Numerical investigation of mixed convection flow over a heated horizontal plate of finite length

Abstract

The present numerical study concerns the steady two-dimensional laminar mixed convection flow of Newtonian fluid over a heated horizontal plate of finite length at a zero angle of attack for large Peclet and small Prandtl and Richardson numbers. The plate is located in a horizontal channel of finite height. Buoyancy induces a uniform hydrostatic pressure jump at the trailing edge and across the thermal wake, which is compensated by a perturbation of the outer potential flow according to the Kutta condition. Counter-intuitively, the total lift force acting on the plate points in the opposite direction compared to the buoyancy force. The numerical solution obtained with the Finite Element solver FEniCS is compared to an analytical boundary-layer solution from the literature. For small values of the Richardson number (Ri), an excellent agreement between the numerical and analytical solutions is observed. When Ri exceeds a certain threshold, the flow separates near the leading edge at the lower side of the plate. For some narrow intervals of Ri, three co-existing solutions of the governing equations are found, which differ by the size of the separation bubble. The flow separation can be suppressed by bending the leading edge.