Laminar conjugate forced convection over a flat plate. Multiplicities and stability

The multiple solutions of a conjugate heat transfer problem modeling laminar forced convection on one side of a flat plate and multi-boiling cooling on the other side has been numerically studied. The hydrodynamic and thermal boundary layers are treated by means of an integral technique coupled with axial conduction along the plate. The boiling process is modeled by a simple and generalized heat transfer coefficient valid for all three boiling regimes. Two problems with different boundary conditions have been considered and up to five solutions have been numerically calculated. The analysis reveals that the longitudinal conduction along the plate together with the nonlinear boiling curve, are the key processes responsible for the multiplicity features of the problem whereas the modified Brun number and the conduction-convection parameter significantly affect the solution. The boundary conditions have a profound effect on the bifurcation structure but they do not affect the stability properties since for both problems out of the five solutions three are stable and two unstable. Stability analysis shows that there exists a temperature distribution where all boiling modes may be present simultaneously along the plate.