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We can assume that all of the power loss will be converted to heat, therefore the heat generated will be considered 43.78W. For the sake of simplicity, we are also assuming all of this heat is being transferred to the heat sink attached to the motor controller. Also, the airflow will not be evenly distributed across each fin with the two fans, but for the sake of simplicity we are assuming it is. (assume 36 fins)
Q = hAtotal(Tobject−Tambient) (Newton’s Law of Cooling)
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Re = ρvL/μ (Reynold’s number)
v = Q 4.16m/ A s (Air velocity caused by fans) (250.497m/s)
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Q = Volumetric flow rate (1.26 m³/s), 1CFM=0.0283m3/s
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, I used a an online calculator )
ρ is the air density (typically 1200 g/m³ at room temperature).
v is the airflow velocity (m/s), which can be estimated from the fan's specifications.
L is a characteristic length (0.250m)
μ is the dynamic viscosity of air (0.01918 g/ms)
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Q = ((0.023 ⋅ ρvL/μ0.8 ⋅ Pr0.33 ⋅ (L/D)0.5 ⋅ k)/L)Atotal(Tobject−Tambient) (heat transferred
Q =
Sources:
https://www.engineersedge.com/physics/viscosity_of_air_dynamic_and_kinematic_14483.htm
Nusselt number and the factors influencing it for perforated fin array of different shapes
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