Optimal Spacings for Mixed Convection

This paper completes the description of geometry optimization in stacks of parallel plates that generate heat. The spacing between plates, or the number of plates in a fixed volume, has been maximized in two limits: pure natural convection and pure forced convection. In this paper, the in-between regime of mixed convection is modeled numerically. After simulating the flow and temperature fields in configurations with a variety of spacings, this paper reports the optimal spacings and the dimensionless groups that govern them (Rayleigh number, pressure drop number, mixed convection ratio). It shows that the numerical results match the results in the limits of natural convection and forced convection. The paper constructs a correlation that bridges the gap between the two limits, and provides a single formula for optimal spacings covering the entire domain, from natural convection to forced convection.