Be very careful when you disconnect them, stock heater core had plastic pipes , twisting or bending the hose can break the pipes, then you will have to replace the core. I just complted this job and it is not too bad if you have the right tech sources. If interested sign up for the online tech manual alldat.com. the cost is $14.95 a year but well worth it. Remove the two heater hoses at the firewall and flush the heater core through there.
cost to replace heater core 1994 corsica
A Haynes or chiltons manual has the how to. Or do a search for a forum for Chevy corsica specific
Drain the water from your 1990 Chevy Corsica cooling system. Remove the heater core water supply hoses. Remove the heater core retaining bolts. Reverse the process to install the new heater core.
Its located in the center of the vehicle below the dash.................
your heater core is leaking
inside dashboard on passenger side
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Under dash, near firewall, passenger side.
Run a new one from the blower motor body to ground
Heater box drain It is just below the heater hose conections, If the heater core leaks it drains the coolant outside to keep the carpet dry.
Leak in heater core
I was just browsing online for Chevy Corsica heater core and found they were being sold for $53 at 1aauto.com plus free shipping. It looks like a decent deal to me and the suppliers seem pretty competent in the aftermarket auto parts business. You can check out their website for more details.