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thermal systems, Mechanical Engineering

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A motor coil can be modeled as a hollow copper cylinder with an outer diameter
of 50 mm, an inner diameter of 40 mm, and a length of 60 mm. The motor stalls
at time t ¼ 0 and, at this point, the copper experiences a step input in electrical
heating of P0  u(t), where P0 is 350 W. Assume that there is little time for
significant heat loss to the environment so that the copper cylinder can be
considered to be insulated. If the initial temperature is 30 C, find the temperature as a function of time, T(t), analytically using Laplace transforms. Calculate
the time required to reach the breakdown temperature of the wire insulation,
which is approximately 250 C. Write a script file in MATLAB® to: (a) determine
the time for the copper to reach 250 C using the command find; and (b) plot T(t)
over this time interval. Copper has a density of 8960 kg/m3 and a specific heat of
390 J/kg-C.

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