The present paper aims at weak non-linear stability analysis followed by linear analysis of finite-amplitude Rayleigh–Benard magnetoconvection problem in an electrically conducting Newtonian liquid with heat source/sink. It is showed that the internal Rayleigh number, thermorheological parameter and Chandrasekhar number influence the onset of stationary convection and Nusselt number. The generalised Lorenz model derived for the problem is essentially the classical Lorenz model with its coefficients depending on the variable heat source (sink), viscosity and the applied magnetic field. The result of the parameters’ influence on the critical Rayleigh number explains their effect on the Nusselt number as well. The effect of increasing strength of the magnetic field in stabilising the system and diminishing heat transport is demonstrated. But the heat source and variable viscosity work together to make the system unstable, as their effect enhances heat transfer.

中文翻译：

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具有热源的温敏牛顿液体中的非线性瑞利-贝纳德磁对流

本文针对弱非线性稳定性分析，然后对具有热源/散热器的导电牛顿液体中的有限振幅瑞利-贝纳德磁对流问题进行线性分析。结果表明，内部瑞利数、热流变参数和钱德拉塞卡数会影响固定对流的开始和努塞尔数。针对该问题导出的广义洛伦兹模型本质上是经典洛伦兹模型，其系数取决于可变热源（汇）、粘度和外加磁场。参数对临界瑞利数的影响结果也解释了它们对努塞尔数的影响。证明了增加磁场强度在稳定系统和减少热传输方面的效果。