The effect of convective heat transfer on unsteady boundary-layer separation (Q2711502)

The author considers an extremely interesting problem, namely the unsteady evolution of a boundary layer induced by a rectilinear vortex convecting above a heated surface. The model problem is representative of interactions that occur when vortices encounter solid surfaces in at high Reynolds number Re and high Grashof number Gr. The author formulates the problem in the Boussinesq limit, and coupled unsteady boundary-layer momentum and energy equations are solved numerically using the Lagrangian formulation. The flow is initiated in an impulsive start at time \(t= 0\), after which a boundary layer with thickness proportional to \(t^{1/2}\) forms along the surface. Then the full boundary layer equations are solved numerically on a uniform grid in computational space \((\widehat x,\widehat\zeta)\), using a factored ADI method along with Simpson's rule.NEWLINENEWLINENEWLINEThe results are obtained for different values of plate inclination angle \(\theta\), mixed convection parameters \(\text{Gr/Re}^2\) or \(\text{Gr/Re}^{5/2}\) with the Prandtl number \(\text{Pr} = 1\). It is found that there is a strong coupling between the fluid flow and heat transfer within the boundary layer. The abrupt changes in the flow field, as the boundary layer separates from the plate, cause severe gradients in the temperature field and in the convective heat transfer coefficient along the surface. In addition, the erupting boundary layer ejects a spire of high-temperature fluid from the surface into the outer flow, significantly enhancing thermal mixing. The results also show that, depending on the orientation of the surface, buoyancy forces acting on the heated fluid near the surface can alter the flow such that the eruptive process is accelerated or delayed.