Engineering, 04.05.2020 22:34 derrishamckenzie22

During normal operation, an electrical component experiences a constant rate of ohmic dissipation ini g = 0.01 W that causes the conversion of electrical to thermal energy. The component has conductivity k = 10 W/m-K, density r = 1000 kg/m3 , and specific heat capacity c = 100 J/kg-K. The surface of the component is cooled by convection with air at T[infinity] = 20ºC and heat transfer coefficient h = 10 W/m2 -K. The volume of the component is V = 1x10-7 m3 and its surface area is As = 1x10-5 m2.
a. Is a lumped capacitance model of the component appropriate? Justify your answer
b. Assume that your answer to (a) is yes. What is the steady-state temperature of the 0m component?
c. Assume that your answer to (a) is yes. What is the lumped capacitance time constant of the component? At time t - 0, the power to the circuit is shut off and the ohmic dissipation in the component decays to zero according to where τ 6-25 s is the electrical time constant of the circuit.
d. Sketch the temperature of the component as a function of time after the circuit is shut off Be sure to indicate where the temperature starts, where it ends up, and approximately how long it takes to get there.
e. Derive the ordinary differential equation for this problem.
f. What is the initial condition for this problem?

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