Transient heat transfer in heat exchangers

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firavia
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Considering an engine generating thermal heat at 140 kw and when the generation starts the thermal equilibrium of the engine will be distrubed , a radiator is installed to cool the engine this radiator cool the engine through flow of water and water is cooled inside a heat exchanger with air .
I set a transient equation to my system but I am still unable to solve it please check my equation if it is correct and if there is anything missing .

Qgen+mdot.cp water.(Tentring water - T exiting water)=[tex]\rho[/tex]C .V . dTengine/dt
P.S:ignoring radiation trasfer.
Qgen = 140 kw .
mdot water=0.37m3/s.
cpwater=4.1855 J/(g·K)
C cast iron=0.46
Rho=7870KG/m3.
v=>volume=0.01m3.
Initial conditions:
at t=0sec Tengine = 45 Deg Twater entring = 30 deg c
How can I design a radiator for such system , after solving the equation I still have 2 unknowns Thot air and T2 engine .
From the above how can I identify the area of my heat exchanger ?
 
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Pleas I would like to know where I am wrong
 
Nobody want to help me ?!