Why Does My Minivan Make A Noise That Sounds Like Flowing Water For A Few Minutes After I Start It?

Nothing to worry about. It is your coolant in the hose returning to the radiator.You hear it so noticably because the coolant or radiator fluid, is also the source for heat in your vehicle. After the fluid leaves the radiator it has been cooled down, as it runs through the engine it gets hot, at this point it runs by your heater to supply heat to the blower, or fan to heat the interior before returning to the radiator to be cooled down again. When you turn your engine off some of this is left in the heater hose, when you start up you here it sucking away back to the radiator. This process happens whether you are using your heater or not.