Geometric optimization of channels for laminar forced convection in a volume with maximal heat transfer density
This paper develops analytically the optimal sizes (hydraulic diameters) of parallel channels that penetrate and cool a volume with uniformly distributed internal heat generation. The coolant is single phase, and the flow is laminar. The total volume and the volume fraction occupied by the channels (φ) are fixed. The objective is to achieve maximal heat transfer rate per total volume used. Optimal channel sizes and maximum global thermal conductances between volume and coolant are reported for round tubes. The optimization is based on the intersection of asymptotes method. The optimal geometry is determined as trade-off between the operating extremes of each channel, thin and many channels with fully developed flow, vs. wide and few channels with distinct boundary layers. In forced convection, the optimal channel size scales as the flow length times the pressure drop number (Be) raised to the power -1/4.
