Galerkin法研究磁场和热辐射作用下的非牛顿纳米流体在垂直平板间的流动和自然对流换热特性

摘要

研究了在磁场和热辐射作用下,非牛顿纳米流体在两个无限大的垂直平板间流动的自然对流换热和流动特性.首先,采用相似变换法,将偏微分形式的动量和能量守恒方程转化为特殊边界条件下的非线性常微分方程组.应用Galerkin方法(GM),获得非线性常微分方程组的解析解,并给出了非线性常微分方程组的数值解.对比分析解析解和数值解,验证了模型的准确性、精度和可靠性.最后,综合考虑了磁场、辐射参数和纳米流体体积分数等参数对速度、摩擦阻力系数和Nusselt数分布的影响.结果表明,随着磁力作用的增大,速度场、摩擦阻力系数和热性能下降.辐射参数虽然对增强的速度场影响不大,但降低了摩擦阻力系和Nusselt数的影响.%The main goal of this paper is to investigate natural convective heat transfer and flow characteristics of non-Newtonian nanofluid streaming between two infinite vertical flat plates in the presence of magnetic field and thermal radiation. Initially, a similarity transformation is used to convert momentum and energy conservation equations in partial differential forms into non-linear ordinary differential equations (ODE) applying meaningful boundary conditions. In order to obtain the non-linear ODEs analytically, Galerkin method (GM) is employed. Subsequently, the ODEs are also solved by a reliable numerical solution. In order to test the accuracy, precision and reliability of the analytical method, results of the analytical analysis are compared with the numerical results. With respect to the comparisons, fairly good compatibilities with insignificant errors are observed. Eventually, the impacts of effective parameters including magnetic and radiation parameters and nanofluid volume fraction on the velocity, skin friction coefficient and Nusselt number distributions are comprehensively described. Based on the results, it is revealed that with increasing the role of magnetic force, velocity profile, skin friction coefficient and thermal performance descend. Radiation parameter has insignificant influence on velocity profile while it obviously has augmentative and decreasing effects on skin friction and Nusselt number, respectively.