This article intends to explore the onset of free convection flow of silver nanofluid in an enclosed square cavity filled with saturated porous medium bounded by adiabatic horizontal walls and isothermal vertical walls at different temperatures using a two-temperature thermal non-equilibrium model. The flow is assumed to follow Darcy law. The governing boundary layer equations are obtained based on Boussinesq approximation and Darcy model. The governing equations for fluid flow are reduced to partial differential equations with the help of non-dimensional transformation. Peaceman–Rachford alternating direction implicit (ADI) scheme is employed to solve the transformed flow equations. The physical clarification of streamlines and isotherms for liquid and solid for pertinent flow parameters is discussed graphically. The physical parameter such as average Nusselt number for fluid and solid phase, for different parameters such as inter-phase heat transfer coefficient and modified conductivity ratio is presented through graphs as well. One of the important findings is that with smaller values of the Rayleigh number Ra the centrally arranged core vortex is formed in streamlines, while the isotherms of liquid and solid phases are stratified in vertical direction close to the vertical walls. Meanwhile, it is also perceived that the vortices expand with an increasing values of Rayleigh number along the horizontal direction.

本文旨在使用双温度热非平衡模型探索银纳米流体在充满饱和多孔介质的封闭方腔中的自由对流的开始，该多孔介质以绝热水平壁和等温垂直壁为界，在不同温度下。假定流动遵循达西定律。基于Boussinesq近似和Darcy模型得到控制边界层方程。在无量纲变换的帮助下，流体流动的控制方程被简化为偏微分方程。Peaceman-Rachford 交替方向隐式 (ADI) 方案用于求解转换后的流动方程。以图形方式讨论了有关流动参数的液体和固体的流线和等温线的物理澄清。流体和固相的平均努塞尔数等物理参数，以及相间传热系数和修正电导率等不同参数的物理参数也通过图表呈现。重要的发现之一是，瑞利数的值越小Ra中心布置的核心涡流以流线形式形成，而液相和固相的等温线在靠近垂直壁的垂直方向上分层。同时，还可以看出，随着瑞利数值的增加，涡流沿水平方向扩展。