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A watermelon is taken out of the refrigerator at a uniform temperature of 5 degree C and is exposed to 27 degree 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 of watermelon rho = 120 kg/m3, diameter of the watermelon D = 40 cm, specific heat capacity c = 4200 J/(kg middot degree C), and heat transfer coefficient h = 15 W/(m2 middot degree 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 degree C?

A watermelon is taken out of the refrigerator at a uniform temperature of 5°c and is exposed to 27°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 of watermelon p 120 kg/m3, diameter of the watermelon d 40 cm, specific heat capacity c 4200 jv(kg °c), and heat transfer coefficient h 15 w/(m2 oc). a. derive the differential equation relating the watermelons temperature 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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