The proposed RC vehicle will create peak power for a short burst, followed by a rest time. The vehicle's speed controller will generate heat due to the internal resistance, and it is important that the controller be kept below a maximum operating temperature; preliminary tests indicate that an unmodified speed controller will overheat. The maximum surface temperature is given to be 50 degrees Celsius, and the freestream temperature is assumed to be 25 degrees Celsius.

For this model, the full-power burst will last 30 seconds, and subsequently rest for 30 more seconds to complete one cycle. There will be 10 cycles required for the model to remain under the maximum surface temperature, but reaching a heat limit underneath the maximum is highly desired. It is also highly desirable to keep the controller as cool as possible, while simultaneously keeping the weight as low as possible for the quickest RC car acceleration.

There is a maximum fin clearance above the speed controller of 45 mm, and the fins have a maximum base coverage of 30%. The fins also have a minimum thickness of 1.2 mm for structural integrity. The convection coefficient will depend on the fin base area coverage, given by this assumed model:

h = h0 - C(% coverage)^2, where h0 = 50 W/m^2 K and C = 500 W/m^2 K

Lumped capacity is an effective approximation for this design problem because fins are thin and chosen materials are likely to have very high thermal conductivity. Calculating many configurations of the Biot number often returned values of less than 0.1, signifying that lumped capacity is valid; this was reaffirmed with the final design once chosen.

Included in the lumped capacity model is the heat source (from the speed controller), radiation, and convection from the fins and base area, as shown below.