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.