Collector Circ Pump for Small Pool

[RSquirrel]

I am planning to fabricate an open-loop, 4'x8' solar collector utilizing 81 feet of serpentined 1/2" ePEX tubing (yes, the tubing will be totally protected from direct sunlight). The PEX tubing has an inside diameter in the range of 0.461" to 0.509". At this length, the total volume within the collector computes to approximately 0.70 to 0.86 gallons of water.

Initially, I will use just one collector panel, with the option of adding a second one, based on need and degree of success.

I will be mounting the collector(s) in an optimally-pointed location (with adjustable angle) on the roof of the pool house for a small (~3000 gallon) above-ground pool (3 psi head - top of collector to surface of pool). So, I will need a small circulation pump (no, I cannot use the system pump - it does not have sufficient capacity beyond what is needed for filtration).

What formulas and/or rules-of-thumb can anyone suggest to determine minimum, optimum, maximum flow rate (gph) for said pump, in order to maximize solar gain (or more specifically, transfer of heat into the pool)?

If a second collector is added (same elevation), should it be in parallel or series with the first?