Numerical computation of the heat transfer and fluid mechanics in the laminar wall jet and comparison to the self-similar solutions

Abstract

Despite its importance as a canonical two-dimensional flow, the laminar wall jet has not been extensively studied using modern computational fluid dynamic methods. As in the laminar boundary layer, existence of analytical self-similar solutions make the problem particularly attractive for validating CFD code, yet we have found little archival work in which it has been used for this purpose. In the present study, we present a numerical investigation of the steady, laminar, and two-dimensional plane wall jet with constant properties. A finite-volume approach is used to solve the governing equations using self-similar inlet boundary conditions for the velocity and temperature profiles. The thermal solution is investigated for isothermal boundary condition at the wall. Velocity and temperature profiles are reported at various locations downstream and show an excellent agreement with the similarity solution obtained by Glauert [1] and Schwarz, et al. [2] respectively. In addition, the skin friction coefficient and the Nusselt number are investigated and compared with the analytical solutions presented by Glauert [1] and Mitachi, et al. [3] respectively, and very good agreement is observed. Despite its simplicity, it is shown that proper convergence of the numerical solutions of the wall jet to the expected analytical solutions requires care in specification of the jet inlet conditions, and the boundary conditions on the computational domain boundaries.