磁致空气自然对流的数学模型

Numerical analysis of magnetically induced free convection in air

为研究流体磁化率随温度变化的磁致自然对流产生的原因和物理机理,推导了磁浮升力的表达式,并分别对顺磁性流体和逆磁性流体进行了分析。以磁致空气自然对流为对象,对不可压、定常、层流流动提出其数学模型。在对数学模型量纲归一化分析的基础上,得到了磁Rayleigh数Ram公式。对二维封闭方腔内磁致空气自然对流在两种不同Ram工况下的流动和换热特性进行了数值模拟。结果表明,磁致自然对流的行为由流体的性质和Ram决定,对于给定的流体和几何形状,Ram确定了磁致自然对流的流动形态和换热特性。

The magnetic buoyancy forces were analyzed for paramagnetic and diamagnetic fluids based on the physical mechanism of magnetically induced free convection arising from the susceptibility variation with temperature. The mathematical model considers incompressible, steadystate, laminar flow with magnetically induced free convection of air based on a onedimensional analysis of the mathematical model. A magnetic Rayleigh number, Ram, was developed. Numerical simulations of magnetically induced free convection in a 2D square enclosure for two different Ram show that the magnetically induced free convection is a function of the fluid properties and Ram. The flow and heat transfer of magnetically induced free convection is a strong function of Ram for given fluid and geometry.