Laminar plane fountains impinging on a ceiling with an opposing heat flux

The behaviour of unsteady planar strong fountains, impinging on a ceiling with an opposing heat flux on the ceiling, is investigated numerically for 8.0⩽Fr⩽30.08.0⩽Fr⩽30.0 at Re=50Re=50 and Pr=7Pr=7. The height of the ceiling is varied in 10⩽H/Xin⩽2510⩽H/Xin⩽25, where XinXin is the half-width of the fountain source, and the non-dimensional gradient of the temperature difference between the fountain source and the ceiling is varied for 0.2⩽Δθ/(H/Xin)⩽1.80.2⩽Δθ/(H/Xin)⩽1.8. It is found that the fountain does not hit the ceiling, but instead stagnates and spreads at some distance from the ceiling due to the stratification of the fluids in the immediate vicinity of the ceiling. The scaling and direct numerical simulation results show that the augmented spreading distance Hd+XdHd+Xd has the scaling of Hd+Xd∼XinFr2/9(H/Xin)1/2[Δθ/(H/Xin)]-1/3Hd+Xd∼XinFr2/9(H/Xin)1/2[Δθ/(H/Xin)]-1/3 in the range studied, where HdHd is the maximum fountain height, XdXd is the spreading distance measured at HdHd, respectively.