Figure 7.18 shows a liquid-level system in which two tanks have cross-sectional areas A1 and A2, respectively. The volume flow rate into tank 1 is qi. A pump is connected to the bottom….

## 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/m^{3}, diameter

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

*h *= 15 W/(m^{2}・°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?