An anomalous self-similar solution for a laminar wall jet flowing up a heated vertical wall

摘要

A free convection wall jet flow with a prescribed wall temperature which enables the boundary-layer equations to be reduced to similarity form is treated. It is seen that there is a finite range sigma(1) < sigma < sigma(0) of the Prandtl number a for which there are solutions. The singular nature of the solution as sigma -> sigma(0) and sigma -> sigma(1) is examined. An alternative (convective) boundary condition characterized by the parameter A is also considered with critical values lambda(c) of lambda dependent on sigma being found. An examination of these critical points shows that they can exist only in the range sigma(1) < sigma < sigma(0). The values of lambda(c) become singular at these limits and achieve a maximum value within this range giving only a finite range of both a and A for solutions to exist. (C) 2019 Elsevier Masson SAS. All rights reserved.