传导-辐射对沿垂直平面有热泳的瞬时自然对流的影响

研究存在热辐射时,热泳微粒的沉积,对沿垂直平面瞬态自然对流边界层流动的影响,垂直平面浸没在光密灰色流体中.分析中采用Rosseland扩散近似表示辐射热通量项.将控制方程简化为抛物线型的偏微分方程组,然后在整个时间段0≤τ<∞,利用有限差分法数值求解.还得到了小数值时间和大数值时间的渐近解,发现渐近解和数值解吻合很得好.而且,流体,20℃和1个标准大气压下的空气,即Prandtl数Pr为0.7时,用图形给出了不同物理参数,即热辐射参数Rd、表面温度参数θw和热泳参数λ,对瞬时的表面剪切应力τw、表面热传输率qw和组分浓度扩散率(传质率)mw的影响,以及对瞬时的速度、温度和浓度分布曲线的影响.

Conduction-Radiation Effect on Transient Natural Convection Along a Vertical Flat Surface With Thermophoresis

The present paper concerns with the effect of thermophoretic particle deposition on the transient natural convection laminar flow along a vertical flat surface which was immersed in an optically dense gray fluid in the presence of thermal radiation.In the analysis the radiative heat flux term was expressed by adopting the Rosseland diffusion approximation.The governing equations were reduced to a set of parabolic partial differential equations which were then solved numerically with a finite difference scheme in the entire time regime,0 ≤τ < ∞.Asymptotic solutions were also obtained for sufficiently small and large times.Excellent agreement was found between the asymptotic and the numerical solutions.Moreover,the effects of different physical parameters,namely the thermal radiation parameter,Rd,the surface temperature parameter,θw,and the thermophoretic parameter,λ,on the transient surface shear stress,τw,the rate of surface heat transfer,qw,and the rate of species concentration,mw as well as on the transient velocity,temperature and concentration profiles were shown graphically for a fluid as air for which the Prandtl number,Pr,is 0.7 at 20℃ and 1 atm pressure.