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The motor controller will be screwed (M4) onto an aluminum heat sink which will be enclosed by a multi print 3-D printed (cracks sealed with JB weld) ASA enclosure with splash proof connectors and lid. The heat sink will need to be cut and drilled. An intake duct may need to be attached to provide air from the wheel well. This enclosure will be mounted behind the back right wheel (wheel with motor) and onto tabs from the frame.
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Pr = 0.71 (Prandtl number for air at ambient temp 100F)
Re = ρvL/μ (Reynold’s number)
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ρ is the air density (typically 1.2 kg/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 (1.918E-5 kg/ms, at ambient temp 100F)
We can calculate Nusselt’s number (Nu) with the Dittus-Boelter Equation which is used for turbulent flow through a smooth pipe. Although our enclosed fins are more akin to a rectangular prism.
Nu = 0.023 ⋅ Re0.8 ⋅ Pr0.33 ⋅ (L/D)0.5 (Nusselt’s number for airflow parallel to fins)
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L = Length of the fin (in the direction of the flow, 0.250m)
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Nu = hL/k (Nusselt’s number equation relating to h)
h: is the heat transfer coefficient
L: is the characteristic length (0.250m)
k: is the thermal conductivity air (0.026 W/mk, at ambient temp 100F)
h = (0.023 ⋅ Re0.8 ⋅ Pr0.33 ⋅ (L/D)0.5 ⋅ k)/L
Q = ((0.023 ⋅ Re0.8 ⋅ Pr0.33⋅ (L/D)0.5 ⋅ k)/L)Atotal(Tobject−Tambient)
Q = ((0.023 ⋅ ρvL/μ0.8 ⋅ Pr0.33⋅ (L/D)0.5 ⋅ k)/L)Atotal(Tobject−Tambient) (heat transferred)
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Assuming the highest temperature conditions of 100F, we can estimate that the ambient temperature within the aeroshell will be able to reach at least 120-130F given that it’s outside in the sun all day and the battery, motor controller, MPPT’s, and other electronics are producing heat that’s not entirely expelled outside the aeroshell. The MPPT shutoff temperature is 70C (158F). With our effective ΔT value, the motor controller will hover dangerously close to it’s max temperature given bad weather conditions and continuous high current draw, which is dangerous and affects performance.
Conclusion: The cooling efficiency without ducts is questionable, but should be adequate if we add ducts leading from the wheel well to provide cooler air for convection.
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