Stewart Industries sells its finished product for $9 per unit. Its fixed operating costs are $20,000, and the variable operating cost per unit is $5. a. Calculate the firm’s….
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
D = 35 cm, specific heat capacity c = 4200 J/(kg・°C), and heat transfer coefficient
h = 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?