Simple analysis of mixed convection with uniform heat flux

Abstract

When a fluid is forced to flow over a vertical, flat plate, generating uniform heat flux, heat is transferred by forced convection. The temperature difference between the surface and the fluid creates changes in the fluid density, causing natural convection. Therefore forced convection is always coupled with natural convection. In the case of loss of cooling accident (LOCA) in a nuclear reactor, the heat transferred by forced convection can be of the same order of magnitude as that of natural convection, forming a mixed-convection heat transfer mode. When the fluid is forced to flow in the upward direction, we have an assisting mixed convection (AMC), and when the fluid is forced in the opposite direction to the buoyant motion, the condition is opposing mixed convection (OMC). A simple analysis is presented, which evaluates the heat transfer coefficient in AMC and in OMC. The analysis assumes that the hydrodynamic and the thermal boundary layers are the same. It assumes, further, that the velocity profile within the boundary layer is a superposition of pure forced and pure natural convection. A characteristic parameter, β =3.5 U ∞/Г L is defined which indicates the relative influence of each pure convection mode in the mixed convection phenomena. For AMC a correlation is proposed as follows: Nu m Re x 0.5 = [0.483 Pr f 1 2 ] 3+ 0.616 (Rɑ x ∗ 1 5 Re x 0.5 Pr f 0.8+Pr f 1 5 3 1 3 For OMC, the solution is obtained by dividing the analysis into two regions: the first, a region dominated by forced convection, and the second, a region dominated by natural convection.