Mixed convection flow over a horizontal plate: The effect of far field conditions and the structure of the wake

Abstract

The plane, horizontal, mixed convection flow over a heated or cooled plate exhibits paradoxical properties. Buoyancy-induced perturbations grow logarithmically with increasing distance of external boundaries from the plate, leading to an unbounded flow solution in an infinite domain. Although this sensitivity to far-field boundary conditions was identified analytically 25 years ago, it is often overlooked in numerical studies. The present work investigates the effect of far-field conditions on the mixed convection flow over a horizontal plate situated far downstream of a flow straightener. Our numerical results for Prandtl numbers (Pr) of 0.02 and 0.7, a Peclet number (Pe) of 100, and Richardson numbers (Ri) up to 0.226 are compared with a known analytical solution. Although developed for small Prandtl numbers, the analytical solution also holds qualitatively for Pr = 0.7. We also compare the wake structure behind a heated plate to a recent asymptotic solution for a Prandtl number of order unity, achieving excellent agreement. Finally, we analyze a plate with both heated and cooled sections, resulting in zero net heat supply, for a large Reynolds number of 20,000 and Ri = 0 and 0.3. The decay rate of the thermal wake is determined, and a self-similar structure is identified. It is shown that in the case of zero net heat supply, a second-order expansion of the far wake is necessary to describe the outer flow perturbation. Thus, our findings underscore the significance of far-field boundary conditions and offer new insights into the structure and evolution of horizontal thermal wakes.