Transient heat transfer in heat exchangers

AI Thread Summary
The discussion focuses on transient heat transfer in a cooling system for an engine generating 140 kW of thermal heat. The radiator cools the engine using water, which is then cooled in a heat exchanger with air. The user has set up a transient equation but is struggling to solve it, seeking validation and assistance with the equation. Key parameters include water flow rate, specific heat, and initial temperatures, but the user is left with two unknowns, Thot air and T2 engine, complicating the design of the radiator and heat exchanger area. The user expresses frustration over a lack of support in resolving these issues.
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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)=\rhoC .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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