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

Abstract

The present study is concerned with the laminar mixed convection flow over a heated horizontal plate of finite length at zero angle of attack. Two different types of outer boundary conditions are considered. In the first case, the plate is placed in a channel with an infinite extent in the downstream direction and a uniform inlet velocity at a finite upstream distance from the plate. In the second case, the plate is located in a semi-infinite space, where a zero vertical velocity is prescribed at a finite distance in front of the plate. The numerical solution of the Navier-Stokes equations for a large Reynolds number Re = 20000 is computed with the Finite Element Method and compared to the boundary layer solutions of Müllner and Schneider [1] and Schneider [2], which are valid for a vanishing Prandtl number (inviscid flow) and a small Richardson number. Goal-oriented adaptive mesh refinement is employed in order to resolve the thin viscous sub-layer. The numerical solution converges to the boundary layer solution when the Prandtl number is decreased. In the case of a plate inside a channel the agreement between the numerical and asymptotic solutions is better the larger the channel height because the effect of the viscous sub-layer on the outer flow diminishes. The hydrostatic pressure difference between the lower and the upper side of the plate together with the Kutta condition at the trailing edge induce a circulation with a global effect on the flow around the plate. For the plate inside a channel and higher Richardson numbers, this additional circulation flow leads to flow separation at the bottom side of the heated plate. For certain parameters, we find multiple solutions of the steady two-dimensional Navier-Stokes equations which differ by the size of the separation bubble.

References [1] M. Müllner and W. Schneider, Heat Mass Transf. 46, 1097-1110 (2010). [2] W. Schneider, Proc. 3rd Eur. Therm. Sci. Conf., 195-198 (2000)