You must use the energy conservation principle to an elementary exchange length dx.
If you apply this principle you will have two equations: one for the cold fluid and one for the hot fluid.
You can assume many steady state donditions and to simulate with thsi way.
Otherwise, you have to take into acount the therma mass of the heat exchanger solving differential equations.
I don't no exactly what you do mean by dynamic condition. If you mean that the mass flow rate or temperatures are changing with time, then you need to make a transfer function for your system and find the time response, whatever it would be, say heat transfer rate, as a function of time. Steady state condition means that all variables are constants. This is in contrast with the dynamic mode.
I don't know exactly what you after mate, however, use the energy balance to find the amount of heat transfer from cold fluid to hot fluid by assuming that there is no heat losing, and the formula as below:
Cpcold * mass flowrate cold * temperature cold= Cphot * mass flowrate hot* temperature hot
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