realistic Result

“…Recently Hayat et al (2015) studied the mixed convection flow of non-Newtonian nanofluid over a stretching surface including the effect of thermal radiation, heat source/sink and first order chemical reaction by taking Casson fluid model. Author's group, Bhadauria and Agarwal (2011a, b, c), , 2014, 2014a and Agarwal et al ( , 2012 studied thermal stability of nanofluid, considering various physical models and boundary conditions.…”