Laminar flow in trapezoidal grooves at finite Bond numbers with shear stress at the liquid-vapor interface by the method of fundamental solutions
Keywords:
flow in trapezoidal groove, liquid-vapor interface, method of fundamental solutions, Bond number, MathematicaAbstract
The problem of determination of Poiseuille number for a steady gravitational flow of liquid in an inclined open trapezoidal groove is addressed. The solution comprises of two parts. First, for a given groove's dimension, liquid-solid contact angle, and the Bond number, the shape of the free surface is determined starting from the Young- Laplace equation. The shooting method is used for solution of a two-point boundary value problem. Then, having determined the shape of the free surface and slope the groove, the fully developed laminar flow is determined. The boundary value problem is solved using the method of fundamental solutions. Given the distribution of liquid velocity, the Poiseuille number, as a function of the other parameters of the model is analysed.
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