The extraordinary enhancement in heat transfer efficiency of nanofluids at extremely low volume fractions has attracted a lot of attention in identifying the governing mechanisms. The nanoscale effects, Brownian motion (random motion of particles inside the base fluid) and thermophoresis (diffusion of particles due to temperature gradient) are found to be important slip mechanisms in nanofluids. Based on these findings, a set of partial differential equations for conservation laws for nanofluids was formed. Since then, a large number of mathematical studies on convective heat transfer in nanofluids became feasible. The present paper summarizes the studies pertaining to instability of a horizontal nanofluid layer under the impact of various parameters such as rotation, magnetic field, Hall currents and LTNE effects in both porous and non-porous medium. Initially, investigations were made using the model considering fixed initial and boundary conditions on the layer, gradually the model was revised in the light of more practical boundary conditions and recently it has been modified to get new and more interesting results. The exhaustive analysis of instability problems is presented in the paper and prospects for future research are also identified.

中文翻译：

---

纳米流体中的瑞利-贝纳德不稳定性：全面综述

在极低的体积分数下，纳米流体传热效率的显着提高引起了人们对控制机理的广泛关注。纳米尺度效应，布朗运动（基液内部颗粒的随机运动）和热泳（由于温度梯度引起的颗粒扩散）被发现是纳米流体中重要的滑动机理。基于这些发现，形成了一组纳米流体守恒定律的偏微分方程。从那时起，关于纳米流体中对流传热的大量数学研究变得可行。本文总结了与水平纳米流体层在各种参数（例如旋转，磁场，霍尔电流和LTNE在多孔和非多孔介质中的影响。最初，使用考虑了固定的初始条件和边界条件的模型进行了研究，然后根据更实际的边界条件对模型进行了修改，最近对模型进行了修改以获取新的和更有趣的结果。本文对不稳定问题进行了详尽的分析，并确定了未来的研究前景。