Car Radiators: what is the mathematical approach that I should follow to somehow estimate the external heat transfer coefficient in the air side flowing externally through the fins and tubes?
I hope I can give you a general Idea. The radiator of the vehicle having different configuration setup whether you are considering a coolant-oil exchanger or not.However, in simple setup you can consider the heat transfer coolant side to the external air by considering the system as a series of thermal resistances for a 1D simple-steady heat flow analysis
convection->conduction->convection
considering the radiator area ,A and length, L
heat flow,q=Q/A (q , Q are flows)
- Coolant side : ( Temperature of coolant - Temperature of coolant,wall) = (1/h,coolant)*(heat flow)
- Wall side: ( Temperature of coolant,wall - Temperature of air,wall) = (L/k)*(heat flow)
- Air Side: ( Temperature of air,wall - Temperature of air) = (1/h,air)*(heat flow)
- The average values of the conduction and convection can be taken as h,c=3000 W/(m2K) , k= 200-400 W/mK ( depending on the radiator material) , h,a= 100 W/(m2K) ( This gives the main contribution-> air side)
- Kr= 1/(1/hc + L/k + 1/ha)
Then by considering the final result we have Q=Kr*A*(T,coolant - T,air)
This is a very simple model , however the radiator is much more complex than a metal plate as considered above because the global heat transfer coefficient also depends on the type of technology you are considering ( braze-welded or mechanical welded) or may be a full aluminum radiator . You can also consider the ATB ( Air to boil ) index or ETD ( External Temperature difference ) to know the safety limit for the coolant temperature.
This is a good question with lots of possible answers. In addition to the very helpful answer given by @Usman Salim, there is a bit more to add.
For an introduction to the mathematics of a polymeric hollow fiber heat exchanger as car radiator, see Section 1 in
https://www.researchgate.net/publication/305728841_Polymeric_Hollow_Fiber_Heat_Exchanger_as_an_Automotive_Radiator
A mathematical model used to study the effect of radiator fins blockage by clay soil is given in Section 2.1 in
https://www.researchgate.net/publication/279841751_Effect_of_Radiator_Fins_Blockage_by_Clay_Soil_on_the_Engine_Cooling_Temperature
Article Effect of Radiator Fins Blockage by Clay Soil on the Engine ...
Article Polymeric Hollow Fiber Heat Exchanger as an Automotive Radiator:
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