Abstract
In this paper, we study the effect of local thermal non-equilibrium on the linear thermal instability in a horizontal layer of a Newtonian nanofluid. The nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. A two-temperature model has been used for the effect of local thermal non-equilibrium among the particle and fluid phases. The linear stability is based on normal mode technique and for nonlinear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. We observe that for linear instability, the value of Rayleigh number can be increased by a substantial amount on considering a bottom heavy suspension of nano particles. The effect of various parameters on Rayleigh number has been presented graphically. A weak nonlinear theory based on the truncated representation of Fourier series method has been used to find the concentration and the thermal Nusselt numbers. The behavior of the concentration and thermal Nusselt numbers is also investigated by solving the finite amplitude equations using a numerical method.
Highlights
Natural convection in fluids has been a topic of interest for researchers like Nield and Bejan [1], Pop and Ingham [2], Ingham and Pop [3], Vafai [4,5], Vadasz [6], due to its appearance in industry and machineries where heat transfer is encountered
Natural convection has been studied in nanofluids by Buongiorno [8], Tzou [9,10], Kim et al [11,12,13], and based on these results in the current decade by Nield and Kuznetsov [14], Kuznetsov and Nield [15] for the Horton-Rogers-Lapwood Problem of onset of thermal instability in a porous medium saturated by a nanofluid, using Darcy and Brinkman models, respectively, and incorporating the effects of Brownian motion and thermophoresis of Nanoparticles
The LTNE model of convective heat transfer in porous medium has been dealt by Kuznetsov and Nield [15], Agarwal and Bhadauria [20], Bhadauria and Agarwal [18,19] to claim that the effect of LTNE can be significant for some circumstances but remains insignificant for typical dilute nanofluids
Summary
Natural convection in fluids has been a topic of interest for researchers like Nield and Bejan [1], Pop and Ingham [2], Ingham and Pop [3], Vafai [4,5], Vadasz [6], due to its appearance in industry and machineries where heat transfer is encountered. Natural convection has been studied in nanofluids by Buongiorno [8], Tzou [9,10], Kim et al [11,12,13], and based on these results in the current decade by Nield and Kuznetsov [14], Kuznetsov and Nield [15] for the Horton-Rogers-Lapwood Problem of onset of thermal instability in a porous medium saturated by a nanofluid, using Darcy and Brinkman models, respectively, and incorporating the effects of Brownian motion and thermophoresis of Nanoparticles They found that the critical thermal Rayleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy, by the presence of. The LTNE model of convective heat transfer in porous medium has been dealt by Kuznetsov and Nield [15], Agarwal and Bhadauria [20], Bhadauria and Agarwal [18,19] to claim that the effect of LTNE can be significant for some circumstances but remains insignificant for typical dilute nanofluids
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