竖直平板Blasius流层流边界层流动与传热耦合解

对考虑辐射传热、流体黏度随温度变化、有和无滑移边界条件下的可渗透竖直平板Blasius流层流边界层的无量纲速度场与温度场进行了深入研究.经相似变换将描述速度场与温度场耦合的偏微分方程组转换成非线性常微分方程组,用Runge-Kutta法对常微分方程组进行了数值求解.研究了无量纲参数对无量纲速度场及温度场的影响,着重分析了滑移边界条件下速度和温度随无量纲参数的变化规律.结果表明:吸入时边界层变薄,喷注时边界层加厚;对比于无滑移边界条件,滑移边界条件下速度、温度边界层变薄;随着变黏度参数a或喷注与吸入参数的增大,壁面摩擦因数、局部努塞尔数Nu增大,速度和温度边界层变薄;随着普朗特数Pr、热辐射参数R的增加,或毕渥数Bi,布林克曼数Br的减小, 温度边界层变薄. 

Coupling solutions of flow and heat transfer in the Blasius laminar boundary layer flow over a vertical flat plate

The combined effects of thermal radiation, temperature dependent viscosity, slip and no-slip boundary conditions over a permeable vertical flat plate on the dimensionless velocity and temperature fields of Blasius laminar boundary layer flow were deeply investigated. By taking similarity variables, the coupled partial differential equations describing the velocity and temperature fields were transformed into nonlinear ordinary differential equations, and then solved numerically using the Runge-Kutta method. The effects of dimensionless parameters on the velocity and temperature fields were investigated with a focus on the analysis of velocity and temperature profiles, with the dimensionless parameters varying under the slip boundary condition. The results indicate that the existence of suction will make the boundary layer thinner, and the boundary layer will be thicker in the case of injection. In contrast with no-slip boundary conditions, the boundary layers of velocity and temperature are all thinner at wall slip boundary conditions. Increasing either the variable viscosity parameter a or the injection and suction parameter will increase the local skin friction coefficient and the local Nusselt number Nu while reducing the velocity and temperature boundary layers thickness. Furthermore, the temperature boundary layer thickness will decrease as the Biot number Bi, Brinkmann number Br decrease or as the Prandtl number Pr and thermal radiation parameter R increase.