Isn't heat dissipation the flow rate of heat?

Q = area* k * delta_T / thickness

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IRStuff:
The 1D heat equation you provided is not relevant to what I need to know (you also have the sign wrong). I know how much heat (in Watts) the liquid coolant carries away and I just want to calculate the required mass flow rate. I know the temperatures at the inlet and outlet so I know the coolant temperature rise. I also know the specific heat of the coolant. So I think it might be this simple but it's been so long since I did any thermodynamics or heat transfer calculations involving moving fluids that I'm a bet pensive on the subject.

Tunalover

Yes, it's that simple.

OK, had you included that information, initially, it would have been much clearer.

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From you second post that explains more then your first equation is correct dm/dt=Q/Cp*delta as long as you have no heat loss (and or gain) after the coolant has picked up its Q value.