Mine did that and it's air in the cooling system going through the heater core. Give it some time and it will go away. Be sure to watch you over flow bottle in case it gets low when the air escapes.

 

If there is air in the system, go back to whoever did your radiator and have them bleed the coolant again.

 

I recently had my radiator replaced (likely coolant flushed during the replacement process). As soon as I got my car back, I heard a water flowing / sloshing sound around driver's seat. The sound occurs when I start the engine, accelerate, make turns, and decelerate. It is not audible on the highway or outside of the car. It is barely audible when the windows are open. The sound also happens regardless whether I have AC on or off.

I spoke with 2 different mechanics, and they don't know what is the cause of the sound.

I found online that water flowing / sloshing sound happens with a clogged evaporator drain. But there is no water in the car.

Your cooling system was not properly bled. There is air in your heater core and the sloshing is coming from there.

I have an 06 but I think yours is the same. Remove the intake tube and right behind it are the two heater hoses. Take the top one loose and pour coolant into your radiator until coolant comes out of the tube or heater core.

If they had the heater hoses off, They put them back on wrong. They need to be swapped.

Honestly, if the work was done at a shop, bring it back to them. I'm 99.9% sure there's air in the heater core.

Have them bleed the system until the noise goes away.

Running water sound = air in cooling system

 

Amen to that. Let the engine idle with the radiator cap off and AC set on high. Let the coolant temperature come up to where fans cycle on and off several times. Stop engine and carefully remove cap. Let vehicle sit for half hour or so so that any air still in system can escape. Top off coolant level is required. Fill surge tank to top mark. Go for it cowboy. Regards

 

+1 incomplete purging of air.