喷注壁面外掠平板层流边界层速度和温度的HPM-Padé解析解

运用HPM-Padé(同伦摄动-帕德逼近)法导出了当喷注流体速度与距平板前缘距离的平方根成反比时,不可压缩常物性流体外掠平板层流边界层内无量纲速度和无量纲温度解析表达式,无量纲流函数1阶导数的HPM-Padé解析解与4阶龙格库塔法的数值解结果一致.利用HPM-Padé解析解研究了喷注系数和流体Prandtl数对速度和温度分布的影响.结果表明:Prandtl数越大,温度边界层越薄,壁面温度梯度越大;喷注系数越大,速度边界层厚度和温度边界层厚度越大,壁面速度梯度和壁面温度梯度越小,壁面喷注对平板有隔热作用;当喷注系数为0.619时,壁面的速度梯度和温度梯度为零,高温来流向壁面的传热被喷注流体完全阻隔.

Analytical solutions of velocity and temperature in laminar boundary layer over a flat plate with wall injection flow using HPM-Padé method

The HPM-Padé method was used to derive the analytical expression of dimensionless velocity and dimensionless temperature in the laminar boundary layer of a constant property, incompressible fluid over a flat plate with injection flow, when the injection fluid velocity is inversely proportional to the square root of the distance from the leading edge of the flat plate. The analytical solution produced by the HPM-Padé approximation of the first order derivative dimensionless stream function was consistent with the numerical solutions produced from the fourth order Runge-Kutta method. Analysis on the effects of injection coefficient and Prandtl number on the velocity and temperature distributions was performed using the analytical solutions obtained by the HPM-Padé method. Results show that, as Prandtl number increases, the temperature boundary layer becomes thinner and the temperature gradient on the wall becomes larger. As the injection coefficient increases, the thickness of temperature and velocity boundary layers increases. Furthermore, both wall velocity gradient and wall dimensionless temperature gradient decreases as the injection coefficient increases and injection on the wall creates an insulation effect. When injection coefficient is 0.619, wall velocity gradient and temperature gradient are both zero and the heat transfer from the high temperature flow to the wall is completely blocked by the injection fluid.