Derive the differential equation relating the watermelon’s temperature T(t) and the air temperature.

A watermelon is taken out of the refrigerator at a uniform temperature of 3°C and is exposed to 32°C air. Assume that the watermelon can be approximated as a sphere and the temperature of the watermelon is uniform. The estimated parameters are density ρ = 120 kg/m3, diameter

= 35 cm, specific heat capacity = 4200 J/(kg・°C), and heat transfer coefficient

= 15 W/(m2・°C).

a. Derive the differential equation relating the watermelon’s temperature T(t) and the air temperature.

b. Using the differential equation obtained in Part (a), construct a Simulink block diagram and find the temperature of the watermelon.

c. Build a Simscape model of the system.

d. Based on the simulation results obtained in Parts (b) and (c), how long will it take before the watermelon is warmed up to 20°C?

 

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