Mixed convection heat transfer of water about a vertical surface of variable heat flux with density inversion

Laminar mixed convection boundary layer flow of water about a vertical plate is studied including density inversion effects. The plate surface is subjected to an arbitrary heat flux that is a function of vertical distance from the leading edge. Both aiding and opposing mixed convection situations are considered in the study. The dimensionless forms of stream function and temperature are expanded in terms of perturbation elements and universal functions. The differentials of the heat flux, which are functions of vertical distance, are used as perturbation elements to obtain universal functions. The results for universal functions required to find temperature and velocity profiles are obtained. The obtained universal functions are valid for any arbitrary wall heat flux variation. The universal applicability of results is demonstrated for power-law variation of wall heat flux. The velocity and temperature variation, boundary layer thickness, Nusselt numbers and skin friction coefficient are presented for various values of mixed convection parameter, wall flux power index, for both aiding and opposing mixed convection. For a given combination of Grashof and Reynolds numbers, the heat transfer rates and skin friction coefficient are found to increase almost linearly with wall flux power index, in the parameter range of the study, for both the cases of aiding and opposing mixed convection. The present results of special cases are found to match well with the results available in the literature.