If you have any flow through the core, this might work....
In the past I have had to circulate descaling fluids through various types of coils/ heat exchangers. What I used was a bucket or some type of drum, a small circulation pump
and the cleaning agent. I have used caustic soda,,,,Tri sodium phosphate,,,,dishwasher detergent...and other proprietary chemicals depending upon the task at hand...
I've used pool pumps, submersible pumps, even cheap drill driven pumps...
Basically create a loop from the bucket thru the pump, thru the coil back into the bucket and let it run....my personal go to for cleaning out a cooling system after a blown head gasket where there is oil in the radiator is TSP or dishwasher detergent....both are non sudsing,,clean well and flush out and neturalize easily with some baking soda...
Hope this helps!!