Cylindrical cookies (radius: 1 cm and height 0.5 cm) are cooled on a conveyer belt after exiting an oven. The cookies enter the conveyer belt at 200 C. The goal is for the cookies to exit the conveyer belt at 40 C. The conveyer belt is 10 m long and the heat transfer coefficient is 25 W/m²-K. The properties of the cookies are: 

C_p (specific heat): 1000 J/kg-K

K (thermal conductivity) = 1 W/m-K

ρ (density)  = 2000 kg/m³. 

What should the speed of the conveyer belt be for the cookies to leave at 40 C? 

1. 1. Choose the appropriate transport equation for energy conservation and reduce the equation by eliminating all the zero terms. 
2. 2. Solve the differential equation that you obtained in part (a) to get a general solution for the temperature variation as a function of one arbitrary constant C_{1 .}
3. 3. Employing your initial conditions associated with this problem, evaluate the values of the constants C_{1 .}
4. 4. Using the temperature variation as a function of time that you obtained in Part (c), determine the time taken by the cookies to cool to the desired temperature. 
5. 5. Determine the speed at which the conveyer belt should move to accomplish this?